Progress in 3D object understanding relies on the category-level canonicalization of 3D objects, i.e., bringing 3D instances into a consistent position and orientation. Most related works assume complete 3D representations, while real-world applications often require solving the more challenging task of canonicalizing from partial views, i.e., short videos that cover only a part of the object. We introduce C3PO, a method capable of canonicalizing partial views from arbitrary object categories by enforcing geometric and feature-level appearance consistency of overlapping views. We represent partial views as 3D point clouds obtained via structure-from-motion, where each point carries a feature vector that is extracted from 2 D images using a novel feature extractor capable of estimating generalizable correspondence features. Notably, our correspondence features are learned on a large dataset and generalize to object categories not seen during training. On top of this, we introduce an efficient pairwise-registration framework that aligns partial object representations into a globally consistent canonical frame. Experiments on synthetic and real-world benchmarks demonstrate that C3PO significantly outperforms existing methods.

The task of establishing correspondences between two 3D shapes is a long-standing challenge in computer vision. While numerous studies address full-full and partial-full 3D shape matching, only a limited number of works have explored the partial-partial setting, very likely due to its unique challenges: we must compute accurate correspondences while at the same time find the unknown overlapping region. Nevertheless, partial-partial 3D shape matching reflects the most realistic setting, as in many real-world cases, such as 3D scanning, shapes are only partially observable. In this work, we introduce the first integer linear programming approach specifically designed to address the distinctive challenges of partial-partial shape matching. Our method leverages geometric consistency as a strong prior, enabling both robust estimation of the overlapping region and computation of neighbourhood-preserving correspondences. We empirically demonstrate that our approach achieves high-quality matching results both in terms of matching error and smoothness. Moreover, we show that our method is more scalable than previous formalisms. Our code is publicly available at https://github.com/vikiehm/partial-geco.

Understanding dynamic 3D scenes is crucial for extended reality (XR) and autonomous driving. Incorporating semantic information into 3D reconstruction enables holistic scene representations, unlocking immersive and interactive applications. To this end, we introduce TRASE, a novel tracking-free 4D segmentation method for dynamic scene understanding. TRASE learns a 4D segmentation feature field in a weakly-supervised manner, leveraging a soft-mined contrastive learning objective guided by SAM masks. The resulting feature space is semantically coherent and well-separated, and final object-level segmentation is obtained via unsupervised clustering. This enables fast editing, such as object removal, composition, and style transfer, by directly manipulating the scene's Gaussians. We evaluate TRASE on five dynamic benchmarks, demonstrating state-of-the-art segmentation performance from unseen viewpoints and its effectiveness across various interactive editing tasks. Our project page is available at: https://yunjinli.github.io/project-sadg/

Recovering a 4D motion from sparse visual information (such as two temporal frames of a subject) is a significant challenge. While humans are able to hallucinate the missing information in a plausible way, generative AI struggles due to a lack of high-quality training data and heavy computing requirements. To overcome these limitations, we propose TwoSquared, a method that obtains a 4D plausible sequence from just two 2D RGB images corresponding to the beginning and the end of the action. We propose to solve the problem in two steps: 1) first, obtaining a 3D reconstruction of the initial and final status, and 2) model the intermediate sequence as a physically plausible deformation. Our method does not require templates or class-specific prior knowledge, and can operate with arbitrary in-the-wild examples. We demonstrate our capabilities in a number of different objects, diverse in terms of nature, class, and deformation, surpassing video-based alternatives, which cannot achieve the same level of consistency.

Synthesizing controllable 6-DOF object manipulation trajectories in 3D environments is essential for enabling robots to interact with complex scenes, yet remains challenging due to the need for accurate spatial reasoning, physical feasibility, and multimodal scene understanding. Existing approaches often rely on 2D or partial 3D representations, limiting their ability to capture full scene geometry and constraining trajectory precision. We present GMT, a multimodal transformer framework that generates realistic and goal-directed object trajectories by jointly leveraging 3D bounding box geometry, point cloud context, semantic object categories, and target end poses. The model represents trajectories as continuous 6-DOF pose sequences and employs a tailored conditioning strategy that fuses geometric, semantic, contextual, and goal-oriented information. Extensive experiments on synthetic and real-world benchmarks demonstrate that GMT outperforms state-of-the-art human motion and human-object interaction baselines, such as CHOIS and GIMO, achieving substantial gains in spatial accuracy and orientation control. Our method establishes a new benchmark for learning-based manipulation planning and shows strong generalization to diverse objects and cluttered 3D environments.

We present ViSTA-SLAM as a real-time monocular visual SLAM system that operates without requiring camera intrinsics, making it broadly applicable across diverse camera setups. At its core, the system employs a lightweight symmetric two-view association (STA) model as the frontend, which simultaneously estimates relative camera poses and regresses local pointmaps from only two RGB images. This design reduces model complexity significantly, the size of our frontend is only 35% that of comparable state-of-the-art methods, while enhancing the quality of two-view constraints used in the pipeline. In the backend, we construct a specially designed Sim(3) pose graph that incorporates loop closures to address accumulated drift. Extensive experiments demonstrate that our approach achieves superior performance in both camera tracking and dense 3D reconstruction quality compared to current methods. Github repository: https://github.com/zhangganlin/vista-slam

We present HI-SLAM2, a geometry-aware Gaussian SLAM system that achieves fast and accurate monocular scene reconstruction using only RGB input. Existing Neural SLAM or 3DGS-based SLAM methods often trade off between rendering quality and geometry accuracy, our research demonstrates that both can be achieved simultaneously with RGB input alone. The key idea of our approach is to enhance the ability for geometry estimation by combining easy-to-obtain monocular priors with learning-based dense SLAM, and then using 3D Gaussian splatting as our core map representation to efficiently model the scene. Upon loop closure, our method ensures on-the-fly global consistency through efficient pose graph bundle adjustment and instant map updates by explicitly deforming the 3D Gaussian units based on anchored keyframe updates. Furthermore, we introduce a grid-based scale alignment strategy to maintain improved scale consistency in prior depths for finer depth details. Through extensive experiments on Replica, ScanNet, and ScanNet++, we demonstrate significant improvements over existing Neural SLAM methods and even surpass RGB-D-based methods in both reconstruction and rendering quality.

Digital Terrain Models (DTMs) represent the bare-earth elevation and are important in numerous geospatial applications. Such data models cannot be directly measured by sensors and are typically generated from Digital Surface Models (DSMs) derived from LiDAR or photogrammetry. Traditional filtering approaches rely on manually tuned parameters, while learning-based methods require well-designed architectures, often combined with post-processing. To address these challenges, we introduce Ground Diffusion (GrounDiff), the first diffusion-based framework that iteratively removes non-ground structures by formulating the problem as a denoising task. We incorporate a gated design with confidence-guided generation that enables selective filtering. To increase scalability, we further propose Prior-Guided Stitching (PrioStitch), which employs a downsampled global prior automatically generated using GrounDiff to guide local high-resolution predictions. We evaluate our method on the DSM-to-DTM translation task across diverse datasets, showing that GrounDiff consistently outperforms deep learning-based state-of-the-art methods, reducing RMSE by up to 93% on ALS2DTM and up to 47% on USGS benchmarks. In the task of road reconstruction, which requires both high precision and smoothness, our method achieves up to 81% lower distance error compared to specialized techniques on the GeRoD benchmark, while maintaining competitive surface smoothness using only DSM inputs, without task-specific optimization. Our variant for road reconstruction, GrounDiff+, is specifically designed to produce even smoother surfaces, further surpassing state-of-the-art methods. The project page is available at https://deepscenario.github.io/GrounDiff/.

Event cameras have gained significant attention due to their bio-inspired properties, such as high temporal resolution and high dynamic range. However, obtaining large-scale labeled ground-truth data for event-based vision tasks remains challenging and costly, which hinders the development of the event-based algorithm. In this paper, we present ControlEvents, a diffusion-based generative model designed to synthesize unlimited high-quality event data guided by diverse control signals such as class text labels, 2D skeletons, and 3D body poses. Our key insight is to leverage the diffusion prior from foundation models, such as Stable Diffusion, enabling high-quality event data generation with minimal fine-tuning and limited labeled data. Our method streamlines the data generation process and significantly reduces the cost of producing labeled event datasets. We demonstrate the effectiveness of our approach by synthesizing event data for visual recognition, 2D skeleton estimation, and 3D body pose estimation. Our experiments show that the synthesized labeled event data enhances model performance in all tasks. Additionally, our approach can generate events based on unseen text labels during training, illustrating the powerful text-based generation capabilities inherited from foundation models.

Monocular 3D detection relies on just a single camera and is therefore easy to deploy. Yet, achieving reliable 3D understanding from monocular images requires substantial annotation, and 3D labels are especially costly. To maximize performance under constrained labeling budgets, it is essential to prioritize annotating samples expected to deliver the largest performance gains. This prioritization is the focus of active learning. Curiously, we observed two significant limitations in active learning algorithms for 3D monocular object detection. First, previous approaches select entire images, which is inefficient, as non-informative instances contained in the same image also need to be labeled. Secondly, existing methods rely on uncertainty-based selection, which in monocular 3D object detection creates a bias toward depth ambiguity. Consequently, distant objects are selected, while nearby objects are overlooked.To address these limitations, we propose IDEAL-M3D, the first instance-level pipeline for monocular 3D detection. For the first time, we demonstrate that an explicitly diverse, fast-to-train ensemble improves diversity-driven active learning for monocular 3D. We induce diversity with heterogeneous backbones and task-agnostic features, loss weight perturbation, and time-dependent bagging. IDEAL-M3D shows superior performance and significant resource savings: with just 60% of the annotations, we achieve similar or better AP3Don KITTI validation and test set results compared to training the same detector on the whole dataset.

Classical self-calibration techniques either perform computationally expensive bundle adjustment to estimate all camera parameters or initialize the focal lengths alone by globally averaging fundamental matrices, typically ignoring radial distortion. Both strategies can degrade accuracy in large-scale Structure from Motion pipelines. We present a calibration method that overcomes these limitations by averaging focal lengths and radial distortion parameters using radial fundamental matrices. This method avoids costly point-wise optimization. Our algorithm minimizes the geometric distance between an observed fundamental matrix and the essential-matrix manifold. This provides a mathematically consistent and highly scalable framework for calibrating the camera’s intrinsic parameters. Experiments on diverse real-world datasets demonstrate that our joint estimator provides more precise focal length and distortion parameter estimates than existing methods. Furthermore, we demonstrate that naive, independent distortion averaging is suboptimal, which reinforces the importance of joint focal-radial estimation. These results underscore the importance of incorporating radial distortion averaging into modern self-calibration methods to improve reconstruction accuracy and stability.

Predicting 6-DoF grasp poses from a single RGB-D frame has recently achieved impressive accuracy, yet performance collapses when the target object is heavily occluded by clutter. In this paper, we establish the first benchmark dataset for TARget-driven Grasping under Occlusions, named TARGO, and our model that remains robust under occlusion, TARGO-Net. Our main contributions are: 1) We first recognize the visual occlusion challenge in 6-DoF grasping using single RGB-D images, and found that even the current SOTA models suffer under high occlusion. 2) We propose TARGO dataset, which can be used to train and test 6-DoF grasp models under different visual occlusion severities, and evaluate model robustness in real-world scenarios. 3) We further devise TARGO-Net, a transformer-based grasping model involving a target completion module and target-scene cross-attention, that performs most robustly across all visual occlusion levels. 4) We discover that other than visual occlusion, number of occluders and target minimum dimension also contribute to grasp success. The dataset and codes are publicly available at https://targo-benchmark.github.io .

Abstract Visual odometry (VO) is fundamental to autonomous navigation, robotics, and augmented reality. While self-supervised learning has eliminated the need for expensive ground-truth labels in monocular VO, dynamic objects and occlusions that violate the static scene assumption lead to erroneous pose estimates. Existing uncertainty-based methods filter unreliable regions but rely solely on single-frame information, neglecting temporal consistency across consecutive frames. We present Combined Projected Uncertainty (CoProU), a principled probabilistic formulation that propagates and fuses uncertainties across temporal frames. Our key insight is that robust uncertainty estimation requires combining target frame uncertainty with projected uncertainty from reference frames, enabling effective identification of dynamic regions and temporal inconsistencies. We demonstrate CoProU’s versatility through two complementary frameworks. CoProU-VO-2F employs a decoupled architecture with CNN-based pose encoder and vision transformer-based depth encoder for two-frame visual odometry. CoProU-VO-MF extends our approach to multi-frame scenarios using a unified transformer architecture with coupled encoders that produce shared representations for ego-motion and geometry estimation. This demonstrates that CoProU, though originally formulated for frame pairs, generalizes naturally to multi-frame settings through pairwise application. Comprehensive experiments validate our contributions. CoProU-VO-2F achieves substantial improvements over state-of-the-art two-frame methods, reducing ATE by up to 63% on KITTI and 33% on nuScenes. CoProU-VO-MF achieves 45% lower average ATE across KITTI, nuScenes, and Waymo compared to the large-scale pretrained VGGT baseline. Extensive ablation studies confirm the effectiveness of temporal uncertainty propagation and CoProU’s adaptability across different architectural paradigms. Please check out our Project Page .

We propose SNI-SLAM++, a tightly-coupled semantic SLAM system utilizing neural implicit representation, that simultaneously performs accurate semantic mapping, high-quality surface reconstruction, and robust camera tracking. Our system tightly integrates visual appearance, geometry, and semantics through five key components: (i) We introduce hierarchical semantic representation to allow multi-level semantic comprehension for top-down structured semantic mapping of the scene. (ii) To fully utilize the correlation between multiple attributes of the environment, we integrate appearance, geometry and semantic features through cross-attention for feature collaboration. This strategy enables a more multifaceted understanding of the environment, thereby allowing SNI-SLAM++ to remain robust even when single attribute is defective. (iii) We design an internal fusion-based decoder to obtain semantic, RGB, and Truncated Signed Distance Field (TSDF) values from multi-level features for accurate decoding. (iv) We introduce a semantics-coupled tracking framework that tightly incorporates semantic constraints for camera pose estimation in neural implicit SLAM. This framework leverages the multi-view consistency of semantics to construct a pose graph and perform semantic loop closure optimization, enabling robust tracking. (v) We propose a feature loss to update the scene representation at the feature level. Compared with low-level losses such as RGB loss and depth loss, our feature loss is capable of guiding the network optimization on a higher level. Our SNI-SLAM++ demonstrates superior performance over all recent visual SLAM methods in terms of mapping and tracking accuracy on the datasets of Replica, ScanNet, TUM-RGBD, and ScanNet++, while also showing excellent capabilities in accurate semantic segmentation and 3D semantic mapping.

Recent advances in 3D Gaussian Splatting have shown promising results. Existing methods typically assume static scenes and/or multiple images with prior poses. Dynamics, sparse views, and unknown poses significantly increase the problem complexity due to insufficient geometric constraints. To overcome this challenge, we propose a method that can use only two images without prior poses to fit Gaussians in dynamic environments. To achieve this, we introduce two technical contributions. First, we propose an object-level two-view bundle adjustment. This strategy decomposes dynamic scenes into piece-wise rigid components, and jointly estimates the relative camera motion and dynamic object motions for dynamic Gaussian initialization. Second, we design an SE(3) field-driven Gaussian training method. It enables fine-grained motion modeling through learnable per-Gaussian transformations. Our method leads to high-fidelity novel view synthesis of dynamic scenes while accurately preserving temporal consistency and object motion. Experiments on both synthetic and real-world datasets demonstrate that our method significantly outperforms state-of-the-art approaches designed for the cases of static environments, multiple images, and/or known poses. Our project page is available at https://colin-de.github.io/DynSUP/.

Cross-modal place recognition methods are flexible GPS-alternatives under varying environment conditions and sensor setups. However, this task is non-trivial since extracting consistent and robust global descriptors from different modalities is challenging. To tackle this issue, we propose Voxel-Cross-Pixel (VXP), a novel camera-to-LiDAR place recognition framework that enforces local similarities in a self-supervised manner and effectively brings global context from images and LiDAR scans into a shared feature space. Specifically, VXP is trained in three stages: first, we deploy a visual transformer to compactly represent input images. Secondly, we establish local correspondences between image-based and point cloud-based feature spaces using our novel geometric alignment module. We then aggregate local similarities into an expressive shared latent space. Extensive experiments on the three benchmarks (Oxford RobotCar, ViViD++ and KITTI) demonstrate that our method surpasses the state-of-the-art cross-modal retrieval by a large margin. Our evaluations show that the proposed method is accurate, efficient and light-weight. Our project page is available at: https://yunjinli.github.io/projects-vxp/.

The interest in matching non-rigidly deformed shapes represented as raw point clouds is rising due to the prolif-eration of low-cost 3D sensors. Yet, the task is challenging since point clouds are irregular and there is a lack of in-trinsic shape information. We propose to tackle these chal-lenges by learning a new shape representation - a per-point high dimensional embedding, in an embedding space where semantically similar points share similar embeddings. The learned embedding has multiple beneficial properties: it is aware of the underlying shape geometry and is robust to shape deformations and various shape artefacts, such as noise and partiality. Consequently, this embedding can be directly employed to retrieve high-quality dense corre-spondences through a simple nearest neighbor search in the embedding space. Extensive experiments demonstrate new state-of-the-art results and robustness in numerous chal-lenging non-rigid shape matching benchmarks and show its great potential in other shape analysis tasks, such as seg-mentation.

Unsupervised panoptic segmentation aims to partition an image into semantically meaningful regions and distinct object instances without training on manually annotated data. In contrast to prior work on unsupervised panoptic scene understanding, we eliminate the need for object-centric training data, enabling the unsupervised understanding of complex scenes. To that end, we present the first unsupervised panoptic method that directly trains on scene-centric imagery. In particular, we propose an approach to obtain high-resolution panoptic pseudo labels on complex scene-centric data, combining visual representations, depth, and motion cues. Utilizing both pseudo-label training and a panoptic self-training strategy yields a novel approach that accurately predicts panoptic segmentation of complex scenes without requiring any human annotations. Our approach significantly improves panoptic quality, e.g., surpassing the recent state of the art in unsupervised panoptic segmentation on Cityscapes by 9.4 % points in PQ.

Probabilistic human motion prediction aims to forecast multiple possible future movements from past observations. While current approaches report high diversity and realism, they often generate motions with undetected limb stretching and jitter. To address this, we introduce SkeletonDiffusion, a latent diffusion model that embeds an explicit inductive bias on the human body within its architecture and training. We present a new nonisotropic Gaussian diffusion formulation that aligns with the natural kinematic structure of the human skeleton and models relationships between body parts. Results show that our approach outperforms isotropic alternatives, consistently generating realistic predictions while avoiding artifacts such as limb distortion. Additionally, we identify a limitation in commonly used diversity metrics, which may favor models that produce inconsistent limb lengths within the same sequence. SkeletonDiffusion sets a new benchmark on three real-world datasets, outperforming various baselines across multiple evaluation metrics. We release the code on our project page.

Dimensionality reduction is a fundamental task that aims to simplify complex data by reducing its feature dimensionality while preserving essential patterns, with core applications in data analysis and visualisation. To preserve the underlying data structure, multi-dimensional scaling (MDS) methods focus on preserving pairwise dissimilarities, such as distances. They optimise the embedding to have pairwise distances as close as possible to the data dissimilarities. However, the current standard is limited to embedding data in Riemannian manifolds. Motivated by the lack of asymmetry in the Riemannian metric of the embedding space, this paper extends the MDS problem to a natural asymmetric generalisation of Riemannian manifolds called Finsler manifolds. Inspired by Euclidean space, we define a canonical Finsler space for embedding asymmetric data. Due to its simplicity with respect to geodesics, data representation in this space is both intuitive and simple to analyse. We demonstrate that our generalisation benefits from the same theoretical convergence guarantees. We reveal the effectiveness of our Finsler embedding across various types of non-symmetric data, highlighting its value in applications such as data visualisation, dimensionality reduction, directed graph embedding, and link prediction.

Open-vocabulary semantic segmentation models associate vision and text to label pixels from an undefined set of classes using textual queries, providing versatile performance on novel datasets. However, large shifts between training and test domains degrade their performance, requiring fine-tuning for effective real-world applications. We introduce Semantic Library Adaptation (SemLA), a novel framework for training-free, test-time domain adaptation. SemLA leverages a library of LoRA-based adapters indexed with CLIP embeddings, dynamically merging the most relevant adapters based on proximity to the target domain in the embedding space. This approach constructs an ad-hoc model tailored to each specific input without additional training. Our method scales efficiently, enhances explainability by tracking adapter contributions, and inherently protects data privacy, making it ideal for sensitive applications. Comprehensive experiments on a 20-domain benchmark built over 10 standard datasets demonstrate SemLA ’s superior adaptability and performance across diverse settings, establishing a new standard in domain adaptation for open-vocabulary semantic segmentation.

In this work we address various shape matching problems that can be cast as finding cyclic paths in a product graph. This involves for example 2D-3D shape matching, 3D shape matching, or the matching of a contour to a graph. In this context, matchings are typically obtained as the minimum cost cycle in the product graph. Instead, inspired by related works on model-based image segmentation [68], we consider minimum ratio cycles, which we combine with the recently introduced conjugate product graph in order to allow for higher-order matching costs. With that, on the one hand we avoid the bias of obtaining matchings that involve fewer/shorter edges, while on the other hand we are able to impose powerful geometric regularisation, e.g. to avoid zigzagging. In our experiments we demonstrate that this not only leads to improved matching accuracy in most cases, but also to significantly reduced runtimes (up to two orders of magnitude, depending on the setting). Our GPU implementations are publicly available: https://github.com/paul0noah/product-graph-cycles/.

Generating realistic intermediate shapes between non-rigidly deformed shapes is a challenging task in computer vision, especially with unstructured data (e.g., point clouds) where temporal consistency across frames is lacking, and topologies are changing. Most interpolation methods are designed for structured data (i.e., meshes) and do not apply to real-world point clouds. In contrast, our approach, 4Deform, leverages neural implicit representation (NIR) to enable free topology changing shape deformation. Unlike previous mesh-based methods that learn vertex-based deformation fields, our method learns a continuous velocity field in Euclidean space. Thus, it is suitable for less structured data such as point clouds. Additionally, our method does not require intermediate-shape supervision during training; instead, we incorporate physical and geometrical constraints to regularize the velocity field. We reconstruct intermediate surfaces using a modified level-set equation, directly linking our NIR with the velocity field. Experiments show that our method significantly outperforms previous NIR approaches across various scenarios (e.g., noisy, partial, topology-changing, non-isometric shapes) and, for the first time, enables new applications like 4D Kinect sequence upsampling and real-world high-resolution mesh deformation.

The platonic representation hypothesis suggests that vision and language embeddings become more homogeneous as model and dataset sizes increase. In particular, pairwise distances within each modality become more similar. This suggests that as foundation models mature, it may become possible to match vision and language embeddings in a fully unsupervised fashion, i.e. without parallel data. We present the first feasibility study, and investigate conformity of existing vision and language foundation models in the context of unsupervised, or "blind", matching. First, we formulate unsupervised matching as a quadratic assignment problem and introduce a novel heuristic that outperforms previous solvers. We also develop a technique to find optimal matching problems, for which a non-trivial match is very likely. Second, we conduct an extensive study deploying a range of vision and language models on four datasets. Our analysis reveals that for many problem instances, vision and language representations can be indeed matched without supervision. This finding opens up the exciting possibility of embedding semantic knowledge into other modalities virtually annotation-free. As a proof of concept, we showcase an unsupervised classifier, which achieves non-trivial classification accuracy without any image-text annotation.

We tackle the problem of automatic calibration of radially distorted cameras in challenging conditions. Accurately determining distortion parameters typically requires either 1) solving the full Structure from Motion (SfM) problem involving camera poses, 3D points, and the distortion parameters, which is only possible if many images with sufficient overlap are provided, or 2) relying heavily on learning-based methods that are comparatively less accurate. In this work, we demonstrate that distortion calibration can be decoupled from 3D reconstruction, maintaining the accuracy of SfM-based methods while avoiding many of the associated complexities. This is achieved by working in Projective space, where the geometry is unique up to a homography, which encapsulates all camera parameters except for distortion. Our proposed method, Projective Radial Distortion Averaging, averages multiple distortion estimates in a fully projective framework without creating 3d points and full bundle adjustment. By relying on pairwise projective relations, our methods support any feature-matching approaches without constructing point tracks across multiple images.

Estimating camera motion and intrinsics from casual videos is a core challenge in computer vision. Traditional bundle-adjustment based methods, such as SfM and SLAM, struggle to perform reliably on arbitrary data. Although specialized SfM approaches have been developed for handling dynamic scenes, they either require intrinsics or computationally expensive test-time optimization and often fall short in performance. Recently, methods like Dust3r have reformulated the SfM problem in a more data-driven way. While such techniques show promising results, they are still 1) not robust towards dynamic objects and 2) require labeled data for supervised training. As an alternative, we propose AnyCam, a fast transformer model that directly estimates camera poses and intrinsics from a dynamic video sequence in feed-forward fashion. Our intuition is that such a network can learn strong priors over realistic camera poses. To scale up our training, we rely on an uncertainty-based loss formulation and pre-trained depth and flow networks instead of motion or trajectory supervision. This allows us to use diverse, unlabelled video datasets obtained mostly from YouTube. Additionally, we ensure that the predicted trajectory does not accumulate drift over time through a lightweight trajectory refinement step. We test AnyCam on established datasets, where it delivers accurate camera poses and intrinsics both qualitatively and quantitatively. Furthermore, even with trajectory refinement, Any-Cam is significantly faster than existing works for SfM in dynamic settings. Finally, by combining camera information, uncertainty, and depth, our model can produce high-quality 4D pointclouds. For more details and code, please check out our project page: fwmb.github.io/anycam

Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics. While most research has focused on finding correspondences in settings where at least one of the shapes is complete, the realm of partial-to-partial shape matching remains under-explored. Yet, it is important since in many applications shapes are only observed partially due to occlusion or scanning. Finding correspondences between partial shapes comes with an additional challenge: We not only want to identify correspondences between points on either shape but also have to determine which points of each shape actually have a partner. To tackle this challenging problem, we present EchoMatch, a novel framework for partial-to-partial shape matching that incorporates the concept of correspondence reflection to enable an overlap prediction within a functional map framework. With this approach, we show that we can outperform current SOTA methods in challenging partial-to-partial shape matching problems. Our code is available at https://echo-match.github.io.

Cooperative perception can increase the view field and decrease the occlusion of an ego vehicle, hence improving the perception performance and safety of autonomous driving. Despite the success of previous works on cooperative object detection, they mostly operate on dense Bird’s Eye View (BEV) feature maps, which are computationally demanding and can hardly be extended to long-range detection problems. More efficient fully sparse frameworks are rarely explored. In this work, we design a fully sparse framework, SparseAlign, with three key features: an enhanced sparse 3D backbone, a query-based temporal context learning module, and a robust detection head specially tailored for sparse features. Extensive experimental results on both OPV2V and DAIR-V2X datasets show that our framework, despite its sparsity, outperforms the state of the art with less communication bandwidth requirements. In addition, experiments on the OPV2Vt and DAIR-V2Xt datasets for time-aligned cooperative object detection also show a significant performance gain compared to the baseline works.

Localizing events in videos based on semantic queries is a pivotal task in video understanding research and user-oriented applications like video search. Yet, current research predominantly relies on natural language queries (NLQs), overlooking the potential of using multimodal queries (MQs) that incorporate images to flexibly represent semantic queries, particularly when it is difficult to express non-verbal or unfamiliar concepts in words. To bridge this gap, we introduce ICQ, a new benchmark designed for localizing events in videos with MQs, alongside an evaluation dataset ICQ-Highlight. To adapt and reevaluate existing video localization models for this new task, we propose 3 Multimodal Query Adaptation methods and a novel Surrogate Fine-Tuning strategy, serving as strong baseline methods. ICQ systematically benchmarks 12 state-of-the-art backbone models, spanning from specialized video localization models to Video Large Language Models. Our extensive experiments highlight the high potential of using MQs in real-world applications. We believe this is a first step toward video event localization with MQs1.

Hongyi Luo, Qing Cheng, Daniel Matos, Hari Krishna Gadi, Yanfeng Zhang, Lu Liu, Yongliang Wang, Niclas Zeller, Daniel Cremers, Liqiu Meng. Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing. 2025.

Recent advances in feature learning have shown that self-supervised vision foundation models can capture semantic correspondences but often lack awareness of underlying 3D geometry. GECO addresses this gap by producing geometrically coherent features that semantically distinguish parts based on geometry (e.g., left/right eyes, front/back legs). We propose a training framework based on optimal transport, enabling supervision beyond keypoints, even under occlusions and disocclusions. With a lightweight architecture, GECO runs at 30 fps, 98.2% faster than prior methods, while achieving state-of-the-art performance on PFPascal, APK, and CUB, improving PCK by 6.0%, 6.2%, and 4.1%, respectively. Finally, we show that PCK alone is insufficient to capture geometric quality and introduce new metrics and insights for more geometry-aware feature learning. Link to project page: https://reginehartwig.github.io/publications/geco/

Semantic scene completion (SSC) aims to infer both the 3D geometry and semantics of a scene from single images. In contrast to prior work on SSC that heavily relies on expensive ground-truth annotations, we approach SSC in an unsupervised setting. Our novel method, SceneDINO, adapts techniques from self-supervised representation learning and 2D unsupervised scene understanding to SSC. Our training exclusively utilizes multi-view consistency self-supervision without any form of semantic or geometric ground truth. Given a single input image, SceneDINO infers the 3D geometry and expressive 3D DINO features in a feed-forward manner. Through a novel 3D feature distillation approach, we obtain unsupervised 3D semantics. In both 3D and 2D unsupervised scene understanding, SceneDINO reaches state-of-the-art segmentation accuracy. Linear probing our 3D features matches the segmentation accuracy of a current supervised SSC approach. Additionally, we showcase the domain generalization and multi-view consistency of SceneDINO, taking the first steps towards a strong foundation for single image 3D scene understanding.

Volumetric scene reconstruction from a single image is crucial for a broad range of applications like autonomous driving and robotics. Recent volumetric reconstruction methods achieve impressive results, but generally require expensive 3D ground truth or multi-view supervision. We propose to leverage pre-trained 2D diffusion models and depth prediction models to generate synthetic scene geometry from a single image. This can then be used to distill a feed-forward scene reconstruction model. Our experiments on the challenging KITTI-360 and Waymo datasets demonstrate that our method matches or outperforms state-of-the-art baselines that use multi-view supervision, and offers unique advantages, for example regarding dynamic scenes.

We tackle the problem of localizing traffic cameras within a 3D reference map and propose a novel image-to-point cloud registration (I2P) method, TrafficLoc, in a coarse-tofine matching fashion. To overcome the lack of large-scale real-world intersection datasets, we first introduce Carla Intersection, a new simulated dataset with 75 urban and rural intersections in Carla. We find that current I2P methods struggle with cross-modal matching under large viewpoint differences, especially at traffic intersections. TrafficLoc thus employs a novel Geometry-guided Attention Loss (GAL) to focus only on the corresponding geometric regions under different viewpoints during 2D-3D feature fusion. To address feature inconsistency in paired image patch-point groups, we further propose Inter-intra Contrastive Learning (ICL) to enhance separating 2D patch/3D group features within each intra-modality and introduce Dense Training Alignment (DTA) with soft-argmax for improving position regression. Extensive experiments show our TrafficLoc greatly improves the performance over the SOTA I2P methods (up to 86%) on Carla Intersection and generalizes well to real-world data. TrafficLoc also achieves new SOTA performance on KITTI and NuScenes datasets, demonstrating the superiority across both in-vehicle and traffic cameras. Our project page is publicly available at https://tum-luk.github.io/projects/trafficloc/.

In this work, we introduce the first unsupervised method that simultaneously predicts time-varying neural implicit surfaces and deformations between pairs of point clouds. We propose to model the point movement using an explicit velocity field and directly deform a time-varying implicit field using the modified level-set equation. This equation utilizes an iso-surface evolution with Eikonal constraints in a compact formulation, ensuring the integrity of the signed distance field. By applying a smooth, volume-preserving constraint to the velocity field, our method successfully recovers physically plausible intermediate shapes. Our method is able to handle both rigid and non-rigid deformations without any intermediate shape supervision. Our experimental results demonstrate that our method significantly outperforms existing works, delivering superior results in both quality and efficiency.

Odometry is crucial for the navigation of autonomous vehicles in unknown environments. While cameras and LiDARs are commonly used to estimate the ego-motion of a vehicle, these sensors face limitations under bad lighting and severe weather conditions. Automotive radars overcome these challenges, but radar point clouds are generally sparse and noisy, making it difficult to identify useful features within a radar scan. In this paper, we address the problem of ego-motion estimation using a single automotive radar sensor. We propose a simple, yet effective, heuristic-based method to extract the ground plane from single radar scans and perform ground plane matching between consecutive scans. Additionally, we perform a windowed factor-graph optimization of the poses together with the ground plane, improving the accuracy of the pose estimation. We put our work to the test using the 4DRadarDataset. Our findings illustrate the state-of-the-art performance of our odometry approach compared to existing alternatives that use radar point clouds.

We tackle the problem of monocular 3D object detection across different sensors, environments, and camera setups. In this paper, we introduce a novel unsupervised domain adaptation approach, MonoCT, that generates highly accurate pseudo labels for self-supervision. Inspired by our observation that accurate depth estimation is critical to mitigating domain shifts, MonoCT introduces a novel Generalized Depth Enhancement (GDE) module with an ensemble concept to improve depth estimation accuracy. Moreover, we introduce a novel Pseudo Label Scoring (PLS) module by exploring inner-model consistency measurement and a Diversity Maximization (DM) strategy to further generate high-quality pseudo labels for self-training. Extensive experiments on six benchmarks show that MonoCT outperforms existing SOTA domain adaptation methods by large margins (~21% minimum for AP Mod.) and generalizes well to car, traffic camera and drone views.

Humanoid robots and mixed reality headsets benefit from the use of head-mounted sensors for tracking. While advancements in visual-inertial odometry (VIO) and simultaneous localization and mapping (SLAM) have produced new and high-quality state-of-the-art tracking systems, we show that these are still unable to gracefully handle many of the challenging settings presented in the head-mounted use cases. Common scenarios like high-intensity motions, dynamic occlusions, long tracking sessions, low-textured areas, adverse lighting conditions, saturation of sensors, to name a few, continue to be covered poorly by existing datasets in the literature. In this way, systems may inadvertently overlook these essential real-world issues. To address this, we present the Monado SLAM dataset, a set of real sequences taken from multiple virtual reality headsets. We release the dataset under a permissive CC BY 4.0 license, to drive advancements in VIO/SLAM research and development.

Road surface reconstruction from aerial images is fundamental for autonomous driving, urban planning, and virtual simulation, where smoothness, compactness, and accuracy are critical quality factors. Existing reconstruction methods often produce artifacts and inconsistencies that limit usability, while downstream tasks have a tendency to represent roads as planes for simplicity but at the cost of accuracy. We introduce FlexRoad, the first framework to directly address road surface smoothing by fitting Non-Uniform Rational B-Splines (NURBS) surfaces to 3D road points obtained from photogrammetric reconstructions or geodata providers. Our method at its core utilizes the Elevation-Constrained Spatial Road Clustering (ECSRC) algorithm for robust anomaly correction, significantly reducing surface roughness and fitting errors. To facilitate quantitative comparison between road surface reconstruction methods, we present GeoRoad Dataset (GeRoD), a diverse collection of road surface and terrain profiles derived from openly accessible geodata. Experiments on GeRoD and the photogrammetry-based DeepScenario Open 3D Dataset (DSC3D) demonstrate that FlexRoad considerably surpasses commonly used road surface representations across various metrics while being insensitive to various input sources, terrains, and noise types. By performing ablation studies, we identify the key role of each component towards high-quality reconstruction performance, making FlexRoad a generic method for realistic road surface modeling.

Accurate 3D trajectory data is crucial for advancing autonomous driving. Yet, traditional datasets are usually captured by fixed sensors mounted on a car and are susceptible to occlusion. Additionally, such an approach can precisely reconstruct the dynamic environment in the close vicinity of the measurement vehicle only, while neglecting objects that are further away. In this paper, we introduce the DeepScenario Open 3D Dataset (DSC3D), a high-quality, occlusion-free dataset of 6 degrees of freedom bounding box trajectories acquired through a novel monocular camera drone tracking pipeline. Our dataset includes more than 175,000 trajectories of 14 types of traffic participants and significantly exceeds existing datasets in terms of diversity and scale, containing many unprecedented scenarios such as complex vehicle-pedestrian interaction on highly populated urban streets and comprehensive parking maneuvers from entry to exit. DSC3D dataset was captured in five various locations in Europe and the United States and include: a parking lot, a crowded inner-city, a steep urban intersection, a federal highway, and a suburban intersection. Our 3D trajectory dataset aims to enhance autonomous driving systems by providing detailed environmental 3D representations, which could lead to improved obstacle interactions and safety. We demonstrate its utility across multiple applications including motion prediction, motion planning, scenario mining, and generative reactive traffic agents. Our interactive online visualization platform and the complete dataset are publicly available at app.deepscenario.com, facilitating research in motion prediction, behavior modeling, and safety validation.

Supervised learning has demonstrated to be an effective strategy in training neural networks for vehicle navigation. However, it requires labeled data, which may not be available when a large number of vehicles need to be controlled simultaneously. In contrast, Deep Reinforcement Learning (DRL) circumvents the necessity for ground truth labels through environmental exploration. However, most concurrent DRL approaches either tend to operate in the discrete action/state space or do not consider the vehicle kinematics. In this paper, we use DRL to control multiple vehicles while also considering their kinematics. The task is for all the vehicles to reach their desired destination/target while avoiding collisions with each other or static obstacles in an unconstrained environment. For this, we propose a decentralized Proximal Policy Optimization (PPO) based DRL agent that independently provides control commands to each vehicle. The agent is based on two separate PPO models. The first is used to drive each vehicle to the proximity of its target. Once within the target's proximity, the second model is used to park that vehicle at the correct position and orientation. The decentralized nature of the algorithm allows each agent to rely only on information about its current state and target, along with details regarding the closest obstacle/agent. By scaling this approach to all vehicles, simultaneous navigation of multiple vehicles can be achieved. Experimental results show a collective strategy that allows consistent results across a wide range of scenarios while scaling to situations with up to 20 vehicles and 12 stationary obstacles.

Dense and versatile image representations underpin the success of virtually all computer vision applications. However, state-of-the-art networks, such as transformers, produce low-resolution feature grids, which are suboptimal for dense prediction tasks. To address this limitation, we present *FlowFeat*, a high-resolution and multi-task feature representation. The key ingredient behind FlowFeat is a novel distillation technique that embeds a distribution of plausible apparent motions, or *motion profiles*. By leveraging optical flow networks and diverse video data, we develop an effective self-supervised training framework that statistically approximates the apparent motion. With its remarkable level of spatial detail, FlowFeat encodes a compelling degree of geometric and semantic cues while exhibiting high temporal consistency. Empirically, FlowFeat significantly enhances the representational power of five state-of-the-art encoders and alternative upsampling strategies across three dense tasks: video object segmentation, monocular depth estimation and semantic segmentation. Training FlowFeat is computationally inexpensive and robust to inaccurate flow estimation, remaining highly effective even when using unsupervised flow networks. Our work takes a step forward towards reliable and versatile dense image representations.

Accurate visual localization from aerial views is a fundamental problem with applications in mapping, large-area inspection, and search-and-rescue operations. In many scenarios, these systems require high-precision localization while operating with limited resources (e.g., no internet connection or GNSS/GPS support), making large image databases or heavy 3D models impractical. Surprisingly, little attention has been given to leveraging orthographic geodata as an alternative paradigm, which is lightweight and increasingly available through free releases by governmental authorities (e.g., the European Union). To fill this gap, we propose OrthoLoC, the first large-scale dataset comprising 16,425 UAV images from Germany and the United States with multiple modalities. The dataset addresses domain shifts between UAV imagery and geospatial data. Its paired structure enables fair benchmarking of existing solutions by decoupling image retrieval from feature matching, allowing isolated evaluation of localization and calibration performance. Through comprehensive evaluation, we examine the impact of domain shifts, data resolutions, and covisibility on localization accuracy. Finally, we introduce a refinement technique called AdHoP, which can be integrated with any feature matcher, improving matching by up to 95% and reducing translation error by up to 63%. The dataset and code are available at: https://deepscenario.github.io/OrthoLoC .

Semantic Scene Completion (SSC) has emerged as a pivotal approach for jointly learning scene geometry and semantics, enabling downstream applications such as navigation in mobile robotics. The recent generalization to Panoptic Scene Completion (PSC) advances the SSC domain by integrating instance-level information, thereby enhancing object-level sensitivity in scene understanding. While PSC was introduced using LiDAR modality, methods based on camera images remain largely unexplored. Moreover, recent Transformer-based approaches utilize a fixed set of learned queries to reconstruct objects within the scene volume. Although these queries are typically updated with image context during training, they remain static at test time, limiting their ability to dynamically adapt specifically to the observed scene. To overcome these limitations, we propose IPFormer, the first method that leverages context-adaptive instance proposals at train and test time to address vision-based 3D Panoptic Scene Completion. Specifically, IPFormer adaptively initializes these queries as panoptic instance proposals derived from image context and further refines them through attention-based encoding and decoding to reason about semantic instance-voxel relationships. Extensive experimental results show that our approach achieves state-of-the-art in-domain performance, exhibits superior zero-shot generalization on out-of-domain data, and achieves a runtime reduction exceeding 14$\times$. These results highlight our introduction of context-adaptive instance proposals as a pioneering effort in addressing vision-based 3D Panoptic Scene Completion. Code available at https://github.com/markus-42/ipformer.

Recent cooperative perception datasets have played a crucial role in advancing smart mobility applications by enabling information exchange between intelligent agents, helping to overcome challenges such as occlusions and improving overall scene understanding. While some existing real-world datasets incorporate both vehicle-to-vehicle and vehicle-to-infrastructure interactions, they are typically limited to a single intersection or a single vehicle. A comprehensive perception dataset featuring multiple connected vehicles and infrastructure sensors across several intersections remains unavailable, limiting the benchmarking of algorithms in diverse traffic environments. Consequently, overfitting can occur, and models may demonstrate misleadingly high performance due to similar intersection layouts and traffic participant behavior. To address this gap, we introduce UrbanIng-V2X, the first large-scale, multi-modal dataset supporting cooperative perception involving vehicles and infrastructure sensors deployed across three urban intersections in Ingolstadt, Germany. UrbanIng-V2X consists of 34 temporally aligned and spatially calibrated sensor sequences, each lasting 20 seconds. All sequences contain recordings from one of three intersections, involving two vehicles and up to three infrastructure-mounted sensor poles operating in coordinated scenarios. In total, UrbanIng-V2X provides data from 12 vehicle-mounted RGB cameras, 2 vehicle LiDARs, 17 infrastructure thermal cameras, and 12 infrastructure LiDARs. All sequences are annotated at a frequency of 10 Hz with 3D bounding boxes spanning 13 object classes, resulting in approximately 712k annotated instances across the dataset. We provide comprehensive evaluations using state-of-the-art cooperative perception methods and publicly release the codebase, dataset, HD map, and a digital twin of the complete data collection environment via https://github.com/thi-ad/UrbanIng-V2X.

The bidirectional reflectance distribution function (BRDF) is an essential tool to capture the complex interaction of light and matter. Recently, several works have employed neural methods for BRDF modeling, following various strategies, ranging from utilizing existing parametric models to purely neural parametrizations. While all methods yield impressive results, a comprehensive comparison of the different approaches is missing in the literature. In this work, we present a thorough evaluation of several approaches, including results for qualitative and quantitative reconstruction quality and an analysis of reciprocity and energy conservation. Moreover, we propose two extensions that can be added to existing approaches: A novel additive combination strategy for neural BRDFs that split the reflectance into a diffuse and a specular part, and an input mapping that ensures reciprocity exactly by construction, while previous approaches only ensure it by soft constraints.

Facade semantic segmentation is a long-standing challenge in photogrammetry and computer vision. Although the last decades have witnessed the influx of facade segmentation methods, there is a lack of comprehensive facade classes and data covering the architectural variability. In ZAHA11Project page: https://github.com/OloOcki/zaha, we introduce Level of Facade Generalization (LoFG), novel hierarchical facade classes designed based on international urban modeling standards, ensuring compatibility with real-world challenging classes and uniform methods' comparison. Realizing the LoFG, we present to date the largest semantic 3D facade segmentation dataset, providing 601 million annotated points at five and 15 classes of LoFG2 and LoFG3, respectively. More-over, we analyze the performance of baseline semantic segmentation methods on our introduced LoFG classes and data, complementing it with a discussion on the unresolved challenges for facade segmentation. We firmly believe that ZAHA shall facilitate further development of 3D facade semantic segmentation methods, enabling robust segmentation indispensable in creating urban digital twins.

Several strategies using neural network algorithms have been established to automate the process of evaluating parameters regarding the freeze–thaw resistance of hardened concrete from image data. However, the performance of such models is dependent on the quality of the datasets used for training. Hand-labeling concrete image data is challenging, where especially small micro air voids (<300 μ m) can be overlooked. This potentially leads to algorithms that are unable to accurately detect the micro air void content, despite being required by current standards (e.g. DIN EN 480-11). To account for this, a method was developed using confocal laser scanning microscopy and the “Segment Anything” model. Acquiring surface height-data through confocal laser scanning microscopy expendites the labeling process and creates more reliable training data due to the detectability of air voids through height differences. Furthermore, by combining the height-data with RGB-images it was possible to accurately distinguish between air voids, aggregates and cement paste with high repeatability between repeated labeling iterations. Keeping high magnification levels (120-480x) enabled the detection of air voids down to 5 μ m. The framework and dataset presented in this study are fundamental for further development of new neural network based algorithms, specialized for the characterization and evaluation of the freeze–thaw resistance of concrete.

Abstract Finding correspondences between 3D deformable shapes is an important and long‐standing problem in geometry processing, computer vision, graphics, and beyond. While various shape matching datasets exist, they are mostly static or limited in size, restricting their adaptation to different problem settings, including both full and partial shape matching. In particular the existing partial shape matching datasets are small (fewer than 100 shapes) and thus unsuitable for data‐hungry machine learning approaches. Moreover, the type of partiality present in existing datasets is often artificial and far from realistic. To address these limitations, we introduce a generic and flexible framework for the procedural generation of challenging full and partial shape matching datasets. Our framework allows the propagation of custom annotations across shapes, making it useful for various applications. By utilising our framework and manually creating cross‐dataset correspondences between seven existing (complete geometry) shape matching datasets, we propose a new large benchmark BeCoS with a total of 2543 shapes. Based on this, we offer several challenging benchmark settings, covering both full and partial matching, for which we evaluate respective state‐of‐the‐art methods as baselines. Visualisations and code of our benchmark can be found at: https://nafieamrani.github.io/BeCoS/ .

Abstract In this paper, we present a novel visual SLAM and long-term localization benchmark for autonomous driving in challenging conditions based on the large-scale 4Seasons dataset. The proposed benchmark provides drastic appearance variations caused by seasonal changes and diverse weather and illumination conditions. While significant progress has been made in advancing visual SLAM on small-scale datasets with similar conditions, there is still a lack of unified benchmarks representative of real-world scenarios for autonomous driving. We introduce a new unified benchmark for jointly evaluating visual odometry, global place recognition, and map-based visual localization performance which is crucial to successfully enable autonomous driving in any condition. The data has been collected for more than one year, resulting in more than 300 km of recordings in nine different environments ranging from a multi-level parking garage to urban (including tunnels) to countryside and highway. We provide globally consistent reference poses with up to centimeter-level accuracy obtained from the fusion of direct stereo-inertial odometry with RTK GNSS. We evaluate the performance of several state-of-the-art visual odometry and visual localization baseline approaches on the benchmark and analyze their properties. The experimental results provide new insights into current approaches and show promising potential for future research. Our benchmark and evaluation protocols will be available at https://go.vision.in.tum.de/4seasons .

We present HI-SLAM2, a geometry-aware Gaussian SLAM system that achieves fast and accurate monocular scene reconstruction using only RGB input. Existing Neural SLAM or 3DGS-based SLAM methods often trade off between rendering quality and geometry accuracy, our research demonstrates that both can be achieved simultaneously with RGB input alone. The key idea of our approach is to enhance the ability for geometry estimation by combining easy-to-obtain monocular priors with learning-based dense SLAM, and then using 3D Gaussian splatting as our core map representation to efficiently model the scene. Upon loop closure, our method ensures on-the-fly global consistency through efficient pose graph bundle adjustment and instant map updates by explicitly deforming the 3D Gaussian units based on anchored keyframe updates. Furthermore, we introduce a grid-based scale alignment strategy to maintain improved scale consistency in prior depths for finer depth details. Through extensive experiments on Replica, ScanNet, Waymo Open, ETH3D SLAM and ScanNet++ datasets, we demonstrate significant improvements over existing Neural SLAM methods and even surpass RGB-D-based methods in both reconstruction and rendering quality.

Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property of matchings is geometric consistency, which means that neighboring triangles in one shape are consistently matched to neighboring triangles in the other shape. Moreover, while in practice one often has only access to partial observations of a 3D shape (e.g. due to occlusion, or scanning artifacts), there do not exist any methods that directly address geometrically consistent partial shape matching. In this work we fill this gap by proposing to integrate state-of-the-art deep shape features into a novel integer linear programming partial shape matching formulation. Our optimization yields a globally optimal solution on low resolution shapes, which we then refine using a coarse-to-fine scheme. We show that our method can find more reliable results on partial shapes in comparison to existing geometrically consistent algorithms (for which one first has to fill missing parts with a dummy geometry). Moreover, our matchings are substantially smoother than learning-based state-of-the-art shape matching methods. The code of this work is publicly available at https://github.com/vikiehm/ geometrically-consistent-partial-shape-matching.

3D semantic scene understanding is a fundamental challenge in computer vision. It enables mobile agents to autonomously plan and navigate arbitrary environments. SSC formalizes this challenge as jointly estimating dense geometry and semantic information from sparse observations of a scene. Current methods for SSC are generally trained on 3D ground truth based on aggregated LiDAR scans. This process relies on special sensors and annotation by hand which are costly and do not scale well. To overcome this issue, our work presents the first self-supervised approach to SSC called S4C that does not rely on 3D ground truth data. Our proposed method can reconstruct a scene from a single image and only relies on videos and pseudo segmentation ground truth generated from off-the-shelf image segmentation network during training. Unlike existing methods, which use discrete voxel grids, we represent scenes as implicit semantic fields. This formulation allows querying any point within the camera frustum for occupancy and semantic class. Our architecture is trained through rendering-based self-supervised losses. Nonetheless, our method achieves performance close to fully supervised state-of-the-art methods. Additionally, our method demonstrates strong generalization capabilities and can synthesize accurate segmentation maps for far away viewpoints.

Event cameras offer the exciting possibility of tracking the camera’s pose during high-speed motion and in adverse lighting conditions. Despite this promise, existing event-based monocular visual odometry (VO) approaches demonstrate limited performance on recent benchmarks. To address this limitation, some methods resort to additional sensors such as IMUs, stereo event cameras, or frame-based cameras. Nonetheless, these additional sensors limit the application of event cameras in real-world devices since they increase cost and complicate system requirements. Moreover, relying on a frame-based camera makes the system susceptible to motion blur and HDR. To remove the dependency on additional sensors and to push the limits of using only a single event camera, we present Deep Event VO (DEVO), the first monocular event-only system with strong performance on a large number of real-world benchmarks. DEVO sparsely tracks selected event patches over time. A key component of DEVO is a novel deep patch selection mechanism tailored to event data. We significantly decrease the state-of-the-art pose tracking error on seven real-world benchmarks by up to 97% compared to event-only methods and often surpass or are close to stereo or inertial methods.

Christian Tomani, David Vilar, Markus Freitag, Colin Cherry, Subhajit Naskar, Mara Finkelstein, Xavier Garcia, Daniel Cremers. Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2024.

Bilevel optimization aims to optimize an outer objective function that depends on the solution to an inner optimization problem. It is routinely used in Machine Learning, notably for hyperparameter tuning. The conventional method to compute the so-called hypergradient of the outer problem is to use the Implicit Function Theorem (IFT). As a function of the error of the inner problem resolution, we study the error of the IFT method. We analyze two strategies to reduce this error: preconditioning the IFT formula and reparameterizing the inner problem. We give a detailed account of the impact of these two modifications on the error, highlighting the role played by higher-order derivatives of the functionals at stake. Our theoretical findings explain when super efficiency, namely reaching an error on the hypergradient that depends quadratically on the error on the inner problem, is achievable and compare the two approaches when this is impossible. Numerical evaluations on hyperparameter tuning for regression problems substantiate our theoretical findings.

The Laplace-Beltrami operator (LBO) emerges from studying manifolds equipped with a Riemannian metric. It is often called the swiss army knife of geometry processing as it allows to capture intrinsic shape information and gives rise to heat diffusion, geodesic distances, and a mul-titude of shape descriptors. It also plays a central role in geometric deep learning. In this work, we explore Finsler manifolds as a generalization of Riemannian manifolds. We revisit the Finsler heat equation and derive a Finsler heat kernel and a Finsler-Laplace-Beltrami Operator (FLBO): a novel theoretically justified anisotropic Laplace-Beltrami operator (ALBO). In experimental evaluations we demon-strate that the proposed FLBO is a valuable alternative to the traditional Riemannian-based LBO and ALBOs for spa-tialfiltering and shape correspondence estimation. We hope that the proposed Finsler heat kernel and the FLBO will inspire further exploration of Finsler geometry in the Computer vision community.

Neural approaches have shown a significant progress on camera-based reconstruction. But they require either a fairly dense sampling of the viewing sphere, or pre-training on an existing dataset, thereby limiting their generalizability. In contrast, photometric stereo (PS) approaches have shown great potential for achieving high-quality reconstruction under sparse viewpoints. Yet, they are impractical because they typically require tedious laboratory conditions, are restricted to dark rooms, and often multi-staged, making them subject to accumulated errors. To address these shortcomings, we propose an end-to-end uncalibrated multi-view PS frameworkfor reconstructing high-resolution shapes acquiredfrom sparse viewpoints in a real-world environment. We relax the dark room assumption, and allow a combination of static ambient lighting and dynamic near LED lighting, thereby enabling easy data capture outside the lab. Experimental validation confirms that it outperforms existing baseline approaches in the regime of sparse viewpoints by a large margin. This allows to bring high-accuracy 3D reconstruction from the dark room to the real world, while maintaining a reasonable data capture complexity.

Hierarchy is a natural representation of semantic taxonomies, including the ones routinely used in image segmentation. Indeed, recent work on semantic segmentation reports improved accuracy from supervised training leveraging hierarchical label structures. Encouraged by these results, we revisit the fundamental assumptions behind that work. We postulate and then empirically verify that the reasons for the observed improvement in segmentation accuracy may be entirely unrelated to the use of the semantic hierarchy. To demonstrate this, we design a range of crossdomain experiments with a representative hierarchical approach. We find that on the new testing domains, a flat (non-hierarchical) segmentation network, in which the parents are inferred from the children, has superior segmentation accuracy to the hierarchical approach across the board. Complementing these findings and inspired by the intrinsic properties of hyperbolic spaces, we study a more principled approach to hierarchical segmentation using the Poincare ball model. The hyperbolic representation largely outperforms the previous (Euclidean) hierarchical approach as well and is on par with our flat Euclidean baseline in terms of segmentation accuracy. However, it additionally exhibits surprisingly strong calibration quality of the parent nodes in the semantic hierarchy, especially on the more challenging domains. Our combined analysis suggests that the established practice of hierarchical segmentation may be limited to in-domain settings, whereas flat classifiers generalize substantially better, especially if they are modeled in the hyperbolic space.

We tackle the problem of 3D point cloud localization based on a few natural linguistic descriptions and introduce a novel neural network, Text2Loc, that fully interprets the semantic relationship between points and text. Text2Loc follows a coarse-to-fine localization pipeline: text-submap global place recognition, followed by fine localization. In global place recognition, relational dynamics among each textual hint are captured in a hierarchical transformer with max-pooling (HTM), whereas a balance between positive and negative pairs is maintained using text-submap contrastive learning. Moreover, we propose a novel matching-free fine localization method to further refine the location predictions, which completely removes the need for complicated text-instance matching and is lighter, faster, and more accurate than previous methods. Extensive experiments show that Text2Loc improves the localization accuracy by up to 2 × over the state-of-the-art on the KITTI360Pose dataset. Our project page is publicly available at https://yan-xia.github.io/projects/text2loc/.

Although 3D shape matching and interpolation are highly interrelated, they are often studied separately and applied sequentially to relate different 3D shapes, thus resulting in sub-optimal performance. In this work we present a unified framework to predict both point-wise correspondences and shape interpolation between 3D shapes. To this end, we combine the deep functional map framework with classical surface deformation models to map shapes in both spectral and spatial domains. On the one hand, by incorporating spatial maps, our method obtains more accurate and smooth point-wise correspondences compared to previous functional map methods for shape matching. On the other hand, by introducing spectral maps, our method gets rid of commonly used but computationally expensive geodesic distance constraints that are only valid for near-isometric shape deformations. Furthermore, we propose a novel test-time adaptation scheme to capture both pose-dominant and shape-dominant deformations. Using different challenging datasets, we demonstrate that our method outperforms previous state-of-the-art methods for both shape matching and interpolation, even compared to supervised approaches.

Finding correspondences between 3D shapes is an important and long-standing problem in computer vision, graphics and beyond. A prominent challenge are partial-to-partial shape matching settings, which occur when the shapes to match are only observed incompletely (e.g. from 3D scanning). Although partial-to-partial matching is a highly relevant setting in practice, it is rarely explored. Our work bridges the gap between existing (rather artificial) 3D full shape matching and partial-to-partial real-world set-tings by exploiting geometric consistency as a strong constraint. We demonstrate that it is indeed possible to solve this challenging problem in a variety of settings. For the first time, we achieve geometric consistency for partial-to-partial matching, which is realized by a novel integer non-linear program formalism building on triangle prod-uct spaces, along with a new pruning algorithm based on linear integer programming. Further, we generate a new inter-class dataset for partial-to-partial shape-matching. We show that our method outperforms current SOTA meth-ods on both an established intra-class dataset and our novel inter-class dataset. The code of this work is publicly avail-able.11https://github.com/vikiehm/gc-ppsm

Inferring scene geometry from images via Structure from Motion is a long-standing and fundamental problem in computer vision. While classical approaches and, more re-cently, depth map predictions only focus on the visible parts of a scene, the task of scene completion aims to reason about geometry even in occluded regions. With the popularity of neural radiance fields (NeRFs), implicit represen-tations also became popular for scene completion by pre-dicting so-called density fields. Unlike explicit approaches e.g. voxel-based methods, density fields also allow for ac-curate depth prediction and novel-view synthesis via image-based rendering. In this work, we propose to fuse the scene reconstruction from multiple images and distill this knowl-edge into a more accurate single-view scene reconstruction. To this end, we propose Multi- View Behind the Scenes (MVBTS) to fuse density fields from multiple posed images, trained fully self-supervised only from image data. Using knowledge distillation, we use MVBTS to train a single-view scene completion network via direct supervision called KDBTS. It achieves state-of-the-art performance on occu-pancy prediction, especially in occluded regions.

In recent years, semantic segmentation has become a pivotal tool in processing and interpreting satellite imagery. Yet, a prevalent limitation of supervised learning techniques remains the need for extensive manual annotations by experts. In this work, we explore the potential of generative image diffusion to address the scarcity of annotated data in earth observation tasks. The main idea is to learn the joint data manifold of images and labels, leveraging recent ad-vancements in denoising diffusion probabilistic models. To the best of our knowledge, we are the first to generate both images and corresponding masks for satellite segmentation. We find that the obtained pairs not only display high quality in fine-scale features but also ensure a wide sampling diversity. Both aspects are crucial for earth observation data, where semantic classes can vary severely in scale and occurrence frequency. We employ the novel data instances for downstream segmentation, as a form of data augmentation. In our experiments, we provide comparisons to prior works based on discriminative diffusion models or GANs. We demonstrate that integrating generated samples yields significant quantitative improvements for satellite semantic segmentation - both compared to baselines and when training only on the original data.

Diffusion models have recently revolutionized the field of image synthesis due to their ability to generate photorealistic images. However, one of the major drawbacks of diffusion models is that the image generation process is costly. A large image-to-image network has to be applied many times to iteratively refine an image from random noise. While many recent works propose techniques to reduce the number of required steps, they generally treat the underlying denoising network as a black box. In this work, we investigate the behavior of the layers within the network and find that 1) the layers' output changes smoothly over time, 2) the layers show distinct patterns of change, and 3) the change from step to step is often very small. We hypothesize that many layer computations in the denoising network are redundant. Leveraging this, we introduce block caching, in which we reuse outputs from layer blocks of previous steps to speed up inference. Furthermore, we propose a technique to automatically determine caching schedules based on each block's changes over timesteps. In our experiments, we show through FID, human evaluation and qualitative analysis that Block Caching allows to generate images with higher visual quality at the same computational cost. We demonstrate this for different state-of-the-art models (LDM and EMU) and solvers (DDIM and DPM). Project page: fwmb.github.io/blockcaching

Within the graph learning community, conventional wisdom dictates that spectral convolutional networks may only be deployed on undirected graphs: Only there could the existence of a well-defined graph Fourier transform be guaranteed, so that information may be translated between spatial- and spectral domains. Here we show this traditional reliance on the graph Fourier transform to be superfluous and -- making use of certain advanced tools from complex analysis and spectral theory -- extend spectral convolutions to directed graphs. We provide a frequency-response interpretation of newly developed filters, investigate the influence of the basis used to express filters and discuss the interplay with characteristic operators on which networks are based. In order to thoroughly test the developed theory, we conduct experiments in real world settings, showcasing that directed spectral convolutional networks provide new state of the art results for heterophilic node classification on many datasets and -- as opposed to baselines -- may be rendered stable to resolution-scale varying topological perturbations.

Direct image alignment is a widely used technique for relative 6DoF pose estimation between two images, but its accuracy strongly depends on pose initialization. Therefore, recent end-to-end frameworks increase the convergence basin of the learned feature descriptors with special training objectives, such as the Gauss-Newton loss. However, the training data may exhibit bias toward a specific type of motion and pose initialization, thus limiting the generalization of these methods. In this work, we derive a closed-form solution to the expected optimum of the Gauss-Newton loss. The solution is agnostic to the underlying feature representation and allows us to dynamically adjust the basin of convergence according to our assumptions about the uncertainty in the current estimates. These properties allow for effective control over the convergence in the alignment process. Despite using self-supervised feature embeddings, our solution achieves compelling accuracy w.r.t. the state-of-the-art direct image alignment methods trained end-to-end with pose supervision, and demonstrates improved robustness to pose initialization. Our analytical solution exposes some inherent limitations of end-to-end learning with the Gauss-Newton loss, and establishes an intriguing connection between direct image alignment and feature-matching approaches.

We give extensive empirical evidence against the common belief that variational learning is ineffective for large neural networks. We show that an optimizer called Improved Variational Online Newton (IVON) consistently matches or outperforms Adam for training large networks such as GPT-2 and ResNets from scratch. IVON's computational costs are nearly identical to Adam but its predictive uncertainty is better. We show several new use cases of IVON where we improve finetuning and model merging in Large Language Models, accurately predict generalization error, and faithfully estimate sensitivity to data. We find overwhelming evidence that variational learning is effective. Code is available at https://github.com/team-approx-bayes/ivon.

Photometric bundle adjustment (PBA) is widely used in estimating the camera pose and 3D geometry by assuming a Lambertian world. However, the assumption of photometric consistency is often violated since the non-diffuse reflection is common in real-world environments. The photometric inconsistency significantly affects the reliability of existing PBA methods. To solve this problem, we propose a novel physically-based PBA method. Specifically, we introduce the physically-based weights regarding material, illumination, and light path. These weights distinguish the pixel pairs with different levels of photometric inconsistency. We also design corresponding models for material estimation based on sequential images and illumination estimation based on point clouds. In addition, we establish the first SLAM-related dataset of non-Lambertian scenes with complete ground truth of illumination and material. Extensive experiments demonstrated that our PBA method outperforms existing approaches in accuracy.

Accurate and comprehensive Bird’s Eye View (BEV) semantic segmentation is essential for ensuring safe and proactive navigation in autonomous driving. Although cooperative perception has exceeded the detection capabilities of single-agent systems, prevalent camera-based algorithms in cooperative perception neglect valuable information derived from historical observations. This limitation becomes critical during sensor failures or communication issues as cooperative perception reverts to single-agent perception, leading to degraded performance and incomplete BEV segmentation maps. This paper introduces TempCoBEV, a temporal module designed to incorporate historical cues into current observations, thereby improving the quality and reliability of BEV map segmentations. We propose an importance-guided attention architecture to effectively integrate temporal information that prioritizes relevant properties for BEV map segmentation. TempCoBEV is an independent temporal module that seamlessly integrates into state-of-the-art camera-based cooperative perception models. We demonstrate through extensive experiments on the OPV2V dataset that TempCoBEV performs better than non-temporal models in predicting current and future BEV map segmentations, particularly in scenarios involving communication failures. We show the efficacy of TempCoBEV and its capability to integrate historical cues into the current BEV map, improving predictions under optimal communication conditions by up to 2% and under communication failures by up to 19%. The code is available at https://github.com/cvims/TempCoBEV.

Recent advancements in generative models have highlighted the crucial role of image tokenization in the efficient synthesis of high-resolution images. Tokenization, which transforms images into latent representations, reduces computational demands compared to directly processing pixels and enhances the effectiveness and efficiency of the generation process. Prior methods, such as VQGAN, typically utilize 2D latent grids with fixed downsampling factors. However, these 2D tokenizations face challenges in managing the inherent redundancies present in images, where adjacent regions frequently display similarities. To overcome this issue, we introduce **T**ransformer-based 1-D**i**mensional **Tok**enizer (TiTok), an innovative approach that tokenizes images into 1D latent sequences. TiTok provides a more compact latent representation, yielding substantially more efficient and effective representations than conventional techniques. For example, a 256 × 256 × 3 image can be reduced to just **32** discrete tokens, a significant reduction from the 256 or 1024 tokens obtained by prior methods. Despite its compact nature, TiTok achieves competitive performance to state-of-the-art approaches. Specifically, using the same generator framework, TiTok attains **1.97** gFID, outperforming MaskGIT baseline significantly by 4.21 at ImageNet 256 × 256 benchmark. The advantages of TiTok become even more significant when it comes to higher resolution. At ImageNet 512 × 512 benchmark, TiTok not only outperforms state-of-the-art diffusion model DiT-XL/2 (gFID 2.74 vs. 3.04), but also reduces the image tokens by 64×, leading to **410× faster** generation process. Our best-performing variant can significantly surpasses DiT-XL/2 (gFID **2.13** vs. 3.04) while still generating high-quality samples **74× faster**. Codes and models are available at https://github.com/bytedance/1d-tokenizer

We propose an end-to-end inverse rendering pipeline called SupeRVol that allows us to recover 3D shape and material parameters from a set of color images in a superresolution manner. To this end, we represent both the bidirectional reflectance distribution function’s (BRDF) parameters and the signed distance function (SDF) by multi-layer perceptrons (MLPs). In order to obtain both the surface shape and its reflectance properties, we revert to a differentiable volume renderer with a physically based illumination model that allows us to decouple reflectance and lighting. This physical model takes into account the effect of the camera’s point spread function thereby enabling a reconstruction of shape and material in a super-resolution quality. Experimental validation confirms that SupeRVol achieves state of the art performance in terms of inverse rendering quality. It generates reconstructions that are sharper than the individual input images, making this method ideally suited for 3D modeling from low-resolution imagery.

Event cameras asynchronously capture brightness changes with low latency, high temporal resolution, and high dynamic range. However, annotation of event data is a costly and laborious process, which limits the use of deep learning methods for classification and other semantic tasks with the event modality. To reduce the dependency on labeled event data, we introduce Masked Event Modeling (MEM), a self-supervised framework for events. Our method pretrains a neural network on unlabeled events, which can originate from any event camera recording. Subsequently, the pretrained model is finetuned on a downstream task, leading to a consistent improvement of the task accuracy. For example, our method reaches state-of-the-art classification accuracy across three datasets, N-ImageNet, N-Cars, and N-Caltech101, increasing the top-1 accuracy of previous work by significant margins. When tested on real-world event data, MEM is even superior to supervised RGB-based pretraining. The models pretrained with MEM are also label-efficient and generalize well to the dense task of semantic image segmentation.

Contemporary large-scale visual language models (VLMs) exhibit strong representation capacities, making them ubiquitous for enhancing image and text understanding tasks. They are often trained in a contrastive manner on a large and diverse corpus of images and corresponding text captions scraped from the internet. Despite this, VLMs often struggle with compositional reasoning tasks which require a fine-grained understanding of the complex interactions of objects and their attributes. This failure can be attributed to two main factors: 1) Contrastive approaches have traditionally focused on mining negative examples from existing datasets. However, the mined negative examples might not be difficult for the model to discriminate from the positive. An alternative to mining would be negative sample generation 2) But existing generative approaches primarily focus on generating hard negative texts associated with a given image. Mining in the other direction, i.e., generating negative image samples associated with a given text has been ignored. To overcome both these limitations, we propose a framework that not only mines in both directions but also generates challenging negative samples in both modalities, i.e., images and texts. Leveraging these generative hard negative samples, we significantly enhance VLMs’ performance in tasks involving multimodal compositional reasoning. Our code and dataset are released at https://ugorsahin.github.io/enhancing-multimodal-compositional-reasoning-of-vlm.html.

Neural 3D implicit representations learn priors that are useful for diverse applications, such as single- or multiple-view 3D reconstruction. A major downside of existing approaches while rendering an image is that they require evaluating the network multiple times per camera ray so that the high computational time forms a bottleneck for downstream applications. We address this problem by introducing a novel neural scene representation that we call the directional distance function (DDF). To this end, we learn a signed distance function (SDF) along with our DDF model to represent a class of shapes. Specifically, our DDF is defined on the unit sphere and predicts the distance to the surface along any given direction. Therefore, our DDF allows rendering images with just a single network evaluation per camera ray. Based on our DDF, we present a novel fast algorithm (FIRe) to reconstruct 3D shapes given a posed depth map. We evaluate our proposed method on 3D reconstruction from single-view depth images, where we empirically show that our algorithm reconstructs 3D shapes more accurately and it is more than 15 times faster (per iteration) than competing methods.

We introduce Power Bundle Adjustment as an expansion type algorithm for solving large-scale bundle adjustment problems. It is based on the power series expansion of the inverse Schur complement and constitutes a new family of solvers that we call inverse expansion methods. We theoretically justify the use of power series and we prove the convergence of our approach. Using the real-world BAL dataset we show that the proposed solver challenges the state-of-the-art iterative methods and significantly accelerates the solution of the normal equation, even for reaching a very high accuracy. This easy-to-implement solver can also complement a recently presented distributed bundle adjustment framework. We demonstrate that employing the proposed Power Bundle Adjustment as a subproblem solver significantly improves speed and accuracy of the distributed optimization.

We present G-MSM (Graph-based Multi-Shape Matching), a novel unsupervised learning approach for non-rigid shape correspondence. Rather than treating a collection of input poses as an unordered set of samples, we explicitly model the underlying shape data manifold. To this end, we propose an adaptive multi-shape matching architecture that constructs an affinity graph on a given set of training shapes in a self-supervised manner. The key idea is to combine putative, pairwise correspondences by propagating maps along shortest paths in the underlying shape graph. During training, we enforce cycle-consistency between such optimal paths and the pairwise matches which enables our model to learn topology-aware shape priors. We explore different classes of shape graphs and recover specific settings, like template-based matching (star graph) or learnable ranking/sorting (TSP graph), as special cases in our framework. Finally, we demonstrate state-of-the-art performance on several recent shape correspondence benchmarks, including realworld 3D scan meshes with topological noise and challenging inter-class pairs.111Our implementation is available under the following link: https://github.com/marvin-eisenberger/gmsm-matching

We propose an approach based on convex relaxations for certifiably optimal robust multiview triangulation. To this end, we extend existing relaxation approaches to non-robust multiview triangulation by incorporating a least squares cost function. We propose two formulations, one based on epipolar constraints and one based on fractional reprojection constraints. The first is lower dimensional and remains tight under moderate noise and outlier levels, while the second is higher dimensional and therefore slower but remains tight even under extreme noise and outlier levels. We demonstrate through extensive experiments that the proposed approaches allow us to compute provably optimal re-constructions even under significant noise and a large percentage of outliers.

We propose a differentiable nonlinear least squares framework to account for uncertainty in relative pose estimation from feature correspondences. Specifically, we introduce a symmetric version of the probabilistic normal epipolar constraint, and an approach to estimate the co-variance of feature positions by differentiating through the camera pose estimation procedure. We evaluate our approach on synthetic, as well as the KITTI and EuRoC real-world datasets. On the synthetic dataset, we confirm that our learned covariances accurately approximate the true noise distribution. In real world experiments, we find that our approach consistently outperforms state-of-the-art non-probabilistic and probabilistic approaches, regardless of the feature extraction algorithm of choice.

Inferring a meaningful geometric scene representation from a single image is a fundamental problem in computer vision. Approaches based on traditional depth map prediction can only reason about areas that are visible in the image. Currently, neural radiance fields (NeRFs) can capture true 3D including color, but are too complex to be generated from a single image. As an alternative, we propose to predict an implicit density field from a single image. It maps every location in the frustum of the image to volumetric density. By directly sampling color from the available views instead of storing color in the density field, our scene representation becomes significantly less complex compared to NeRFs, and a neural network can predict it in a single forward pass. The network is trained through self-supervision from only video data. Our formulation allows volume rendering to perform both depth prediction and novel view synthesis. Through experiments, we show that our method is able to predict meaningful geometry for regions that are occluded in the input image. Additionally, we demonstrate the potential of our approach on three datasets for depth prediction and novel-view synthesis.

Place recognition based on point clouds (LiDAR) is an important component for autonomous robots or self-driving vehicles. Current SOTA performance is achieved on accumulated LiDAR submaps using either point-based or voxel-based structures. While voxel-based approaches nicely integrate spatial context across multiple scales, they do not exhibit the local precision of point-based methods. As a result, existing methods struggle with fine-grained matching of subtle geometric features in sparse single-shot Li-DAR scans. To overcome these limitations, we propose CASSPR as a method to fuse point-based and voxel-based approaches using cross attention transformers. CASSPR leverages a sparse voxel branch for extracting and aggregating information at lower resolution and a point-wise branch for obtaining fine-grained local information. CASSPR uses queries from one branch to try to match structures in the other branch, ensuring that both extract self-contained descriptors of the point cloud (rather than one branch dominating), but using both to inform the out-put global descriptor of the point cloud. Extensive experiments show that CASSPR surpasses the state-of-the-art by a large margin on several datasets (Oxford RobotCar, TUM, USyd). For instance, it achieves AR@1 of 85.6% on the TUM dataset, surpassing the strongest prior model by ~15%. Our code is publicly available.1

The goal of Online Domain Adaptation for semantic segmentation is to handle unforeseeable domain changes that occur during deployment, like sudden weather events. However, the high computational costs associated with brute-force adaptation make this paradigm unfeasible for real-world applications. In this paper we propose HAMLET, a Hardware-Aware Modular Least Expensive Training framework for real-time domain adaptation. Our approach includes a hardware-aware back-propagation orchestration agent (HAMT) and a dedicated domain-shift detector that enables active control over when and how the model is adapted (LT). Thanks to these advancements, our approach is capable of performing semantic segmentation while simultaneously adapting at more than 29FPS on a single consumer-grade GPU. Our framework’s encouraging accuracy and speed trade-off is demonstrated on OnDA and SHIFT benchmarks through experimental results.

We propose a novel mixed-integer programming (MIP) formulation for generating precise sparse correspondences for highly non-rigid shapes. To this end, we introduce a projected Laplace-Beltrami operator (PLBO) which combines intrinsic and extrinsic geometric information to measure the deformation quality induced by predicted correspondences. We integrate the PLBO, together with an orientation-aware regulariser, into a novel MIP formulation that can be solved to global optimality for many practical problems. In contrast to previous methods, our approach is provably invariant to rigid transformations and global scaling, initialisation-free, has optimality guarantees, and scales to high resolution meshes with (empirically observed) linear time. We show state-of-the-art results for sparse non-rigid matching on several challenging 3D datasets, including data with inconsistent meshing, as well as applications in mesh-to-point-cloud matching.

Scene reconstructions are often incomplete due to occlusions and limited viewpoints. There have been efforts to use semantic information for scene completion. However, the completed shapes may be rough and imprecise since respective methods rely on 3D convolution and/or lack effective shape constraints. To overcome these limitations, we propose a semantic scene completion method based on deformable deep implicit templates (DDIT). Specifically, we complete each segmented instance in a scene by deforming a template with a latent code. Such a template is expressed by a deep implicit function in the canonical frame. It abstracts the shape prior of a category, and thus can provide constraints on the overall shape of an instance. Latent code controls the deformation of template to guarantee fine details of an instance. For code prediction, we design a neural network that leverages both intra-and inter-instance information. We also introduce an algorithm to transform instances between the world and canonical frames based on geometric constraints and a hierarchical tree. To further improve accuracy, we jointly optimize the latent code and transformation by enforcing the zero-valued isosurface constraint. In addition, we establish a new dataset to solve different problems of existing datasets. Experiments showed that our DDIT outperforms state-of-the-art approaches.

In this work, we propose a novel prior learning method for advancing generalization and uncertainty estimation in deep neural networks. The key idea is to exploit scalable and structured posteriors of neural networks as informative priors with generalization guarantees. Our learned priors provide expressive probabilistic representations at large scale, like Bayesian counterparts of pre-trained models on ImageNet, and further produce non-vacuous generalization bounds. We also extend this idea to a continual learning framework, where the favorable properties of our priors are desirable. Major enablers are our technical contributions: (1) the sums-of-Kronecker-product computations, and (2) the derivations and optimizations of tractable objectives that lead to improved generalization bounds. Empirically, we exhaustively show the effectiveness of this method for uncertainty estimation and generalization.

Calibrating deep learning models to yield uncertainty-aware predictions is crucial as deep neural networks get increasingly deployed in safety-critical applications. While existing post-hoc calibration methods achieve impressive results on in-domain test datasets, they are limited by their inability to yield reliable uncertainty estimates in domain-shift and out-of-domain (OOD) scenarios. We aim to bridge this gap by proposing DAC, an accuracy-preserving as well as Density-Aware Calibration method based on k-nearest-neighbors (KNN). In contrast to existing post-hoc methods, we utilize hidden layers of classifiers as a source for uncertainty-related information and study their importance. We show that DAC is a generic method that can readily be combined with state-of-the-art post-hoc methods. DAC boosts the robustness of calibration performance in domain-shift and OOD, while maintaining excellent in-domain predictive uncertainty estimates. We demonstrate that DAC leads to consistently better calibration across a large number of model architectures, datasets, and metrics. Additionally, we show that DAC improves calibration substantially on recent large-scale neural networks pre-trained on vast amounts of data.

A promise of Generative Adversarial Networks (GANs) is to provide cheap photorealistic data for training and validating AI models in autonomous driving. Despite their huge success, their performance on complex images featuring multiple objects is understudied. While some frameworks produce high-quality street scenes with little to no control over the image content, others offer more control at the expense of high-quality generation. A common limitation of both approaches is the use of global latent codes for the whole image, which hinders the learning of independent object distributions. Motivated by SemanticStyleGAN (SSG), a recent work on latent space disentanglement in human face generation, we propose a novel framework, Urban-StyleGAN, for urban scene generation and manipulation. We find that a straightforward application of SSG leads to poor results because urban scenes are more complex than human faces. To provide a more compact yet disentangled latent representation, we develop a class grouping strategy wherein individual classes are grouped into super-classes. Moreover, we employ an unsupervised latent exploration algorithm in the $\mathcal{S}$-space of the generator and show that it is more efficient than the conventional ${\mathcal{W}^ + }$-space in controlling the image content. Results on the Cityscapes and Mapillary datasets show the proposed approach achieves significantly more controllability and improved image quality than previous approaches on urban scenes and is on par with general-purpose non-controllable generative models (like StyleGAN2) in terms of quality.

Neural networks have recently been used to analyze diverse physical systems and to identify the underlying dynamics. While existing methods achieve impressive results, they are limited by their strong demand for training data and their weak generalization abilities to out-of-distribution data. To overcome these limitations, we propose to combine neural implicit representations for appearance modeling with neural ordinary differential equations (ODEs) for modelling planar physical phenomena to obtain a dynamic scene representation that can be identified directly from visual observations. Our proposed model combines several unique advantages: (i) Contrary to existing approaches that require large training datasets, we are able to identify physical parameters from only a single video. (ii) The use of neural implicit representations enables the processing of high-resolution videos and the synthesis of photo-realistic images. (iii) The embedded neural ODE has a known parametric form that allows for the identification of interpretable physical parameters, and (iv) long-term prediction in state space. (v) Furthermore, the photo-realistic rendering of novel scenes with modified physical parameters becomes possible.

Fine-detailed reconstructions are in high demand in many applications. However, most of the existing RGB-D reconstruction methods rely on pre-calculated accurate camera poses to recover the detailed surface geometry, where the representation of a surface needs to be adapted when optimizing different quantities. In this paper, we present a novel multi-view RGB-D based reconstruction method that tackles camera pose, lighting, albedo, and surface normal estimation via the utilization of a gradient signed distance field (gradient-SDF). The proposed method formulates the image rendering process using specific physically-based model(s) and optimizes the surface’s quantities on the actual surface using its volumetric representation, as opposed to other works which estimate surface quantities only near the actual surface. To validate our method, we investigate two physically-based image formation models for natural light and point light source applications. The experimental results on synthetic and real-world datasets demonstrate that the proposed method can recover high-quality geometry of the surface more faithfully than the state-of-the-art and further improves the accuracy of estimated camera poses1.

Abstract Supervised deep learning methods using image data as input have shown promising results in the context of vehicle control. However, these supervised methods have two main disadvantages: 1) They require a copious amount of labeled training data, which is difficult and expensive to collect. 2) Such models do not perform well, when situations that are not in the distribution of the training set are encountered. This includes deviations from the designated driving behavior. We therefore provide a framework to mitigate these problems from merely an unlabeled sequence of images. Visual Odometry is first used to determine the vehicle trajectory. Model Predictive Control (MPC) then uses this trajectory to implicitly infer the steering labels. Meanwhile, synthesized images at deviated trajectories are included in the training distribution for enhanced robustness of the neural network model. Experimental results demonstrate that the performance of our network is at par with methods requiring additional data collection or supervision. Code and supplementary information is available here: https://github.com/idilsulo/nn-driving

Abstract Many problems in imaging and low-level vision can be formulated as nonconvex variational problems. A promising class of approaches to tackle such problems are convex relaxation methods, which consider a lifting of the energy functional to a higher-dimensional space. However, they come with increased memory requirements due to the lifting. The present paper is an extended version of the earlier conference paper by Ye et al. (in: DAGM German conference on pattern recognition (GCPR), 2021) which combined two recent approaches to make lifting more scalable: product-space relaxation and sublabel-accurate discretization. Furthermore, it is shown that a simple cutting-plane method can be used to solve the resulting semi-infinite optimization problem. This journal version extends the previous conference work with additional experiments, a more detailed outline of the complete algorithm and a user-friendly introduction to functional lifting methods.

Graph matching aims to establish correspondences between vertices of graphs such that both the node and edge attributes agree. Various learning-based methods were recently proposed for finding correspondences between image key points based on deep graph matching formulations. While these approaches mainly focus on learning node and edge attributes, they completely ignore the 3D geometry of the underlying 3D objects depicted in the 2D images. We fill this gap by proposing a trainable framework that takes advantage of graph neural networks for learning a deformable 3D geometry model from inhomogeneous image collections, i.e. a set of images that depict different instances of objects from the same category. Experimentally we demonstrate that our method outperforms recent learning-based approaches for graph matching considering both accuracy and cycle-consistency error, while we in addition obtain the underlying 3D geometry of the objects depicted in the 2D images.

The Sinkhorn operator has recently experienced a surge of popularity in computer vision and related fields. One major reason is its ease of integration into deep learning frameworks. To allow for an efficient training of respective neural networks, we propose an algorithm that obtains analytical gradients of a Sinkhorn layer via implicit differentiation. In comparison to prior work, our framework is based on the most general formulation of the Sinkhorn operator. It allows for any type of loss function, while both the target capacities and cost matrices are differentiated jointly. We further construct error bounds of the resulting algorithm for approximate inputs. Finally, we demonstrate that for a number of applications, simply replacing automatic differentiation with our algorithm directly improves the stability and accuracy of the obtained gradients. Moreover, we show that it is computationally more efficient, particularly when resources like GPU memory are scarce.11Our implementation is available under the following link: https://github.com/marvin-eisenberger/implicit-sinkhorn

The estimation of the relative pose of two camera views is a fundamental problem in computer vision. Kneip et al. proposed to solve this problem by introducing the normal epipolar constraint (NEC). However, their approach does not take into account uncertainties, so that the accuracy of the estimated relative pose is highly dependent on accurate feature positions in the target frame. In this work, we introduce the probabilistic normal epipolar constraint (PNEC) that overcomes this limitation by accounting for anisotropic and inhomogeneous uncertainties in the feature positions. To this end, we propose a novel objective function, along with an efficient optimization scheme that effectively minimizes our objective while maintaining real-time performance. In experiments on synthetic data, we demonstrate that the novel PNEC yields more accurate rotation estimates than the original NEC and several popular relative rotation estimation algorithms. Furthermore, we integrate the proposed method into a state-of-the-art monocular rotation-only odometry system and achieve consistently improved results for the real-world KITTI dataset.

We present a scalable combinatorial algorithm for globally optimizing over the space of geometrically consistent mappings between 3D shapes. We use the mathematically elegant formalism proposed by Windheuser et al. [66] where 3D shape matching was formulated as an integer linear program over the space of orientation-preserving diffeomorphisms. Until now, the resulting formulation had limited practical applicability due to its complicated constraint structure and its large size. We propose a novel primal heuristic coupled with a Lagrange dual problem that is several orders of magnitudes faster compared to previous solvers. This allows us to handle shapes with substantially more triangles than previously solvable. We demonstrate compelling results on diverse datasets, and, even showcase that we can address the challenging setting of matching two partial shapes without availability of complete shapes. Our code is publicly available at http://github.com/paulOnoah/sm-comb.

We present Gradient-SDF, a novel representation for 3D geometry that combines the advantages of implict and explicit representations. By storing at every voxel both the signed distance field as well as its gradient vector field, we enhance the capability of implicit representations with approaches originally formulated for explicit surfaces. As concrete examples, we show that (1) the Gradient-SDF allows us to perform direct SDF tracking from depth images, using efficient storage schemes like hash maps, and that (2) the Gradient-SDF representation enables us to perform photometric bundle adjustment directly in a voxel representation (without transforming into a point cloud or mesh), naturally a fully implicit optimization of geometry and camera poses and easy geometry upsampling. Experimental results confirm that this leads to significantly sharper reconstructions. Since the overall SDF voxel structure is still respected, the proposed Gradient-SDF is equally suited for (GPU) parallelization as related approaches.

Earth observation is a fundamental tool for monitoring the evolution of land use in specific areas of interest. Observing and precisely defining change, in this context, requires both time-series data and pixel-wise segmentations. To that end, we propose the DynamicEarthNet dataset that consists of daily, multi-spectral satellite observations of 75 selected areas of interest distributed over the globe with imagery from Planet Labs. These observations are paired with pixel-wise monthly semantic segmentation labels of 7 land use and land cover (LULC) classes. DynamicEarthNet is the first dataset that provides this unique combination of daily measurements and high-quality labels. In our experiments, we compare several established baselines that either utilize the daily observations as additional training data (semi-supervised learning) or multiple observations at once (spatio-temporal learning) as a point of reference for future research. Finally, we propose a new evaluation metric SCS that addresses the specific challenges associated with time-series semantic change segmentation. The data is available at: https://mediatum.ub.tum.de/1650201.

In this paper, we propose Ventriloquist-Net: A Talking Head Generation model that uses only a speech segment and a single source face image. It places emphasis on emotive expressions. Cues for generating these expressions are implicitly inferred from the speech clip only. We formulate our framework to comprise of independently trained modules to expedite convergence. This not only allows extension to datasets in a semi-supervised manner but also facilitates handling in-the-wild source images. Quantitative and qualitative evaluations on generated videos demonstrate state-of-the-art performance even on unseen input data. Implementation and supplementary videos are available at https://github.com/dipnds/VentriloquistNet.

We address the problem of minimizing a class of energy functions consisting of data and smoothness terms that commonly occur in machine learning, computer vision, and pattern recognition. While discrete optimization methods are able to give theoretical optimality guarantees, they can only handle a finite number of labels and therefore suffer from label discretization bias. Existing continuous optimization methods can find sublabel-accurate solutions, but they are not efficient for large label spaces. In this work, we propose an efficient sublabel-accurate method that utilizes the best properties of both continuous and discrete models. We separate the problem into two sequential steps: (i) global discrete optimization for selecting the label range, and (ii) efficient continuous sublabel-accurate local refinement of a convex approximation of the energy function in the chosen range. Doing so allows us to achieve a boost in time and memory efficiency while practically keeping the accuracy at the same level as continuous convex relaxation methods, and in addition, providing theoretical optimality guarantees at the level of discrete methods. Finally, we show the flexibility of the proposed approach to general pairwise smoothness terms, so that it is applicable to a wide range of regularizations. Experiments on the illustrating example of the image denoising problem demonstrate the properties of the proposed method. The code reproducing experiments is available on https://github.com/nurlanov-zh/sublabel-accurate-alpha-expansion.

In this paper, we present a complete pipeline for 3D semantic mapping solely based on a stereo camera system. The pipeline comprises a direct sparse visual odometry frontend as well as a back-end for global optimization including GNSS integration, and semantic 3D point cloud labeling. We propose a simple but effective temporal voting scheme which improves the quality and consistency of the 3D point labels. Qualitative and quantitative evaluations of our pipeline are performed on the KITTI-360 dataset. The results show the effectiveness of our proposed voting scheme and the capability of our pipeline for efficient large-scale 3D semantic mapping. The large-scale mapping capabilities of our pipeline is furthermore demonstrated by presenting a very large-scale semantic map covering 8000 km of roads generated from data collected by a fleet of vehicles.

Direct methods have shown excellent performance in the applications of visual odometry and SLAM. In this work we propose to leverage their effectiveness for the task of 3D multi-object tracking. To this end, we propose DirectTracker, a framework that effectively combines direct image alignment for the short-term tracking and sliding-window photometric bundle adjustment for 3D object detection. Object proposals are estimated based on the sparse sliding-window pointcloud and further refined using an optimization-based cost function that carefully combines 3D and 2D cues to ensure consistency in image and world space. We propose to evaluate 3D tracking using the recently introduced higher-order tracking accuracy (HOTA) metric and the generalized intersection over union sim-ilarity measure to mitigate the limitations of the conventional use of intersection over union for the evaluation of vision-based trackers. We perform evaluation on the KITTI Tracking benchmark for the Car class and show competitive performance in tracking objects both in 2D and 3D.

Given the importance of getting calibrated predictions and reliable uncertainty estimations, various post-hoc calibration methods have been developed for neural networks on standard multi-class classification tasks. However, these methods are not well suited for calibrating graph neural networks (GNNs), which presents unique challenges such as accounting for the graph structure and the graph-induced correlations between the nodes. In this work, we conduct a systematic study on the calibration qualities of GNN node predictions. In particular, we identify five factors which influence the calibration of GNNs: general under-confident tendency, diversity of nodewise predictive distributions, distance to training nodes, relative confidence level, and neighborhood similarity. Furthermore, based on the insights from this study, we design a novel calibration method named Graph Attention Temperature Scaling (GATS), which is tailored for calibrating graph neural networks. GATS incorporates designs that address all the identified influential factors and produces nodewise temperature scaling using an attention-based architecture. GATS is accuracy-preserving, data-efficient, and expressive at the same time. Our experiments empirically verify the effectiveness of GATS, demonstrating that it can consistently achieve state-of-the-art calibration results on various graph datasets for different GNN backbones.

Neural networks are known to produce poor uncertainty estimations, and a variety of approaches have been proposed to remedy this issue. This includes deep ensemble, a simple and effective method that achieves state-of-the-art results for uncertainty-aware learning tasks. In this work, we explore a combinatorial generalization of deep ensemble called deep combinatorial aggregation (DCA). DCA creates multiple instances of network components and aggregates their combinations to produce diversified model proposals and predictions. DCA components can be defined at different levels of granularity. And we discovered that coarse-grain DCAs can outperform deep ensemble for uncertainty-aware learning both in terms of predictive performance and uncertainty estimation. For fine-grain DCAs, we discover that an average parameterization approach named deep combinatorial weight averaging (DCWA) can improve the baseline training. It is on par with stochastic weight averaging (SWA) but does not require any custom training schedule or adaptation of BatchNorm layers. Furthermore, we propose a consistency enforcing loss that helps the training of DCWA and modelwise DCA. We experiment on in-domain, distributional shift, and out-of-distribution image classification tasks, and empirically confirm the effectiveness of DCWA and DCA approaches.

This paper addresses the task of set prediction using deep feed-forward neural networks. A set is a collection of elements which is invariant under permutation and the size of a set is not fixed in advance. Many real-world problems, such as image tagging and object detection, have outputs that are naturally expressed as sets of entities. This creates a challenge for traditional deep neural networks which naturally deal with structured outputs such as vectors, matrices or tensors. We present a novel approach for learning to predict sets with unknown permutation and cardinality using deep neural networks. In our formulation we define a likelihood for a set distribution represented by a) two discrete distributions defining the set cardinally and permutation variables, and b) a joint distribution over set elements with a fixed cardinality. Depending on the problem under consideration, we define different training models for set prediction using deep neural networks. We demonstrate the validity of our set formulations on relevant vision problems such as: 1) multi-label image classification where we outperform the other competing methods on the PASCAL VOC and MS COCO datasets, 2) object detection, for which our formulation outperforms popular state-of-the-art detectors, and 3) a complex CAPTCHA test, where we observe that, surprisingly, our set-based network acquired the ability of mimicking arithmetics without any rules being coded.

Dual decomposition approaches in nonconvex optimization may suffer from a duality gap. This poses a challenge when applying them directly to nonconvex problems such as MAP-inference in a Markov random field with continuous state spaces. To eliminate such gaps, this paper considers a reformulation of the original nonconvex task in the space of measures. This infinite-dimensional reformulation is then approximated by a semi-infinite one, which is obtained via a piecewise polynomial discretization in the dual. We provide a geometric intuition behind the primal problem induced by the dual discretization and draw connections to optimization over moment spaces. In contrast to existing discretizations which suffer from a grid bias, we show that a piecewise polynomial discretization better preserves the continuous nature of our problem. Invoking results from optimal transport theory and convex algebraic geometry we reduce the semi-infinite program to a finite one and provide a practical implementation based on semidefinite programming. We show, experimentally and in theory, that the approach successfully reduces the duality gap. To showcase the scalability of our approach, we apply it to the stereo matching problem between two images.

Finding shortest paths in a graph is relevant for numerous problems in computer vision and graphics, including image segmentation, shape matching, or the computation of geodesic distances on discrete surfaces. Traditionally, the concept of a shortest path is considered for graphs with scalar edge weights, which makes it possible to compute the length of a path by adding up the individual edge weights. Yet, graphs with scalar edge weights are severely limited in their expressivity, since oftentimes edges are used to encode significantly more complex interrelations. In this work we compensate for this modelling limitation and introduce the novel graph-theoretic concept of a shortest path in a graph with matrix-valued edges. To this end, we define a meaningful way for quantifying the path length for matrix-valued edges, and we propose a simple yet effective algorithm to compute the respective shortest path. While our formalism is universal and thus applicable to a wide range of settings in vision, graphics and beyond, we focus on demonstrating its merits in the context of 3D multi-shape analysis.

We propose a method to estimate the bidirectional reflectance distribution function (BRDF) and shading of complete scenes under static illumination given the 3D scene geometry and a corresponding high dynamic range (HDR) video. By splitting the BRDF into its diffuse and non-diffuse parts we solve the estimation of each component separately. For the diffuse component, we sample the incident illumination at each point in the scene using Monte Carlo ray tracing, allowing us to factor the captured surface color into albedo and shading. We then use a novel ray tracing-based optimization strategy to estimate the non-diffuse parameters of the BRDF. In a variety of experiments, we demonstrate that our method efficiently generates realistic copies of the observed scenes.

Vision-based learning methods for self-driving cars have primarily used supervised approaches that require a large number of labels for training. However, those labels are usually difficult and expensive to obtain. In this paper, we demonstrate how a model can be trained to control a vehicle’s trajectory using camera poses estimated through visual odometry methods in an entirely self-supervised fashion. We propose a scalable framework that leverages trajectory information from several different runs using a camera setup placed at the front of a car. Experimental results on the CARLA simulator demonstrate that our proposed approach performs at par with the model trained with supervision.

We propose a new formulation for the bundle adjustment problem which relies on nullspace marginalization of landmark variables by QR decomposition. Our approach, which we call square root bundle adjustment, is algebraically equivalent to the commonly used Schur complement trick, improves the numeric stability of computations, and allows for solving large-scale bundle adjustment problems with single-precision floating-point numbers. We show in real-world experiments with the BAL datasets that even in single precision the proposed solver achieves on average equally accurate solutions compared to Schur complement solvers using double precision. It runs significantly faster, but can require larger amounts of memory on dense problems. The proposed formulation relies on simple linear algebra operations and opens the way for efficient implementations of bundle adjustment on hardware platforms optimized for single-precision linear algebra processing.

We present NeuroMorph, a new neural network architecture that takes as input two 3D shapes and produces in one go, i.e. in a single feed forward pass, a smooth interpolation and point-to-point correspondences between them. The interpolation, expressed as a deformation field, changes the pose of the source shape to resemble the target, but leaves the object identity unchanged. NeuroMorph uses an elegant architecture combining graph convolutions with global feature pooling to extract local features. During training, the model is incentivized to create realistic deformations by approximating geodesics on the underlying shape space manifold. This strong geometric prior allows to train our model end-to-end and in a fully unsupervised manner without requiring any manual correspondence annotations. NeuroMorph works well for a large variety of input shapes, including non-isometric pairs from different object categories. It obtains state-of-the-art results for both shape correspondence and interpolation tasks, matching or surpassing the performance of recent unsupervised and supervised methods on multiple benchmarks.

Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence methods aim to find a solution between pairs of shapes, even if multiple instances of the same class are available. While isometries are often studied in shape correspondence problems, they have not been considered explicitly in the multi-matching setting. This paper closes this gap by proposing a novel optimisation formulation for isometric multi-shape matching. We present a suitable optimisation algorithm for solving our formulation and provide a convergence and complexity analysis. Our algorithm obtains multi-matchings that are by construction provably cycle-consistent. We demonstrate the superior performance of our method on various datasets and set the new state-of-the-art in isometric multi-shape matching.

We address the problem of uncertainty calibration. While standard deep neural networks typically yield uncalibrated predictions, calibrated confidence scores that are representative of the true likelihood of a prediction can be achieved using post-hoc calibration methods. However, to date, the focus of these approaches has been on in-domain calibration. Our contribution is two-fold. First, we show that existing post-hoc calibration methods yield highly over-confident predictions under domain shift. Second, we introduce a simple strategy where perturbations are applied to samples in the validation set before performing the post-hoc calibration step. In extensive experiments, we demonstrate that this perturbation step results in substantially better calibration under domain shift on a wide range of architectures and modelling tasks.

In this paper, we propose MonoRec, a semi-supervised monocular dense reconstruction architecture that predicts depth maps from a single moving camera in dynamic environments. MonoRec is based on a multi-view stereo setting which encodes the information of multiple consecutive images in a cost volume. To deal with dynamic objects in the scene, we introduce a MaskModule that predicts moving object masks by leveraging the photometric inconsistencies encoded in the cost volumes. Unlike other multi-view stereo methods, MonoRec is able to reconstruct both static and moving objects by leveraging the predicted masks. Furthermore, we present a novel multi-stage training scheme with a semi-supervised loss formulation that does not require LiDAR depth values. We carefully evaluate MonoRec on the KITTI dataset and show that it achieves state-of-theart performance compared to both multi-view and singleview methods. With the model trained on KITTI, we furthermore demonstrate that MonoRec is able to generalize well to both the Oxford RobotCar dataset and the more challenging TUM-Mono dataset recorded by a handheld camera. Code and related materials are available at https://vision.in.tum.de/research/monorec.

We tackle the problem of place recognition from point cloud data and introduce a self-attention and orientation encoding network (SOE-Net) that fully explores the relationship between points and incorporates long-range context into point-wise local descriptors. Local information of each point from eight orientations is captured in a PointOE module, whereas long-range feature dependencies among local descriptors are captured with a self-attention unit. Moreover, we propose a novel loss function called Hard Positive Hard Negative quadruplet loss (HPHN quadruplet), that achieves better performance than the commonly used metric learning loss. Experiments on various benchmark datasets demonstrate superior performance of the proposed network over the current state-of-the-art approaches. Our code is released publicly at https://github.com/Yan-Xia/SOE-Net.

We present the first deep implicit 3D morphable model (i3DMM) of full heads. Unlike earlier morphable face models it not only captures identity-specific geometry, texture, and expressions of the frontal face, but also models the entire head, including hair. We collect a new dataset consisting of 64 people with different expressions and hairstyles to train i3DMM. Our approach has the following favorable properties: (i) It is the first full head morphable model that includes hair. (ii) In contrast to mesh-based models it can be trained on merely rigidly aligned scans, without requiring difficult non-rigid registration. (iii) We design a novel architecture to decouple the shape model into an implicit reference shape and a deformation of this reference shape. With that, dense correspondences between shapes can be learned implicitly. (iv) This architecture allows us to semantically disentangle the geometry and color components, as color is learned in the reference space. Geometry is further disentangled as identity, expressions, and hairstyle, while color is disentangled as identity and hairstyle components. We show the merits of i3DMM using ablation studies, comparisons to state-of-the-art models, and applications such as semantic head editing and texture transfer. We will make our model publicly available1.

In this paper we propose a novel square root sliding-window bundle adjustment suitable for real-time odometry applications. The square root formulation pervades three major aspects of our optimization-based sliding-window estimator: for bundle adjustment we eliminate landmark variables with nullspace projection; to store the marginalization prior we employ a matrix square root of the Hessian; and when marginalizing old poses we avoid forming normal equations and update the square root prior directly with a specialized QR decomposition. We show that the proposed square root marginalization is algebraically equivalent to the conventional use of Schur complement (SC) on the Hessian. Moreover, it elegantly deals with rank-deficient Jacobians producing a prior equivalent to SC with Moore–Penrose inverse. Our evaluation of visual and visual-inertial odometry on real-world datasets demonstrates that the proposed estimator is 36% faster than the baseline. It furthermore shows that in single precision, conventional Hessian-based marginalization leads to numeric failures and reduced accuracy. We analyse numeric properties of the marginalization prior to explain why our square root form does not suffer from the same effect and therefore entails superior performance.

Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a cornerstone of large scale forecasting applications such as numerical weather prediction. As such, it is implemented in current operational systems of weather forecasting agencies across the globe. However, finding a good initial state poses a difficult optimization problem in part due to the non-invertible relationship between physical states and their corresponding observations. We learn a mapping from observational data to physical states and show how it can be used to improve optimizability. We employ this mapping in two ways: to better initialize the non-convex optimization problem, and to reformulate the objective function in better behaved physics space instead of observation space. Our experimental results for the Lorenz96 model and a two-dimensional turbulent fluid flow demonstrate that this procedure significantly improves forecast quality for chaotic systems.

In this paper we propose a framework for inte-grating map-based relocalization into online direct visual odometry. To achieve map-based relocalization for direct methods, we integrate image features into Direct Sparse Odometry (DSO) and rely on feature matching to associate online visual odometry (VO) with a previously built map. The integration of the relocalization poses is threefold. Firstly, they are incorporated as pose priors in the direct image alignment of the front-end tracking. Secondly, they are tightly integrated into the back-end bundle adjustment. Thirdly, an online fusion module is further proposed to combine relative VO poses and global relocalization poses in a pose graph to estimate keyframe-wise smooth and globally accurate poses. We evaluate our method on two multi-weather datasets showing the benefits of integrating different handcrafted and learned features and demonstrating promising improvements on camera tracking accuracy.

Obstacle avoidance is a fundamental and challenging problem for autonomous navigation of mobile robots. In this paper, we consider the problem of obstacle avoidance in simple 3D environments where the robot has to solely rely on a single monocular camera. In particular, we are interested in solving this problem without relying on localization, mapping, or planning techniques. Most of the existing work consider obstacle avoidance as two separate problems, namely obstacle detection, and control. Inspired by the recent advantages of deep reinforcement learning in Atari games and understanding highly complex situations in Go, we tackle the obstacle avoidance problem as a data-driven end-to-end deep learning approach. Our approach takes raw images as input and generates control commands as output. We show that discrete action spaces are outperforming continuous control commands in terms of expected average reward in maze-like environments. Furthermore, we show how to accelerate the learning and increase the robustness of the policy by incorporating predicted depth maps by a generative adversarial network.

Event cameras are bio-inspired vision sensors which measure per pixel brightness changes. They offer numerous benefits over traditional, frame-based cameras, including low latency, high dynamic range, high temporal resolution and low power consumption. Thus, these sensors are suited for robotics and virtual reality applications. To foster the development of 3D perception and navigation algorithms with event cameras, we present the TUM-VIE dataset. It consists of a large variety of handheld and head-mounted sequences in indoor and outdoor environments, including rapid motion during sports and high dynamic range scenarios. The dataset contains stereo event data, stereo grayscale frames at 20Hz as well as IMU data at 200Hz. Timestamps between all sensors are synchronized in hardware. The event cameras contain a large sensor of 1280x720 pixels, which is significantly larger than the sensors used in existing stereo event datasets (at least by a factor of ten). We provide ground truth poses from a motion capture system at 120Hz during the beginning and end of each sequence, which can be used for trajectory evaluation. TUM-VIE includes challenging sequences where state-of-the art visual SLAM algorithms either fail or result in large drift. Hence, our dataset can help to push the boundary of future research on event-based visual-inertial perception algorithms.

In the future, extraterrestrial expeditions will not only be conducted by rovers but also by flying robots. The technical demonstration drone Ingenuity, that just landed on Mars, will mark the beginning of a new era of exploration unhindered by terrain traversability. Robust self-localization is crucial for that. Cameras that are lightweight, cheap and information-rich sensors are already used to estimate the ego-motion of vehicles. However, methods proven to work in man-made environments cannot simply be deployed on other planets. The highly repetitive textures present in the wastelands of Mars pose a huge challenge to descriptor matching based approaches.In this paper, we present an advanced robust monocular odometry algorithm that uses efficient optical flow tracking to obtain feature correspondences between images and a refined keyframe selection criterion. In contrast to most other approaches, our framework can also handle rotation-only motions that are particularly challenging for monocular odometry systems. Furthermore, we present a novel approach to estimate the current risk of scale drift based on a principal component analysis of the relative translation information matrix. This way we obtain an implicit measure of uncertainty. We evaluate the validity of our approach on all sequences of a challenging real-world dataset captured in a Mars-like environment and show that it outperforms state-of-the-art approaches. The source code is publicly available at: https://github.com/DLR-RM/granit.

We address the non-convex optimisation problem of finding a sparse matrix on the Stiefel manifold (matrices with mutually orthogonal columns of unit length) that maximises (or minimises) a quadratic objective function. Optimisation problems on the Stiefel manifold occur for example in spectral relaxations of various combinatorial problems, such as graph matching, clustering, or permutation synchronisation. Although sparsity is a desirable property in such settings, it is mostly neglected in spectral formulations since existing solvers, e.g. based on eigenvalue decomposition, are unable to account for sparsity while at the same time maintaining global optimality guarantees. We fill this gap and propose a simple yet effective sparsity-promoting modification of the Orthogonal Iteration algorithm for finding the dominant eigenspace of a matrix. By doing so, we can guarantee that our method finds a Stiefel matrix that is globally optimal with respect to the quadratic objective function, while in addition being sparse. As a motivating application we consider the task of permutation synchronisation, which can be understood as a constrained clustering problem that has particular relevance for matching multiple images or 3D shapes in computer vision, computer graphics, and beyond. We demonstrate that the proposed approach outperforms previous methods in this domain.

Node features and structural information of a graph are both crucial for semi-supervised node classification problems. A variety of graph neural network (GNN) based approaches have been proposed to tackle these problems, which typically determine output labels through feature aggregation. This can be problematic, as it implies conditional independence of output nodes given hidden representations, despite their direct connections in the graph. To learn the direct influence among output nodes in a graph, we propose the Explicit Pairwise Factorized Graph Neural Network (EPFGNN), which models the whole graph as a partially observed Markov Random Field. It contains explicit pairwise factors to model output-output relations and uses a GNN backbone to model input-output relations. To balance model complexity and expressivity, the pairwise factors have a shared component and a separate scaling coefficient for each edge. We apply the EM algorithm to train our model, and utilize a star-shaped piecewise likelihood for the tractable surrogate objective. We conduct experiments on various datasets, which shows that our model can effectively improve the performance for semi-supervised node classification on graphs.

Abstract Standardized benchmarks have been crucial in pushing the performance of computer vision algorithms, especially since the advent of deep learning. Although leaderboards should not be over-claimed, they often provide the most objective measure of performance and are therefore important guides for research. We present MOTChallenge , a benchmark for single-camera Multiple Object Tracking (MOT) launched in late 2014, to collect existing and new data and create a framework for the standardized evaluation of multiple object tracking methods. The benchmark is focused on multiple people tracking, since pedestrians are by far the most studied object in the tracking community, with applications ranging from robot navigation to self-driving cars. This paper collects the first three releases of the benchmark: (i) MOT15 , along with numerous state-of-the-art results that were submitted in the last years, (ii) MOT16 , which contains new challenging videos, and (iii) MOT17 , that extends MOT16 sequences with more precise labels and evaluates tracking performance on three different object detectors. The second and third release not only offers a significant increase in the number of labeled boxes, but also provide labels for multiple object classes beside pedestrians, as well as the level of visibility for every single object of interest. We finally provide a categorization of state-of-the-art trackers and a broad error analysis. This will help newcomers understand the related work and research trends in the MOT community, and hopefully shed some light into potential future research directions.

In this work, we propose an unsupervised method for learning dense correspondences between shapes using a recent deep functional map framework. Instead of depending on ground-truth correspondences or the computationally expensive geodesic distances, we use heat kernels. These can be computed quickly during training as the supervisor signal. Moreover, we propose a curriculum learning strategy using different heat diffusion times which provide different levels of difficulty during optimization without any sampling mechanism or hard example mining. We present the results of our method on different benchmarks which have various challenges like partiality, topological noise and different connectivity.

In this paper we demonstrate that global photometric bundle adjustment (PBA) over all past keyframes can significantly improve the global accuracy of a monocular SLAM map compared to geometric techniques such as pose-graph optimization or traditional (geometric) bundle adjustment. However, PBA is computationally expensive in runtime, and memory usage can be prohibitively high. In order to address this scalability issue, we formulate PBA as an approximate consensus program. Due to its decomposable structure, the problem can be solved with block coordinate descent in parallel across multiple independent workers, each having lower requirements on memory and computational resources. For improved accuracy and convergence, we propose a novel gauge aware consensus update. Our experiments on real-world data show an average error reduction of 62% compared to odometry and 33% compared to intermediate pose-graph optimization, and that compared to the central optimization on a single machine, our distributed PBA achieves competitive pose-accuracy and cost.

Predicting the biological function of molecules, be it proteins or drug-like compounds, from their atomic structure is an important and long-standing problem. The electron density field and electrostatic potential field of a molecule contain the “raw fingerprint” of how this molecule can fit to binding partners. In this paper, we show that deep learning can predict biological function of molecules directly from their raw 3D approximated electron density and electrostatic potential fields. Protein function based on Enzyme Commission numbers is predicted from the approximated electron density field. In another experiment, the activity of small molecules is predicted with quality comparable to state-of-the-art descriptor-based methods. We propose several alternative computational models for the GPU with different memory and runtime requirements for different sizes of molecules and of databases. We also propose application-specific multi-channel data representations.

We propose to use Simulated Annealing to solve the correspondence problem between near-isometric 3D shapes. Our method gains efficiency through quickly upsampling a sparse correspondence by minimizing the embedding error of new samples on the surfaces and applying simulated annealing to refine the result. The algorithm alternates between sampling additional points on the surface and swapping points within the current solution according to Simulated Annealing theory. Simulated Annealing is a probabilistic method and less prone to get stuck in local extrema which allows us to obtain good results on the NPhard quadratic assignment problem} (QAP). Our method can be used as a stand-alone correspondence pipeline through an initial seed generator as well as to densify a set of sparse input matches. Furthermore, the use of locality sensitive hashing to approximate geodesic distances reduces the computational complexity and memory consumption significantly. This allows our algorithm to run on meshes with over 100k points, an accomplishment that few approaches tackling the QAP directly achieve. We show convincing results on datasets like TOSCA and SHREC'19 Connecitvity.

We present LM-Reloc-a novel approach for visual relocalization based on direct image alignment. In contrast to prior works that tackle the problem with a feature-based formulation, the proposed method does not rely on feature matching and RANSAC. Hence, the method can utilize not only corners but any region of the image with gradients. In particular, we propose a loss formulation inspired by the classical Levenberg-Marquardt algorithm to train LM-Net. The learned features significantly improve the robustness of direct image alignment, especially for relocalization across different conditions. To further improve the robustness of LM-Net against large image baselines, we propose a pose estimation network, CorrPoseNet, which regresses the relative pose to bootstrap the direct image alignment. Evaluations on the CARLA and Oxford RobotCar relocalization tracking benchmark show that our approach delivers more accurate results than previous state-of-the-art methods while being comparable in terms of robustness.

Structured convex optimization on weighted graphs finds numerous applications in machine learning and computer vision. In this work, we propose a novel adaptive preconditioning strategy for proximal algorithms on this problem class. Our preconditioner is driven by a sharp analysis of the local linear convergence rate depending on the "active set" at the current iterate. We show that nested-forest decomposition of the inactive edges yields a guaranteed local linear convergence rate. Further, we propose a practical greedy heuristic which realizes such nested decompositions and show in several numerical experiments that our reconditioning strategy, when applied to proximal gradient or primal-dual hybrid gradient algorithm, achieves competitive performances. Our results suggest that local convergence analysis can serve as a guideline for selecting variable metrics in proximal algorithms.

We propose a novel 3D shape correspondence method based on the iterative alignment of so-called smooth shells. Smooth shells define a series of coarse-to-fine shape approximations designed to work well with multiscale algorithms. The main idea is to first align rough approximations of the geometry and then add more and more details to refine the correspondence. We fuse classical shape registration with Functional Maps by embedding the input shapes into an intrinsic-extrinsic product space. Moreover, we disambiguate intrinsic symmetries by applying a surrogate based Markov chain Monte Carlo initialization. Our method naturally handles various types of noise that commonly occur in real scans, like non-isometry or incompatible meshing. Finally, we demonstrate state-of-the-art quantitative results on several datasets and show that our pipeline produces smoother, more realistic results than other automatic matching methods in real world applications.

Continuous-time trajectory representation has recently gained popularity for tasks where the fusion of high-frame-rate sensors and multiple unsynchronized devices is required. Lie group cumulative B-splines are a popular way of representing continuous trajectories without singularities. They have been used in near real-time SLAM and odometry systems with IMU, LiDAR, regular, RGB-D and event cameras, as well as for offline calibration. These applications require efficient computation of time derivatives (velocity, acceleration), but all prior works rely on a computationally suboptimal formulation. In this work we present an alternative derivation of time derivatives based on recurrence relations that needs O(k) instead of O(k^2) matrix operations (for a spline of order k) and results in simple and elegant expressions. While producing the same result, the proposed approach significantly speeds up the trajectory optimization and allows for computing simple analytic derivatives with respect to spline knots. The results presented in this paper pave the way for incorporating continuous-time trajectory representations into more applications where real-time performance is required.

We present a method to infer physical material parameters, and even external boundaries, from the scanned motion of a homogeneous deformable object via the solution of an inverse problem. Parameters are estimated from real-world data sources such as sparse observations from a Kinect sensor without correspondences. We introduce a novel Lagrangian-Eulerian optimization formulation, including a cost function that penalizes differences to observations during an optimization run. This formulation matches correspondence-free, sparse observations from a single-view depth image with a finite element simulation of deformable bodies. In a number of tests using synthetic datasets and real-world measurements, we analyse the robustness of our approach and the convergence behavior of the numerical optimization scheme.

We propose D3VO as a novel framework for monocular visual odometry that exploits deep networks on three levels -- deep depth, pose and uncertainty estimation. We first propose a novel self-supervised monocular depth estimation network trained on stereo videos without any external supervision. In particular, it aligns the training image pairs into similar lighting condition with predictive brightness transformation parameters. Besides, we model the photometric uncertainties of pixels on the input images, which improves the depth estimation accuracy and provides a learned weighting function for the photometric residuals in direct (feature-less) visual odometry. Evaluation results show that the proposed network outperforms state-of-the-art self-supervised depth estimation networks. D3VO tightly incorporates the predicted depth, pose and uncertainty into a direct visual odometry method to boost both the front-end tracking as well as the back-end non-linear optimization. We evaluate D3VO in terms of monocular visual odometry on both the KITTI odometry benchmark and the EuRoC MAV dataset. The results show that D3VO outperforms state-of-the-art traditional monocular VO methods by a large margin. It also achieves comparable results to state-of-the-art stereo/LiDAR odometry on KITTI and to the state-of-the-art visual-inertial odometry on EuRoC MAV, while using only a single camera.

This paper tackles the problem of data abstraction in the context of 3D point sets. Our method classifies points into different geometric primitives, such as planes and cones, leading to a compact representation of the data. Being based on a semi-global Hough voting scheme, the method does not need initialization and is robust, accurate, and efficient. We use a local, low-dimensional parameterization of primitives to determine type, shape and pose of the object that a point belongs to. This makes our algorithm suitable to run on devices with low computational power, as often required in robotics applications. The evaluation shows that our method outperforms state-of-the-art methods both in terms of accuracy and robustness.

Scene understanding from images is a challenging problem encountered in autonomous driving. On the object level, while 2D methods have gradually evolved from computing simple bounding boxes to delivering finer grained results like instance segmentations, the 3D family is still dominated by estimating 3D bounding boxes. In this paper, we propose a novel approach to jointly infer the 3D rigid-body poses and shapes of vehicles from a stereo image pair using shape priors. Unlike previous works that geometrically align shapes to point clouds from dense stereo reconstruction, our approach works directly on images by combining a photometric and a silhouette alignment term in the energy function. An adaptive sparse point selection scheme is proposed to efficiently measure the consistency with both terms. In experiments, we show superior performance of our method on 3D pose and shape estimation over the previous geometric approach and demonstrate that our method can also be applied as a refinement step and significantly boost the performances of several state-of-the-art deep learning based 3D object detectors. All related materials and demonstration videos are available at the project page https://vision.in.tum.de/research/vslam/direct-shape.

We propose a novel unsupervised learning approach to 3D shape correspondence that builds a multiscale matching pipeline into a deep neural network. This approach is based on smooth shells, the current state-of-the-art axiomatic correspondence method, which requires an a priori stochastic search over the space of initial poses. Our goal is to replace this costly preprocessing step by directly learning good initializations from the input surfaces. To that end, we systematically derive a fully differentiable, hierarchical matching pipeline from entropy regularized optimal transport. This allows us to combine it with a local feature extractor based on smooth, truncated spectral convolution filters. Finally, we show that the proposed unsupervised method significantly improves over the state-of-the-art on multiple datasets, even in comparison to the most recent supervised methods. Moreover, we demonstrate compelling generalization results by applying our learned filters to examples that significantly deviate from the training set.

A novel approach towards depth map super-resolution using multi-view uncalibrated photometric stereo is presented. Practically, an LED light source is attached to a commodity RGB-D sensor and is used to capture objects from multiple viewpoints with unknown motion. This non-static camera-to-object setup is described with a nonconvex variational approach such that no calibration on lighting or camera motion is required due to the formulation of an end-to-end joint optimization problem. Solving the proposed variational model results in high resolution depth, reflectance and camera pose estimates, as we show on challenging synthetic and real-world datasets.

This study explores the use of photometric techniques (shape-from-shading and uncalibrated photometric stereo) for upsampling the low-resolution depth map from an RGB-D sensor to the higher resolution of the companion RGB image. A single-shot variational approach is first put forward, which is effective as long as the target's reflectance is piecewise-constant. It is then shown that this dependency upon a specific reflectance model can be relaxed by focusing on a specific class of objects (e.g., faces), and delegate reflectance estimation to a deep neural network. A multi-shot strategy based on randomly varying lighting conditions is eventually discussed. It requires no training or prior on the reflectance, yet this comes at the price of a dedicated acquisition setup. Both quantitative and qualitative evaluations illustrate the effectiveness of the proposed methods on synthetic and real-world scenarios.

This work is concerned with both the 3D-reconstruction of an object using photometric stereo, and its 2D-segmentation from the background. In contrast with previous works on photometric stereo which assume that a mask of the area of interest has been computed beforehand, we formulate 3D-reconstruction and 2D-segmentation as a joint problem. The proposed variational solution combines a differential formulation of photometric stereo with the classic Chan-Vese model for active contours. Given a set of photometric stereo images, this solution simultaneously infers a binary mask of the object of interest and a depth map representing its 3D-shape. Experiments on real-world datasets confirm the soundness of simultaneously solving both these classic computer vision problems, as the joint approach considerably simplifies the overall 3D-scanning process for the end-user.

In this work, we consider nonconvex composite problems that involve inf-convolution with a Legendre function, which gives rise to an anisotropic generalization of the proximal mapping and Moreau-envelope. In a convex setting such problems can be solved via alternating minimization of a splitting formulation, where the consensus constraint is penalized with a Legendre function. In contrast, for nonconvex models it is in general unclear that this approach yields stationary points to the infimal convolution problem. To this end we analytically investigate local regularity properties of the Moreau-envelope function under prox-regularity, which allows us to establish the equivalence between stationary points of the splitting model and the original inf-convolution model. We apply our theory to characterize stationary points of the penalty objective, which is minimized by the elastic averaging SGD (EASGD) method for distributed training, showing that perfect consensus between the workers is attainable via a finite penalty parameter. Numerically, we demonstrate the practical relevance of the proposed approach on the important task of distributed training of deep neural networks.

Numerous tasks in imaging and vision can be formulated as variational problems over vector-valued maps. We approach the relaxation and convexification of such vectorial variational problems via a lifting to the space of currents. To that end, we recall that functionals with polyconvex Lagrangians can be reparametrized as convex one-homogeneous functionals on the graph of the function. This leads to an equivalent shape optimization problem over oriented surfaces in the product space of domain and codomain. A convex formulation is then obtained by relaxing the search space from oriented surfaces to more general currents. We propose a discretization of the resulting infinite-dimensional optimization problem using Whitney forms, which also generalizes recent "sublabel-accurate" multilabeling approaches.

The last decade has shown a tremendous success in solving various computer vision problems with the help of deep learning techniques. Lately, many works have demonstrated that learning-based approaches with suitable network architectures even exhibit superior performance for the solution of (ill-posed) image reconstruction problems such as deblurring, super-resolution, or medical image reconstruction. The drawback of purely learning-based methods, however, is that they cannot provide provable guarantees for the trained network to follow a given data formation process during inference. In this work we propose energy dissipating networks that iteratively compute a descent direction with respect to a given cost function or energy at the currently estimated reconstruction. Therefore, an adaptive step size rule such as a line-search, along with a suitable number of iterations can guarantee the reconstruction to follow a given data formation model encoded in the energy to arbitrary precision, and hence control the model's behavior even during test time. We prove that under standard assumptions, descent using the direction predicted by the network converges (linearly) to the global minimum of the energy. We illustrate the effectiveness of the proposed approach in experiments on single image super resolution and computed tomography (CT) reconstruction, and further illustrate extensions to convex feasibility problems.

Photometric stereo (PS) techniques nowadays remain constrained to an ideal laboratory setup where modeling and calibration of lighting is amenable. To eliminate such restrictions, we propose an efficient principled variational approach to uncalibrated PS under general illumination. To this end, the Lambertian reflectance model is approximated through a spherical harmonic expansion, which preserves the spatial invariance of the lighting. The joint recovery of shape, reflectance and illumination is then formulated as a single variational problem. There the shape estimation is carried out directly in terms of the underlying perspective depth map, thus implicitly ensuring integrability and bypassing the need for a subsequent normal integration. To tackle the resulting nonconvex problem numerically, we undertake a two-phase procedure to initialize a balloon-like perspective depth map, followed by a “lagged” block coordinate descent scheme. The experiments validate efficiency and robustness of this approach. Across a variety of evaluations, we are able to reduce the mean angular error consistently by a factor of 2-3 compared to the state-of-the-art.

We take the novel perspective to view data not as a probability distribution but rather as a current. Primarily studied in the field of geometric measure theory, k-currents are continuous linear functionals acting on compactly supported smooth differential forms and can be understood as a generalized notion of oriented k-dimensional manifold. By moving from distributions (which are 0-currents) to k-currents, we can explicitly orient the data by attaching a k-dimensional tangent plane to each sample point. Based on the flat metric which is a fundamental distance between currents, we derive FlatGAN, a formulation in the spirit of generative adversarial networks but generalized to k-currents. In our theoretical contribution we prove that the flat metric between a parametrized current and a reference current is Lipschitz continuous in the parameters. In experiments, we show that the proposed shift to k>0 leads to interpretable and disentangled latent representations which behave equivariantly to the specified oriented tangent planes.

The ability of deep learning models to generalize well across different scenarios depends primarily on the quality and quantity of annotated data. Labeling large amounts of data for all possible scenarios that a model may encounter would not be feasible; if even possible. We propose a framework to deal with limited labeled training data and demonstrate it on the application of vision-based vehicle control. We show how limited steering angle data available for only one condition can be transferred to multiple different weather scenarios. This is done by leveraging unlabeled images in a teacher-student learning paradigm complemented with an image-to-image translation network. The translation network transfers the images to a new domain, whereas the teacher provides soft supervised targets to train the student on this domain. Furthermore, we demonstrate how utilization of auxiliary networks can reduce the size of a model at inference time, without affecting the accuracy. The experiments show that our approach generalizes well across multiple different weather conditions using only ground truth labels from one domain.

We present a direct visual-inertial odometry (VIO) method which estimates the motion of the sensor setup and sparse 3D geometry of the environment based on measurements from a rolling-shutter camera and an inertial measurement unit (IMU). The visual part of the system performs a photometric bundle adjustment on a sparse set of points. This direct approach does not extract feature points and is able to track not only corners, but any pixels with sufficient gradient magnitude. Neglecting rolling-shutter effects in the visual part severely degrades accuracy and robustness of the system. In this paper, we incorporate a rolling-shutter model into the photometric bundle adjustment that estimates a set of recent keyframe poses and the inverse depth of a sparse set of points. IMU information is accumulated between several frames using measurement preintegration, and is inserted into the optimization as an additional constraint between selected keyframes. For every keyframe we estimate not only the pose but also velocity and biases to correct the IMU measurements. Unlike systems with global-shutter cameras, we use both IMU measurements and rolling-shutter effects of the camera to estimate velocity and biases for every state. Last, we evaluate our system on a new dataset that contains global-shutter and rolling-shutter images, IMU data and ground-truth poses for ten different sequences, which we make publicly available. Evaluation shows that the proposed method outperforms a system where rolling shutter is not modelled and achieves similar accuracy to the global-shutter method on global-shutter data.

Abstract We present a novel approach for solving the correspondence problem between a given pair of input shapes with non‐rigid, nearly isometric pose difference. Our method alternates between calculating a deformation field and a sparse correspondence. The deformation field is constructed with a low rank Fourier basis which allows for a compact representation. Furthermore, we restrict the deformation fields to be divergence‐free which makes our morphings volume preserving. This can be used to extract a correspondence between the inputs by deforming one of them along the deformation field using a second order Runge‐Kutta method and resulting in an alignment of the inputs. The advantages of using our basis are that there is no need to discretize the embedding space and the deformation is volume preserving. The optimization of the deformation field is done efficiently using only a subsampling of the orginal shapes but the correspondence can be extracted for any mesh resolution with close to linear increase in runtime. We show 3D correspondence results on several known data sets and examples of natural intermediate shape sequences that appear as a by‐product of our method.

Video Object Segmentation, and video processing in general, has been historically dominated by methods that rely on the temporal consistency and redundancy in consecutive video frames. When the temporal smoothness is suddenly broken, such as when an object is occluded, or some frames are missing in a sequence, the result of these methods can deteriorate significantly. This paper explores the orthogonal approach of processing each frame independently, i.e., disregarding the temporal information. In particular, it tackles the task of semi-supervised video object segmentation: the separation of an object from the background in a video, given its mask in the first frame. We present Semantic One-Shot Video Object Segmentation (OSVOS$^\mathrm {S}$S), based on a fully-convolutional neural network architecture that is able to successively transfer generic semantic information, learned on ImageNet, to the task of foreground segmentation, and finally to learning the appearance of a single annotated object of the test sequence (hence one shot). We show that instance-level semantic information, when combined effectively, can dramatically improve the results of our previous method, OSVOS. We perform experiments on two recent single-object video segmentation databases, which show that OSVOS$^\mathrm {S}$S is both the fastest and most accurate method in the state of the art. Experiments on multi-object video segmentation show that OSVOS$^\mathrm {S}$S obtains competitive results.

We propose an algorithm for real-time 6DOF pose tracking of rigid 3D objects using a monocular RGB camera. The key idea is to derive a region-based cost function using temporally consistent local color histograms. While such region-based cost functions are commonly optimized using first-order gradient descent techniques, we systematically derive a Gauss-Newton optimization scheme which gives rise to drastically faster convergence and highly accurate and robust tracking performance. We furthermore propose a novel complex dataset dedicated for the task of monocular object pose tracking and make it publicly available to the community. To our knowledge, it is the first to address the common and important scenario in which both the camera as well as the objects are moving simultaneously in cluttered scenes. In numerous experiments-including our own proposed dataset-we demonstrate that the proposed Gauss-Newton approach outperforms existing approaches, in particular in the presence of cluttered backgrounds, heterogeneous objects and partial occlusions.

Most shape analysis methods use meshes to discretize the shape and functions on it by piecewise linear functions. Fine meshes are then necessary to represent smooth shapes and compute accurate curvatures or Laplace-Beltrami eigenfunctions at large computational costs. We avoid this bottleneck by representing smooth shapes as subdivision surfaces and using the subdivision scheme to parametrize smooth surface functions with few control parameters. We propose a model to fit a subdivision surface to input samples that, unlike previous methods, can be applied to noisy and partial scans from depth sensors. The task is formulated as an optimization problem with robust data terms and solved with a sequential quadratic program that outperforms the solvers previously used to fit subdivision surfaces to noisy data. Our experiments show that the compression of a subdivision representation does not affect the accuracy of the Laplace-Beltrami operator and allows to compute shape descriptors, geodesics, and shape matchings at a fraction of the computational cost of mesh representations.

The use of structural information in 3D scanning is becoming more and more popular. However, most approaches exploit this structural information either in the form of geometric primitives (mostly planes) or known rigid bodies, but not both. We overcome this limitation and propose an object representation that combines primitive and non-primitive objects using one unified formulation that is based on signed distance fields. Object pose manifolds are introduced to represent the rigid movement of primitives and non-primitives in a natural way. We show that different components of volumetric scanning, such as global trajectory optimization or geometry completion and denoising, benefit from our formulation.

Vision-based motion estimation and 3D reconstruction, which have numerous applications (e.g., autonomous driving, navigation systems for airborne devices and augmented reality) are receiving significant research attention. To increase the accuracy and robustness, several researchers have recently demonstrated the benefit of using large field-of-view cameras for such applications. In this paper, we provide an extensive review of existing models for large field-of-view cameras. For each model we provide projection and unprojection functions and the subspace of points that result in valid projection. Then, we propose the Double Sphere camera model that well fits with large field-of-view lenses, is computationally inexpensive and has a closed-form inverse. We evaluate the model using a calibration dataset with several different lenses and compare the models using the metrics that are relevant for Visual Odometry, i.e., reprojection error, as well as computation time for projection and unprojection functions and their Jacobians. We also provide qualitative results and discuss the performance of all models.

We tackle highly nonconvex, nonsmooth composite optimization problems whose objectives comprise a Moreau-Yosida regularized term. Classical nonconvex proximal splitting algorithms, such as nonconvex ADMM, suffer from lack of convergence for such a problem class. To overcome this difficulty, in this work we consider a lifted variant of the Moreau-Yosida regularized model and propose a novel multiblock primal-dual algorithm that intrinsically stabilizes the dual block. We provide a complete convergence analysis of our algorithm and identify respective optimality qualifications under which stationarity of the original model is retrieved at convergence. Numerically, we demonstrate the relevance of Moreau-Yosida regularized models and the efficiency of our algorithm on robust regression as well as joint feature selection and semi-supervised learning.

We present a novel preconditioning technique for proximal optimization methods that relies on graph algorithms to construct effective preconditioners. Such combinatorial preconditioners arise from partitioning the graph into forests. We prove that certain decompositions lead to a theoretically optimal condition number. We also show how ideal decompositions can be realized using matroid partitioning and propose efficient greedy variants thereof for large-scale problems. Coupled with specialized solvers for the resulting scaled proximal subproblems, the preconditioned algorithm achieves competitive performance in machine learning and vision applications.

We put forward a principled variational approach for up-sampling a single depth map to the resolution of the companion color image provided by an RGB-D sensor. We combine heterogeneous depth and color data in order to jointly solve the ill-posed depth super-resolution and shape-from-shading problems. The low-frequency geometric information necessary to disambiguate shape-from-shading is extracted from the low-resolution depth measurements and, symmetrically, the high-resolution photometric clues in the RGB image provide the high-frequency information required to disambiguate depth super-resolution.

This paper introduces a novel algorithm for transductive inference in higher-order MRFs, where the unary energies are parameterized by a variable classifier. The considered task is posed as a joint optimization problem in the continuous classifier parameters and the discrete label variables. In contrast to prior approaches such as convex relaxations, we propose an advantageous decoupling of the objective function into discrete and continuous subproblems and a novel, efficient optimization method related to ADMM. This approach preserves integrality of the discrete label variables and guarantees global convergence to a critical point. We demonstrate the advantages of our approach in several experiments including video object segmentation on the DAVIS data set and interactive image segmentation.

Dynamic environments are challenging for visual SLAM as moving objects can impair camera pose tracking and cause corruptions to be integrated into the map. In this paper, we propose a method for robust dense RGB-D SLAM in dynamic environments which detects moving objects and simultaneously reconstructs the background structure. While most methods employ implicit robust penalisers or outlier filtering techniques in order to handle moving objects, our approach is to simultaneously estimate the camera motion as well as a probabilistic static/dynamic segmentation of the current RGB-D image pair. This segmentation is then used for weighted dense RGB-D fusion to estimate a 3D model of only the static parts of the environment. By leveraging the 3D model for frame-to-model alignment, as well as static/dynamic segmentation, camera motion estimation has reduced overall drift - as well as being more robust to the presence of dynamics in the scene. Demonstrations are presented which compare the proposed method to related state-of-the-art approaches using both static and dynamic sequences. The proposed method achieves similar performance in static environments and improved accuracy and robustness in dynamic scenes.

We present VI-DSO, a novel approach for visual-inertial odometry, which jointly estimates camera poses and sparse scene geometry by minimizing photometric and IMU measurement errors in a combined energy functional. The visual part of the system performs a bundle-adjustment like optimization on a sparse set of points, but unlike key-point based systems it directly minimizes a photometric error. This makes it possible for the system to track not only corners, but any pixels with large enough intensity gradients. IMU information is accumulated between several frames using measurement preintegration and is inserted into the optimization as an additional constraint between keyframes. We explicitly include scale and gravity direction into our model and jointly optimize them together with other variables such as poses. As the scale is often not immediately observable using IMU data this allows us to initialize our visual-inertial system with an arbitrary scale instead of having to delay the initialization until everything is observable. We perform partial marginalization of old variables so that updates can be computed in a reasonable time. In order to keep the system consistent we propose a novel strategy which we call “dynamic marginalization”. This technique allows us to use partial marginalization even in cases where the initial scale estimate is far from the optimum. We evaluate our method on the challenging EuRoC dataset, showing that VI-DSO outperforms the state of the art.

The Label Propagation (LP) algorithm, first introduced by Zhu and Ghahramani [1], is a semi-supervised method used in transductive learning scenarios, where all data are available already in the beginning. In this work, we present a novel extension of the LP algorithm for applications where data samples are observed sequentially - as is the case in autonomous driving. Specifically, our “Incremental Label Propagation” algorithm efficiently approximates the so called harmonic solution on a nearest-neighbor graph that is regularly updated by new labeled and unlabeled nodes. We achieve this by reformulating the original algorithm based on an active set of nodes and by introducing a threshold to decide whether the label of a given node should be updated or not. Our method can also deal with graphs that are not fully connected, and we give a formal convergence proof for this general case. In experiments on the challenging KITTI benchmark data stream, we show superior performance in terms of both test accuracy and number of required training labels compared to state-of-the-art online learning methods.

In this paper we present an extension of Direct Sparse Odometry (DSO) [1] to a monocular visual SLAM system with loop closure detection and pose-graph optimization (LDSO). As a direct technique, DSO can utilize any image pixel with sufficient intensity gradient, which makes it robust even in featureless areas. LDSO retains this robustness, while at the same time ensuring repeatability of some of these points by favoring corner features in the tracking frontend. This repeatability allows to reliably detect loop closure candidates with a conventional feature-based bag-of-words (BoW) approach. Loop closure candidates are verified geometrically and Sim(3) relative pose constraints are estimated by jointly minimizing 2D and 3D geometric error terms. These constraints are fused with a co-visibility graph of relative poses extracted from DSO's sliding window optimization. Our evaluation on publicly available datasets demonstrates that the modified point selection strategy retains the tracking accuracy and robustness, and the integrated pose-graph optimization significantly reduces the accumulated rotation-, translation- and scale-drift, resulting in an overall performance comparable to state-of-the-art feature-based systems, even without global bundle adjustment.

Visual odometry and SLAM methods have a large variety of applications in domains such as augmented reality or robotics. Complementing vision sensors with inertial measurements tremendously improves tracking accuracy and robustness, and thus has spawned large interest in the development of visual-inertial (VI) odometry approaches. In this paper, we propose the TUM VI benchmark, a novel dataset with a diverse set of sequences in different scenes for evaluating VI odometry. It provides camera images with 1024×1024 resolution at 20 Hz, high dynamic range and photometric calibration. An IMU measures accelerations and angular velocities on 3 axes at 200 Hz, while the cameras and IMU sensors are time-synchronized in hardware. For trajectory evaluation, we also provide accurate pose ground truth from a motion capture system at high frequency (120 Hz) at the start and end of the sequences which we accurately aligned with the camera and IMU measurements. The full dataset with raw and calibrated data is publicly available. We also evaluate state-of-the-art VI odometry approaches on our dataset.

Direct Sparse Odometry (DSO) is a visual odometry method based on a novel, highly accurate sparse and direct structure and motion formulation. It combines a fully direct probabilistic model (minimizing a photometric error) with consistent, joint optimization of all model parameters, including geometry-represented as inverse depth in a reference frame-and camera motion. This is achieved in real time by omitting the smoothness prior used in other direct methods and instead sampling pixels evenly throughout the images. Since our method does not depend on keypoint detectors or descriptors, it can naturally sample pixels from across all image regions that have intensity gradient, including edges or smooth intensity variations on essentially featureless walls. The proposed model integrates a full photometric calibration, accounting for exposure time, lens vignetting, and non-linear response functions. We thoroughly evaluate our method on three different datasets comprising several hours of video. The experiments show that the presented approach significantly outperforms state-of-the-art direct and indirect methods in a variety of real-world settings, both in terms of tracking accuracy and robustness.

We present a method to match three dimensional shapes under non-isometric deformations, topology changes and partiality. We formulate the problem as matching between a set of pair-wise and point-wise descriptors, imposing a continuity prior on the mapping, and propose a projected descent optimization procedure inspired by difference of convex functions (DC) programming.

We propose a combinatorial solution for the problem of non-rigidly matching a 3D shape to 3D image data. To this end, we model the shape as a triangular mesh and allow each triangle of this mesh to be rigidly transformed to achieve a suitable matching to the image. By penalising the distance and the relative rotation between neighbouring triangles our matching compromises between the image and the shape information. In this paper, we resolve two major challenges: Firstly, we address the resulting large and NP-hard combinatorial problem with a suitable graph-theoretic approach. Secondly, we propose an efficient discretisation of the unbounded 6-dimensional Lie group SE(3). To our knowledge this is the first combinatorial formulation for non-rigid 3D shape-to-image matching. In contrast to existing local (gradient descent) optimisation methods, we obtain solutions that do not require a good initialisation and that are within a bound of the optimal solution. We evaluate the proposed combinatorial method on the two problems of non-rigid 3D shape-to-shape and non-rigid 3D shape-to-image registration and demonstrate that it provides promising results.

This paper tackles the task of semi-supervised video object segmentation, i.e., the separation of an object from the background in a video, given the mask of the first frame. We present One-Shot Video Object Segmentation (OSVOS), based on a fully-convolutional neural network architecture that is able to successively transfer generic semantic information, learned on ImageNet, to the task of foreground segmentation, and finally to learning the appearance of a single annotated object of the test sequence (hence one-shot). Although all frames are processed independently, the results are temporally coherent and stable. We perform experiments on two annotated video segmentation databases, which show that OSVOS is fast and improves the state of the art by a significant margin (79.8% vs 68.0%).

In many real-world scenarios, labeled data for a specific machine learning task is costly to obtain. Semi-supervised training methods make use of abundantly available unlabeled data and a smaller number of labeled examples. We propose a new framework for semi-supervised training of deep neural networks inspired by learning in humans. Associations are made from embeddings of labeled samples to those of unlabeled ones and back. The optimization schedule encourages correct association cycles that end up at the same class from which the association was started and penalizes wrong associations ending at a different class. The implementation is easy to use and can be added to any existing end-to-end training setup. We demonstrate the capabilities of learning by association on several data sets and show that it can improve performance on classification tasks tremendously by making use of additionally available unlabeled data. In particular, for cases with few labeled data, our training scheme outperforms the current state of the art on SVHN.

We present a novel strategy to shrink and constrain a 3D model, represented as a smooth spline-like surface, within the visual hull of an object observed from one or multiple views. This new background or silhouette term combines the efficiency of previous approaches based on an image-plane distance transform with the accuracy of formulations based on raycasting or ray potentials. The overall formulation is solved by alternating an inner nonlinear minization (raycasting) with a joint optimization of the surface geometry, the camera poses and the data correspondences. Experiments on 3D reconstruction and object tracking show that the new formulation corrects several deficiencies of existing approaches, for instance when modelling non-convex shapes. Moreover, our proposal is more robust against defects in the object segmentation and inherently handles the presence of uncertainty in the measurements (e.g. null depth values in images provided by RGB-D cameras).

This paper tackles the photometric stereo problem in the presence of inaccurate lighting, obtained either by calibration or by an uncalibrated photometric stereo method. Based on a precise modeling of noise and outliers, a robust variational approach is introduced. It explicitly accounts for self-shadows, and enforces robustness to cast-shadows and specularities by resorting to redescending M-estimators. The resulting non-convex model is solved by means of a computationally efficient alternating reweighted least-squares algorithm. Since it implicitly enforces integrability, the new variational approach can refine both the intensities and the directions of the lighting.

We introduce a geometry-driven approach for real-time 3D reconstruction of deforming surfaces from a single RGB-D stream without any templates or shape priors. To this end, we tackle the problem of non-rigid registration by level set evolution without explicit correspondence search. Given a pair of signed distance fields (SDFs) representing the shapes of interest, we estimate a dense deformation field that aligns them. It is defined as a displacement vector field of the same resolution as the SDFs and is determined iteratively via variational minimization. To ensure it generates plausible shapes, we propose a novel regularizer that imposes local rigidity by requiring the deformation to be a smooth and approximately Killing vector field, i.e. generating nearly isometric motions. Moreover, we enforce that the level set property of unity gradient magnitude is preserved over iterations. As a result, KillingFusion reliably reconstructs objects that are undergoing topological changes and fast inter-frame motion. In addition to incrementally building a model from scratch, our system can also deform complete surfaces. We demonstrate these capabilities on several public datasets and introduce our own sequences that permit both qualitative and quantitative comparison to related approaches.

Many algorithms for the computation of correspondences between deformable shapes rely on some variant of nearest neighbor matching in a descriptor space. Such are, for example, various point-wise correspondence recovery algorithms used as a post-processing stage in the functional correspondence framework. Such frequently used techniques implicitly make restrictive assumptions (e.g., nearisometry) on the considered shapes and in practice suffer from lack of accuracy and result in poor surjectivity. We propose an alternative recovery technique capable of guaranteeing a bijective correspondence and producing significantly higher accuracy and smoothness. Unlike other methods our approach does not depend on the assumption that the analyzed shapes are isometric. We derive the proposed method from the statistical framework of kernel density estimation and demonstrate its performance on several challenging deformable 3D shape matching datasets.

We propose associative domain adaptation, a novel technique for end-to-end domain adaptation with neural networks, the task of inferring class labels for an unlabeled target domain based on the statistical properties of a labeled source domain. Our training scheme follows the paradigm that in order to effectively derive class labels for the target domain, a network should produce statistically domain invariant embeddings, while minimizing the classification error on the labeled source domain. We accomplish this by reinforcing associations between source and target data directly in embedding space. Our method can easily be added to any existing classification network with no structural and almost no computational overhead. We demonstrate the effectiveness of our approach on various benchmarks and achieve state-of-the-art results across the board with a generic convolutional neural network architecture not specifically tuned to the respective tasks. Finally, we show that the proposed association loss produces embeddings that are more effective for domain adaptation compared to methods employing maximum mean discrepancy as a similarity measure in embedding space.

We introduce a novel method to obtain high-quality 3D reconstructions from consumer RGB-D sensors. Our core idea is to simultaneously optimize for geometry encoded in a signed distance field (SDF), textures from automatically-selected keyframes, and their camera poses along with material and scene lighting. To this end, we propose a joint surface reconstruction approach that is based on Shape-from-Shading (SfS) techniques and utilizes the estimation of spatially-varying spherical harmonics (SVSH) from subvolumes of the reconstructed scene. Through extensive examples and evaluations, we demonstrate that our method dramatically increases the level of detail in the reconstructed scene geometry and contributes highly to consistent surface texture recovery.

While variational methods have been among the most powerful tools for solving linear inverse problems in imaging, deep (convolutional) neural networks have recently taken the lead in many challenging benchmarks. A remaining drawback of deep learning approaches is their requirement for an expensive retraining whenever the specific problem, the noise level, noise type, or desired measure of fidelity changes. On the contrary, variational methods have a plug-and-play nature as they usually consist of separate data fidelity and regularization terms. In this paper we study the possibility of replacing the proximal operator of the regularization used in many convex energy minimization algorithms by a denoising neural network. The latter therefore serves as an implicit natural image prior, while the data term can still be chosen independently. Using a fixed denoising neural network in exemplary problems of image deconvolution with different blur kernels and image demosaicking, we obtain state-of-the-art reconstruction results. These indicate the high generalizability of our approach and a reduction of the need for problem-specific training. Additionally, we discuss novel results on the analysis of possible optimization algorithms to incorporate the network into, as well as the choices of algorithm parameters and their relation to the noise level the neural network is trained on.

In this work we show how sublabel-accurate multilabeling approaches [15, 18] can be derived by approximating a classical label-continuous convex relaxation of nonconvex free-discontinuity problems. This insight allows to extend these sublabel-accurate approaches from total variation to general convex and nonconvex regularizations. Furthermore, it leads to a systematic approach to the discretization of continuous convex relaxations. We study the relationship to existing discretizations and to discrete-continuous MRFs. Finally, we apply the proposed approach to obtain a sublabel-accurate and convex solution to the vectorial Mumford-Shah functional and show in several experiments that it leads to more precise solutions using fewer labels.

In this work we propose a new CNN+LSTM architecture for camera pose regression for indoor and outdoor scenes. CNNs allow us to learn suitable feature representations for localization that are robust against motion blur and illumination changes. We make use of LSTM units on the CNN output, which play the role of a structured dimensionality reduction on the feature vector, leading to drastic improvements in localization performance. We provide extensive quantitative comparison of CNN-based and SIFT-based localization methods, showing the weaknesses and strengths of each. Furthermore, we present a new large-scale indoor dataset with accurate ground truth from a laser scanner. Experimental results on both indoor and outdoor public datasets show our method outperforms existing deep architectures, and can localize images in hard conditions, e.g., in the presence of mostly textureless surfaces, where classic SIFT-based methods fail.

We propose Stereo Direct Sparse Odometry (Stereo DSO) as a novel method for highly accurate real-time visual odometry estimation of large-scale environments from stereo cameras. It jointly optimizes for all the model parameters within the active window, including the intrinsic/extrinsic camera parameters of all keyframes and the depth values of all selected pixels. In particular, we propose a novel approach to integrate constraints from static stereo into the bundle adjustment pipeline of temporal multi-view stereo. Real-time optimization is realized by sampling pixels uniformly from image regions with sufficient intensity gradient. Fixed-baseline stereo resolves scale drift. It also reduces the sensitivities to large optical flow and to rolling shutter effect which are known shortcomings of direct image alignment methods. Quantitative evaluation demonstrates that the proposed Stereo DSO outperforms existing state-of-the-art visual odometry methods both in terms of tracking accuracy and robustness. Moreover, our method delivers a more precise metric 3D reconstruction than previous dense/semi-dense direct approaches while providing a higher reconstruction density than feature-based methods.

Creating 3D maps on robots and other mobile devices has become a reality in recent years. Online 3D reconstruction enables many exciting applications in robotics and AR/VR gaming. However, the reconstructions are noisy and generally incomplete. Moreover, during online reconstruction, the surface changes with every newly integrated depth image which poses a significant challenge for physics engines and path planning algorithms. This paper presents a novel, fast and robust method for obtaining and using information about planar surfaces, such as walls, floors, and ceilings as a stage in 3D reconstruction based on Signed Distance Fields (SDFs). Our algorithm recovers clean and accurate surfaces, reduces the movement of individual mesh vertices caused by noise during online reconstruction and fills in the occluded and unobserved regions. We implemented and evaluated two different strategies to generate plane candidates and two strategies for merging them. Our implementation is optimized to run in real-time on mobile devices such as the Tango tablet. In an extensive set of experiments, we validated that our approach works well in a large number of natural environments despite the presence of significant amount of occlusion, clutter and noise, which occur frequently. We further show that plane fitting enables in many cases a meaningful semantic segmentation of real-world scenes.

In this paper we propose an efficient solution to jointly estimate the camera motion and a piecewise-rigid scene flow from an RGB-D sequence. The key idea is to perform a two-fold segmentation of the scene, dividing it into geometric clusters that are, in turn, classified as static or moving elements. Representing the dynamic scene as a set of rigid clusters drastically accelerates the motion estimation, while segmenting it into static and dynamic parts allows us to separate the camera motion (odometry) from the rest of motions observed in the scene. The resulting method robustly and accurately determines the motion of an RGB-D camera in dynamic environments with an average runtime of 80 milliseconds on a multi-core CPU. The code is available for public use/test.

Visual scene understanding is an important capability that enables robots to purposefully act in their environment. In this paper, we propose a novel deep neural network approach to predict semantic segmentation from RGB-D sequences. The key innovation is to train our network to predict multi-view consistent semantics in a self-supervised way. At test time, its semantics predictions can be fused more consistently in semantic keyframe maps than predictions of a network trained on individual views. We base our network architecture on a recent single-view deep learning approach to RGB and depth fusion for semantic object-class segmentation and enhance it with multi-scale loss minimization. We obtain the camera trajectory using RGB-D SLAM and warp the predictions of RGB-D images into ground-truth annotated frames in order to enforce multi-view consistency during training. At test time, predictions from multiple views are fused into keyframes. We propose and analyze several methods for enforcing multi-view consistency during training and testing. We evaluate the benefit of multi-view consistency training and demonstrate that pooling of deep features and fusion over multiple views outperforms single-view baselines on the NYUDv2 benchmark for semantic segmentation. Our end-to-end trained network achieves state-of-the-art performance on the NYUDv2 dataset in single-view segmentation as well as multi-view semantic fusion.

In this paper, we present a real-time approach to local trajectory replanning for microaerial vehicles (MAVs). Current trajectory generation methods for multicopters achieve high success rates in cluttered environments, but assume that the environment is static and require prior knowledge of the map. In the presented study, we use the results of such planners and extend them with a local replanning algorithm that can handle unmodeled (possibly dynamic) obstacles while keeping the MAV close to the global trajectory. To ensure that the proposed approach is real-time capable, we maintain information about the environment around the MAV in an occupancy grid stored in a three-dimensional circular buffer, which moves together with a drone, and represent the trajectories by using uniform B-splines. This representation ensures that the trajectory is sufficiently smooth and simultaneously allows for efficient optimization.

We propose an algorithm for dense and direct large-scale visual SLAM that runs in real-time on a commodity notebook. A fast variational dense 3D reconstruction algorithm was developed which robustly integrates data terms from multiple images. This mitigates the effect of the aperture problem and is demonstrated on synthetic and real data. An additional property of the variational reconstruction framework is the ability to integrate sparse depth priors (e.g. from RGB-D sensors or LiDAR data) into the early stages of the visual depth reconstruction, leading to an implicit sensor fusion scheme for a variable number of heterogenous depth sensors. Embedded into a keyframe-based SLAM framework, this results in a memory efficient representation of the scene and therefore (in combination with loop-closure detection and pose tracking via direct image alignment) enables us to densely reconstruct large scenes in real-time. Experimental validation on the KITTI dataset shows that our method can recover large-scale and dense reconstructions of entire street scenes in real-time from a driving car.

Abstract Recent efforts in the area of joint object matching approach the problem by taking as input a set of pairwise maps, which are then jointly optimized across the whole collection so that certain accuracy and consistency criteria are satisfied. One natural requirement is cycle‐consistency—namely the fact that map composition should give the same result regardless of the path taken in the shape collection. In this paper, we introduce a novel approach to obtain consistent matches without requiring initial pairwise solutions to be given as input. We do so by optimizing a joint measure of metric distortion directly over the space of cycle‐consistent maps; in order to allow for partially similar and extra‐class shapes, we formulate the problem as a series of quadratic programs with sparsity‐inducing constraints, making our technique a natural candidate for analysing collections with a large presence of outliers. The particular form of the problem allows us to leverage results and tools from the field of evolutionary game theory. This enables a highly efficient optimization procedure which assures accurate and provably consistent solutions in a matter of minutes in collections with hundreds of shapes.

Abstract In this paper, we propose a method for computing partial functional correspondence between non‐rigid shapes. We use perturbation analysis to show how removal of shape parts changes the Laplace–Beltrami eigenfunctions, and exploit it as a prior on the spectral representation of the correspondence. Corresponding parts are optimization variables in our problem and are used to weight the functional correspondence; we are looking for the largest and most regular (in the Mumford–Shah sense) parts that minimize correspondence distortion. We show that our approach can cope with very challenging correspondence settings.

Abstract The concept of using functional maps for representing dense correspondences between deformable shapes has proven to be extremely effective in many applications. However, despite the impact of this framework, the problem of recovering the point‐to‐point correspondence from a given functional map has received surprisingly little interest. In this paper, we analyse the aforementioned problem and propose a novel method for reconstructing pointwise correspondences from a given functional map. The proposed algorithm phrases the matching problem as a regularized alignment problem of the spectral embeddings of the two shapes. Opposed to established methods, our approach does not require the input shapes to be nearly‐isometric, and easily extends to recovering the point‐to‐point correspondence in part‐to‐whole shape matching problems. Our numerical experiments demonstrate that the proposed approach leads to a significant improvement in accuracy in several challenging cases.

We consider an unsupervised image segmentation problem---from figure-ground separation to multiregion partitioning---that consists of maximal distribution separation (in terms of mutual information) with spatial regularity (total variation regularization), which is what we call information-theoretic minimal partitioning. Adopting the bounded variation framework, we provide an in-depth analysis of the problem which establishes theoretical foundations and investigates the structure of the associated energy from a variational perspective. In doing so, we show that the objective exhibits a form of difference of convex functionals, which leads us to a class of large-scale nonconvex optimization problems where convex optimization techniques can be successfully applied. In this regard, we propose sequential convex programming based on the philosophy of stochastic optimization and the Chambolle--Pock primal-dual algorithm. The key idea behind it is to construct a stochastic family of convex approximations of the original nonconvex function and sequentially minimize the associated subproblems. Indeed, its stochastic nature makes it possible to often escape from bad local minima toward near-optimal solutions, where such optimality can be justified in terms of the recent findings in statistical physics regarding a striking characteristic of the high-dimensional landscapes. We experimentally demonstrate such a favorable ability of the proposed algorithm as well as show the capacity of our approach in numerous experiments. The preliminary conference paper can be found in [Y. Kee, M. Souiai, D. Cremers, and J. Kim, Proceedings of the IEEE Conference on Computer Vision and Pattern, Recognition, 2014].

In this paper, we propose an algorithm for robustly fusing digital surface models (DSMs) with different ground sampling distances and confidences, using explicit surface priors to obtain locally smooth surface models. Robust fusion of the DSMs is achieved by minimizing the L1-distance of each pixel of the solution to each input DSM. This approach is similar to a pixel-wise median, and most outliers are discarded. We further incorporate local planarity assumption as an additional constraint to the optimization problem, thus reducing the noise compared with pixel-wise approaches. The optimization is also inherently able to include weights for the input data, therefore allowing to easily integrate invalid areas, fuse multiresolution DSMs, and to weight the input data. The complete optimization problem is constructed as a variational optimization problem with a convex energy functional, such that the solution is guaranteed to converge toward the global energy minimum. An efficient solver is presented to solve the optimization in reasonable time, e.g., running in real time on standard computer vision camera images. The accuracy of the algorithms and the quality of the resulting fused surface models are evaluated using synthetic data sets and spaceborne data sets from different optical satellite sensors.

We propose the first algorithm for non-rigid 2D-to-3D shape matching, where the input is a 2D query shape as well as a 3D target shape and the output is a continuous matching curve represented as a closed contour on the 3D shape. We cast the problem as finding the shortest circular path on the product 3-manifold of the two shapes. We prove that the optimal matching can be computed in polynomial time with a (worst-case) complexity of O(mn2 log(n)), wherem and n denote the number of vertices on the 2D and the 3D shape respectively. Quantitative evaluation confirms that the method provides excellent results for sketch-based deformable 3D shape retrieval.

Recent work has shown that optical flow estimation can be formulated as a supervised learning task and can be successfully solved with convolutional networks. Training of the so-called FlowNet was enabled by a large synthetically generated dataset. The present paper extends the concept of optical flow estimation via convolutional networks to disparity and scene flow estimation. To this end, we propose three synthetic stereo video datasets with sufficient realism, variation, and size to successfully train large networks. Our datasets are the first large-scale datasets to enable training and evaluation of scene flow methods. Besides the datasets, we present a convolutional network for real-time disparity estimation that provides state-of-the-art results. By combining a flow and disparity estimation network and training it jointly, we demonstrate the first scene flow estimation with a convolutional network.

We propose a novel spatially continuous framework for convex relaxations based on functional lifting. Our method can be interpreted as a sublabel-accurate solution to multilabel problems. We show that previously proposed functional lifting methods optimize an energy which is linear between two labels and hence require (often infinitely) many labels for a faithful approximation. In contrast, the proposed formulation is based on a piecewise convex approximation and therefore needs far fewer labels - see Fig. 1. In comparison to recent MRF-based approaches, our method is formulated in a spatially continuous setting and shows less grid bias. Moreover, in a local sense, our formulation is the tightest possible convex relaxation. It is easy to implement and allows an efficient primal-dual optimization on GPUs. We show the effectiveness of our approach on several computer vision problems.

Feature matching is a key step in most Computer Vision tasks involving several views of the same subject. In fact, it plays a crucial role for a successful reconstruction of 3D information of the corresponding material points. Typical approaches to construct stable feature tracks throughout a sequence of images operate via a two-step process: First, feature matches are extracted among all pairs of points of view; these matches are then given in input to a regularizer that provides a final, globally consistent solution. In this paper, we formulate this matching problem as a simultaneous optimization over the entire image collection, without requiring previously computed pairwise matches to be given as input. As our formulation operates directly in the space of feature across multiple images, the final matches are consistent by construction. Our matching problem has a natural interpretation as a non-cooperative game, which allows us to leverage tools and results from Game Theory. We performed a specially crafted set of experiments demonstrating that our approach compares favorably with the state of the art, while retaining a high computational efficiency.

Planes are predominant features of man-made environments which have been exploited in many mapping approaches. In this paper, we propose a real-time capable RGB-D SLAM system that consistently integrates frame-to-keyframe and frame-to-plane alignment. Our method models the environment with a global plane model and - besides direct image alignment - it uses the planes for tracking and global graph optimization. This way, our method makes use of the dense image information available in keyframes for accurate short-term tracking. At the same time it uses a global model to reduce drift. Both components are integrated consistently in an expectation-maximization framework. In experiments, we demonstrate the benefits our approach and its state-of-the-art accuracy on challenging benchmarks.

We present a new Active Learning approach for classifying objects from streams of 3D point cloud data. The major problems here are the non-uniform occurrence of class instances and the unbalanced numbers of samples per class. We show that standard online learning methods based on decision trees perform comparably bad for such data streams, which are however particularly relevant for mobile robots that need to learn semantics persistently. To address this, we use Mondrian forests (MF), a recent online learning algorithm that is independent on the data order. We present an extension of that algorithm and show that MF are less overconfident than standard Random Forests. In experiments on the KITTI benchmark, we show that this leads to a substantially improved classification performance for data streams, rendering our approach very attractive for lifelong robot learning applications.

We propose a novel direct visual-inertial odometry method for stereo cameras. Camera pose, velocity and IMU biases are simultaneously estimated by minimizing a combined photometric and inertial energy functional. This allows us to exploit the complementary nature of vision and inertial data. At the same time, and in contrast to all existing visual-inertial methods, our approach is fully direct: geometry is estimated in the form of semi-dense depth maps instead of manually designed sparse keypoints. Depth information is obtained both from static stereo - relating the fixed-baseline images of the stereo camera - and temporal stereo - relating images from the same camera, taken at different points in time. We show that our method outperforms not only vision-only or loosely coupled approaches, but also can achieve more accurate results than state-of-the-art keypoint-based methods on different datasets, including rapid motion and significant illumination changes. In addition, our method provides high-fidelity semi-dense, metric reconstructions of the environment, and runs in real-time on a CPU.

Proteins are the "building blocks of life", the most abundant organic molecules, and the central focus of most areas of biomedicine. Protein structure is strongly related to protein function, thus structure prediction is a crucial task on the way to solve many biological questions. A contact map is a compact representation of the three-dimensional structure of a protein via the pairwise contacts between the amino acid constituting the protein. We use a convolutional network to calculate protein contact maps from inferred statistical coupling between positions in the protein sequence. The input to the network has an image-like structure amenable to convolutions, but every "pixel" instead of color channels contains a bipartite undirected edge-weighted graph. We propose several methods for treating such "graph-valued images" in a convolutional network. The proposed method outperforms state-of-the-art methods by a large margin. It also allows for a great flexibility with regard to the input data, which makes it useful for studying a wide range of problems.

Abstract Spectral methods have recently gained popularity in many domains of computer graphics and geometry processing, especially shape processing, computation of shape descriptors, distances, and correspondence. Spectral geometric structures are intrinsic and thus invariant to isometric deformations, are efficiently computed, and can be constructed on shapes in different representations. A notable drawback of these constructions, however, is that they areisotropic, i.e., insensitive to direction. In this paper, we show how to construct direction‐sensitive spectral feature descriptors usinganisotropic diffusionon meshes and point clouds. The core of our construction are directed local kernels acting similarly to steerable filters, which are learned in a task‐specific manner. Remarkably, while being intrinsic, our descriptors allow to disambiguate reflection symmetries. We show the application of anisotropic descriptors for problems of shape correspondence on meshes and point clouds, achieving results significantly better than state‐of‐the‐art methods.

Abstract Shape correspondence is a fundamental problem in computer graphics and vision, with applications in various problems including animation, texture mapping, robotic vision, medical imaging, archaeology and many more. In settings where the shapes are allowed to undergo non‐rigid deformations and only partial views are available, the problem becomes very challenging. To this end, we present a non‐rigid multi‐part shape matching algorithm. We assume to be given a reference shape and its multiple parts undergoing a non‐rigid deformation. Each of these query parts can be additionally contaminated by clutter, may overlap with other parts, and there might be missing parts or redundant ones. Our method simultaneously solves for the segmentation of the reference model, and for a dense correspondence to (subsets of) the parts. Experimental results on synthetic as well as real scans demonstrate the effectiveness of our method in dealing with this challenging matching scenario.

This paper discusses the use of absolutely one-homogeneous regularization functionals in a variational, scale space, and inverse scale space setting to define a nonlinear spectral decomposition of input data. We present several theoretical results that explain the relation between the different definitions. Additionally, results on the orthogonality of the decomposition, a Parseval-type identity, and the notion of generalized (nonlinear) eigenvectors closely link our nonlinear multiscale decompositions to the well-known linear filtering theory. Numerical results are used to illustrate our findings.

Even after two decades, the total variation (TV) remains one of the most popular regularizations for image processing problems and has sparked a tremendous amount of research, particularly on moving from scalar to vector-valued functions. In this paper, we consider the gradient of a color image as a three-dimensional matrix or tensor with dimensions corresponding to the spatial extent, the intensity differences between neighboring pixels, and the spectral channels. The smoothness of this tensor is then measured by taking different norms along the different dimensions. Depending on the types of these norms, one obtains very different properties of the regularization, leading to novel models for color images. We call this class of regularizations collaborative total variation (CTV). On the theoretical side, we characterize the dual norm, the subdifferential, and the proximal mapping of the proposed regularizers. We further prove, with the help of the generalized concept of singular vectors, that an $\ell^{\infty}$ channel coupling makes the most prior assumptions and has the greatest potential to reduce color artifacts. Our practical contributions consist of an extensive experimental section, where we compare the performance of a large number of collaborative TV methods for inverse problems such as denoising, deblurring, and inpainting.

Numerous scientific fields rely on elaborate but partly suboptimal data processing pipelines. An example is diffusion magnetic resonance imaging (diffusion MRI), a non-invasive microstructure assessment method with a prominent application in neuroimaging. Advanced diffusion models providing accurate microstructural characterization so far have required long acquisition times and thus have been inapplicable for children and adults who are uncooperative, uncomfortable, or unwell. We show that the long scan time requirements are mainly due to disadvantages of classical data processing. We demonstrate how deep learning, a group of algorithms based on recent advances in the field of artificial neural networks, can be applied to reduce diffusion MRI data processing to a single optimized step. This modification allows obtaining scalar measures from advanced models at twelve-fold reduced scan time and detecting abnormalities without using diffusion models. We set a new state of the art by estimating diffusion kurtosis measures from only 12 data points and neurite orientation dispersion and density measures from only 8 data points. This allows unprecedentedly fast and robust protocols facilitating clinical routine and demonstrates how classical data processing can be streamlined by means of deep learning.

We propose a novel joint registration and segmentation approach to estimate scene flow from RGB-D images. Instead of assuming the scene to be composed of a number of independent rigidly-moving parts, we use non-binary labels to capture non-rigid deformations at transitions between the rigid parts of the scene. Thus, the velocity of any point can be computed as a linear combination (interpolation) of the estimated rigid motions, which provides better results than traditional sharp piecewise segmentations. Within a variational framework, the smooth segments of the scene and their corresponding rigid velocities are alternately refined until convergence. A K-means-based segmentation is employed as an initialization, and the number of regions is subsequently adapted during the optimization process to capture any arbitrary number of independently moving objects. We evaluate our approach with both synthetic and real RGB-D images that contain varied and large motions. The experiments show that our method estimates the scene flow more accurately than the most recent works in the field, and at the same time provides a meaningful segmentation of the scene based on 3D motion.

We propose a novel fast and robust method for obtaining 3D models with high-quality appearance using commodity RGB-D sensors. Our method uses a direct key frame-based SLAM front end to consistently estimate the camera motion during the scan. The aligned images are fused into a volumetric truncated signed distance function representation, from which we extract a mesh. For obtaining a high-quality appearance model, we additionally deblur the low-resolution RGB-D frames using filtering techniques and fuse them into super-resolution key frames. The meshes are textured from these sharp super-resolution key frames employing a texture mapping approach. In experiments, we demonstrate that our method achieves superior quality in appearance compared to other state-of-the-art approaches.

Most current approaches to street-scene 3D reconstruction from a driving car to date rely on 3D laser scanning or tedious offline computation from visual images. In this paper, we compare a real-time capable 3D reconstruction method using a stereo extension of large-scale direct SLAM (LSD-SLAM) with laser-based maps and traditional stereo reconstructions based on processing individual stereo frames. In our reconstructions, small-baseline comparison over several subsequent frames are fused with fixed-baseline disparity from the stereo camera setup. These results demonstrate that our direct SLAM technique provides an excellent compromise between speed and accuracy, generating visually pleasing and globally consistent semi-dense reconstructions of the environment in real-time on a single CPU.

Given the raising interest in light-field technology and the increasing availability of professional devices, a feasible and accurate calibration method is paramount to unleash practical applications. In this paper we propose to embrace a fully non-parametric model for the imaging and we show that it can be properly calibrated with little effort using a dense active target. This process produces a dense set of independent rays that cannot be directly used to produce a conventional image. However, they are an ideal tool for 3D reconstruction tasks, since they are highly redundant, very accurate and they cover a wide range of different baselines. The feasibility and convenience of the process and the accuracy of the obtained calibration are comprehensively evaluated through several experiments.

Convolutional neural networks (CNNs) have recently been very successful in a variety of computer vision tasks, especially on those linked to recognition. Optical flow estimation has not been among the tasks CNNs succeeded at. In this paper we construct CNNs which are capable of solving the optical flow estimation problem as a supervised learning task. We propose and compare two architectures: a generic architecture and another one including a layer that correlates feature vectors at different image locations. Since existing ground truth data sets are not sufficiently large to train a CNN, we generate a large synthetic Flying Chairs dataset. We show that networks trained on this unrealistic data still generalize very well to existing datasets such as Sintel and KITTI, achieving competitive accuracy at frame rates of 5 to 10 fps.

We propose a dense continuous-time tracking and mapping method for RGB-D cameras. We parametrize the camera trajectory using continuous B-splines and optimize the trajectory through dense, direct image alignment. Our method also directly models rolling shutter in both RGB and depth images within the optimization, which improves tracking and reconstruction quality for low-cost CMOS sensors. Using a continuous trajectory representation has a number of advantages over a discrete-time representation (e.g. camera poses at the frame interval). With splines, less variables need to be optimized than with a discrete representation, since the trajectory can be represented with fewer control points than frames. Splines also naturally include smoothness constraints on derivatives of the trajectory estimate. Finally, the continuous trajectory representation allows to compensate for rolling shutter effects, since a pose estimate is available at any exposure time of an image. Our approach demonstrates superior quality in tracking and reconstruction compared to approaches with discrete-time or global shutter assumptions.

This paper presents the idea of learning optimal filters for color image reconstruction based on a novel concept of nonlinear spectral image decompositions recently proposed by Guy Gilboa. We use a multiscale image decomposition approach based on total variation regularization and Bregman iterations to represent the input data as the sum of image layers containing features at different scales. Filtered images can be obtained by weighted linear combinations of the different frequency layers. We introduce the idea of learning optimal filters for the task of image denoising, and propose the idea of mixing high frequency components of different color channels. Our numerical experiments demonstrate that learning the optimal weights can significantly improve the results in comparison to the standard variational approach, and achieves state-of-the-art image denoising results.

Despite their enormous success in solving hard combinatorial problems, convex relaxation approaches often suffer from the fact that the computed solutions are far from binary and that subsequent heuristic binarization may substantially degrade the quality of computed solutions. In this paper, we propose a novel relaxation technique which incorporates the entropy of the objective variable as a measure of relaxation tightness. We show both theoretically and experimentally that augmenting the objective function with an entropy term gives rise to more binary solutions and consequently solutions with a substantially tighter optimality gap. We use difference of convex function (DC) programming as an efficient and provably convergent solver for the arising convex-concave minimization problem. We evaluate this approach on three prominent non-convex computer vision challenges: multi-label inpainting, image segmentation and spatio-temporal multi-view reconstruction. These experiments show that our approach consistently yields better solutions with respect to the original integral optimization problem.

Consumer depth cameras have dramatically improved our ability to track rigid, articulated, and deformable 3D objects in real-time. However, depth cameras have a limited temporal resolution (frame-rate) that restricts the accuracy and robustness of tracking, especially for fast or unpredictable motion. In this paper, we show how to perform model-based object tracking which allows to reconstruct the object's depth at an order of magnitude higher frame-rate through simple modifications to an off-the-shelf depth camera. We focus on phase-based time-of-flight (ToF) sensing, which reconstructs each low frame-rate depth image from a set of short exposure 'raw' infrared captures. These raw captures are taken in quick succession near the beginning of each depth frame, and differ in the modulation of their active illumination. We make two contributions. First, we detail how to perform model-based tracking against these raw captures. Second, we show that by reprogramming the camera to space the raw captures uniformly in time, we obtain a 10x higher frame-rate, and thereby improve the ability to track fast-moving objects.

This paper presents the first method to compute dense scene flow in real-time for RGB-D cameras. It is based on a variational formulation where brightness constancy and geometric consistency are imposed. Accounting for the depth data provided by RGB-D cameras, regularization of the flow field is imposed on the 3D surface (or set of surfaces) of the observed scene instead of on the image plane, leading to more geometrically consistent results. The minimization problem is efficiently solved by a primal-dual algorithm which is implemented on a GPU, achieving a previously unseen temporal performance. Several tests have been conducted to compare our approach with a state-of-the-art work (RGB-D flow) where quantitative and qualitative results are evaluated. Moreover, an additional set of experiments have been carried out to show the applicability of our work to estimate motion in real-time. Results demonstrate the accuracy of our approach, which outperforms the RGB-D flow, and which is able to estimate heterogeneous and non-rigid motions at a high frame rate.

We present a novel efficient algorithm for object classification. Our method is based on the active learning framework, in which training and classification are performed in loops, and new ground truth labels are queried from the supervisor in each loop. Our underlying classifier is from the family of boosting methods, but in contrast to earlier methods, our Confidence Boosting particularly focusses on misclassified samples that have a high classification confidence associated. We show that weighting these samples more than others leads to a decrease of overconfidence, for which we give a formal definition. As a result, our classifier is better suited for active learning, leading to steeper learning curves and less required label queries. We show the benefits of our approach on standard data sets from machine learning and robotics.

We propose a real-time, direct monocular SLAM method for omnidirectional or wide field-of-view fisheye cameras. Both tracking (direct image alignment) and mapping (pixel-wise distance filtering) are directly formulated for the unified omnidirectional model, which can model central imaging devices with a field of view above 180°. This is in contrast to existing direct mono-SLAM approaches like DTAM or LSD-SLAM, which operate on rectified images, in practice limiting the field of view to around 130° diagonally. Not only does this allows to observe - and reconstruct - a larger portion of the surrounding environment, but it also makes the system more robust to degenerate (rotation-only) movement. The two main contribution are (1) the formulation of direct image alignment for the unified omnidirectional model, and (2) a fast yet accurate approach to incremental stereo directly on distorted images. We evaluated our framework on real-world sequences taken with a 185° fisheye lens, and compare it to a rectified and a piecewise rectified approach.

We propose a novel Large-Scale Direct SLAM algorithm for stereo cameras (Stereo LSD-SLAM) that runs in real-time at high frame rate on standard CPUs. In contrast to sparse interest-point based methods, our approach aligns images directly based on the photoconsistency of all high-contrast pixels, including corners, edges and high texture areas. It concurrently estimates the depth at these pixels from two types of stereo cues: Static stereo through the fixed-baseline stereo camera setup as well as temporal multi-view stereo exploiting the camera motion. By incorporating both disparity sources, our algorithm can even estimate depth of pixels that are under-constrained when only using fixed-baseline stereo. Using a fixed baseline, on the other hand, avoids scale-drift that typically occurs in pure monocular SLAM.We furthermore propose a robust approach to enforce illumination invariance, capable of handling aggressive brightness changes between frames - greatly improving the performance in realistic settings. In experiments, we demonstrate state-of-the-art results on stereo SLAM benchmarks such as Kitti or challenging datasets from the EuRoC Challenge 3 for micro aerial vehicles.

We present a novel learning algorithm especially designed for challenging, large-scale classification problems in mobile robotics. Our method addresses two important aims: first it reduces the required amount of interaction with a human supervisor, which increases the level of autonomy of the learning process. And second, it has the capability to update its internal representation online with every new observed data sample, which makes it adaptive to new environments. The proposed method is based on a combination of two established methods, namely Online Star Clustering and Label Propagation, but it extends and modifies these in such a way that significant shortcomings such as classification inaccuracy and run time inefficiency can be resolved. In experiments on large benchmark data sets, we show that our approach can quickly learn to classify 3D objects with a significantly reduced amount of required ground truth labels for training.

BACKGROUND: The demand for high-throughput and objective phenotyping in plant research has been increasing during the last years due to large experimental sites. Sensor-based, non-invasive and automated processes are needed to overcome the phenotypic bottleneck, which limits data volumes on account of manual evaluations. A major challenge for sensor-based phenotyping in vineyards is the distinction between the grapevine in the foreground and the field in the background - this is especially the case for red-green-blue (RGB) images, where similar color distributions occur both in the foreground plant and in the field and background plants. However, RGB cameras are a suitable tool in the field because they provide high-resolution data at fast acquisition rates with robustness to outdoor illumination. RESULTS: This study presents a method to segment the phenotypic classes 'leaf', 'stem', 'grape' and 'background' in RGB images that were taken with a standard consumer camera in vineyards. Background subtraction is achieved by taking two images of each plant for depth reconstruction. The color information is furthermore used to distinguish the leaves from stem and grapes in the foreground. The presented approach allows for objective computation of phenotypic traits like 3D leaf surface areas and fruit-to-leaf ratios. The method has been successfully applied to objective assessment of growth habits of new breeding lines. To this end, leaf areas of two breeding lines were monitored and compared with traditional cultivars. A statistical analysis of the method shows a significant (p <0.001) determination coefficient R (2)= 0.93 and root-mean-square error of 3.0%. CONCLUSIONS: The presented approach allows for non-invasive, fast and objective assessment of plant growth. The main contributions of this study are 1) the robust segmentation of RGB images taken from a standard consumer camera directly in the field, 2) in particular, the robust background subtraction via reconstruction of dense depth maps, and 3) phenotypic applications to monitoring of plant growth and computation of fruit-to-leaf ratios in 3D. This advance provides a promising tool for high-throughput, automated image acquisition, e.g., for field robots.

This paper deals with the analysis of a recent reformulation of the primal-dual hybrid gradient method, which allows one to apply it to nonconvex regularizers. Particularly, it investigates variational problems for which the energy to be minimized can be written as $G(u) + F(Ku)$, where $G$ is convex, $F$ is semiconvex, and $K$ is a linear operator. We study the method and prove convergence in the case where the nonconvexity of $F$ is compensated for by the strong convexity of $G$. The convergence proof yields an interesting requirement for the choice of algorithm parameters, which we show to be not only sufficient, but also necessary. Additionally, we show boundedness of the iterates under much weaker conditions. Finally, in several numerical experiments we demonstrate effectiveness and convergence of the algorithm beyond the theoretical guarantees.

We propose an information-theoretic criterion, entropy estimate, for the joint alignment of a group of shape observations drawn from an unknown shape distribution. Employing a nonparametric density estimation technique with implicit shape representation, we minimize the entropy estimate with respect to the pose parameters of similarity transformations based on gradient descent optimization for which we provide implementation details. We demonstrate the capacity of our approach in numerous experiments with an application of building a shape prior to prostate MR image segmentation.

This paper deals with the problem of reconstructing a depth map from a sequence of differently focused images, also known as depth from focus (DFF) or shape from focus. We propose to state the DFF problem as a variational problem, including a smooth but nonconvex data fidelity term and a convex nonsmooth regularization, which makes the method robust to noise and leads to more realistic depth maps. In addition, we propose to solve the nonconvex minimization problem with a linearized alternating directions method of multipliers, allowing to minimize the energy very efficiently. A numerical comparison to classical methods on simulated as well as on real data is presented.

In this paper, we propose an optimization method for estimating the parameters that typically appear in graph-theoretical formulations of the matching problem for object detection. Although several methods have been proposed to optimize parameters for graph matching in a way to promote correct correspondences and to restrict wrong ones, our approach is novel in the sense that it aims at improving performance in the more general task of object detection. In our formulation, similarity functions are adjusted so as to increase the overall similarity among a reference model and the observed target, and at the same time reduce the similarity among reference and "non-target" objects. We evaluate the proposed method in two challenging scenarios, namely object detection using data captured with a Kinect sensor in a real environment, and intrinsic metric learning for deformable shapes, demonstrating substantial improvements in both settings.

Creating textured 3D scans of indoor environments has experienced a large boost with the advent of cheap commodity depth sensors. However, the quality of the acquired 3D models is often impaired by color seams in the reconstruction due to varying illumination (e.g., Shadows or highlights) and object surfaces whose brightness and color vary with the viewpoint of the camera. In this paper, we propose a direct and simple method to estimate the pure albedo of the texture, which allows us to remove illumination effects from IR and color images. Our approach first computes the illumination-independent albedo in the IR domain, which we subsequently transfer to the color albedo. As shadows and highlights lead to over- and underexposed image regions with little or no color information, we apply an advanced optimization scheme to infer color information in the color albedo from neigh boring image regions. We demonstrate the applicability of our approach to various real-world scenes.

We propose an optimization algorithm for mutual information-based unsupervised figure-ground separation. The algorithm jointly estimates the color distributions of the foreground and background, and separates them based on their mutual information with geometric regularity. To this end, we revisit the notion of mutual information and reformulate it in terms of the photometric variable and the indicator function; and propose a sequential convex optimization strategy for solving the nonconvex optimization problem that arises. By minimizing a sequence of convex sub-problems for the mutual-information-based nonconvex energy, we efficiently attain high quality solutions for challenging unsupervised figure-ground segmentation problems. We demonstrate the capacity of our approach in numerous experiments that show convincing fully unsupervised figure-ground separation, in terms of both segmentation quality and robustness to initialization.

We propose a shape matching method that produces dense correspondences tuned to a specific class of shapes and deformations. In a scenario where this class is represented by a small set of example shapes, the proposed method learns a shape descriptor capturing the variability of the deformations in the given class. The approach enables the wave kernel signature to extend the class of recognized deformations from near isometries to the deformations appearing in the example set by means of a random forest classifier. With the help of the introduced spatial regularization, the proposed method achieves significant improvements over the baseline approach and obtains state-of-the-art results while keeping short computation times.

In this paper we propose a novel volumetric multi-resolution mapping system for RGB-D images that runs on a standard CPU in real-time. Our approach generates a textured triangle mesh from a signed distance function that it continuously updates as new RGB-D images arrive. We propose to use an octree as the primary data structure which allows us to represent the scene at multiple scales. Furthermore, it allows us to grow the reconstruction volume dynamically. As most space is either free or unknown, we allocate and update only those voxels that are located in a narrow band around the observed surface. In contrast to a regular grid, this approach saves enormous amounts of memory and computation time. The major challenge is to generate and maintain a consistent triangle mesh, as neighboring cells in the octree are more difficult to find and may have different resolutions. To remedy this, we present in this paper a novel algorithm that keeps track of these dependencies, and efficiently updates corresponding parts of the triangle mesh. In our experiments, we demonstrate the real-time capability on a large set of RGB-D sequences. As our approach does not require a GPU, it is well suited for applications on mobile or flying robots with limited computational resources.

We present the D-eDVS- a combined event-based 3D sensor - and a novel event-based full-3D simultaneous localization and mapping algorithm which works exclusively with the sparse stream of visual data provided by the D-eDVS. The D-eDVS is a combination of the established PrimeSense RGB-D sensor and a biologically inspired embedded dynamic vision sensor. Dynamic vision sensors only react to dynamic contrast changes and output data in form of a sparse stream of events which represent individual pixel locations. We demonstrate how an event-based dynamic vision sensor can be fused with a classic frame-based RGB-D sensor to produce a sparse stream of depth-augmented 3D points. The advantages of a sparse, event-based stream are a much smaller amount of generated data, thus more efficient resource usage, and a continuous representation of motion allowing lag-free tracking. Our event-based SLAM algorithm is highly efficient and runs 20 times faster than realtime, provides localization updates at several hundred Hertz, and produces excellent results. We compare our method against ground truth from an external tracking system and two state-of-the-art algorithms on a new dataset which we release in combination with this paper.

We present a direct monocular visual odometry system which runs in real-time on a smartphone. Being a direct method, it tracks and maps on the images themselves instead of extracted features such as keypoints. New images are tracked using direct image alignment, while geometry is represented in the form of a semi-dense depth map. Depth is estimated by filtering over many small-baseline, pixel-wise stereo comparisons. This leads to significantly less outliers and allows to map and use all image regions with sufficient gradient, including edges. We show how a simple world model for AR applications can be derived from semi-dense depth maps, and demonstrate the practical applicability in the context of an AR application in which simulated objects can collide with real geometry.

Abstract We consider the problem of stable region detection and segmentation of deformable shapes. We pursue this goal by determining a consensus segmentation from a heterogeneous ensemble of putative segmentations, which are generated by a clustering process on an intrinsic embedding of the shape. The intuition is that the consensus segmentation, which relies on aggregate statistics gathered from the segmentations in the ensemble, can reveal components in the shape that are more stable to deformations than the single baseline segmentations. Compared to the existing approaches, our solution exhibits higher robustness and repeatability throughout a wide spectrum of non‐rigid transformations. It is computationally efficient, naturally extendible to point clouds, and remains semantically stable even across different object classes. A quantitative evaluation on standard datasets confirms the potentiality of our method as a valid tool for deformable shape analysis.

We propose convex relaxations for nonconvex energies on vector-valued functions which are tractable yet as tight as possible. In contrast to existing relaxations, we can handle the combination of nonconvex data terms with coupled regularizers such as $l^2$-regularizers. The key idea is to consider a collection of hypersurfaces with a relaxation that takes into account the entire functional rather than separately treating the data term and the regularizers. We provide a theoretical analysis, detail the implementations for different functionals, present run time and memory requirements, and experimentally demonstrate that the coupled $l^2$-regularizers give systematic improvements regarding denoising, inpainting, and optical flow estimation.

In this paper, we present a novel mapping system that robustly generates highly accurate 3-D maps using an RGB-D camera. Our approach requires no further sensors or odometry. With the availability of low-cost and light-weight RGB-D sensors such as the Microsoft Kinect, our approach applies to small domestic robots such as vacuum cleaners, as well as flying robots such as quadrocopters. Furthermore, our system can also be used for free-hand reconstruction of detailed 3-D models. In addition to the system itself, we present a thorough experimental evaluation on a publicly available benchmark dataset. We analyze and discuss the influence of several parameters such as the choice of the feature descriptor, the number of visual features, and validation methods. The results of the experiments demonstrate that our system can robustly deal with challenging scenarios such as fast camera motions and feature-poor environments while being fast enough for online operation. Our system is fully available as open source and has already been widely adopted by the robotics community.

We propose the adoption of a vector extrapolation technique to accelerate convergence of correspondence problems under the quadratic assignment formulation for attributed graph matching (QAP). In order to capture a broad range of matching scenarios, we provide a class of relaxations of the QAP under elastic net constraints. This allows us to regulate the sparsity/complexity trade-off which is inherent to most instances of the matching problem, thus enabling us to study the application of the acceleration method over a family of problems of varying difficulty. The validity of the approach is assessed by considering three different matching scenarios; namely, rigid and non-rigid three-dimensional shape matching, and image matching for Structure from Motion. As demonstrated on both real and synthetic data, our approach leads to an increase in performance of up to one order of magnitude when compared to the standard methods. 1

We introduce the concept of relative volume constraints in order to account for insufficient information in the reconstruction of 3D objects from a single image. The key idea is to formulate a variational reconstruction approach with shape priors in form of relative depth profiles or volume ratios relating object parts. Such shape priors can easily be derived either from a user sketch or from the object's shading profile in the image. They can handle textured or shadowed object regions by propagating information. We propose a convex relaxation of the constrained optimization problem which can be solved optimally in a few seconds on graphics hardware. In contrast to existing single view reconstruction algorithms, the proposed algorithm provides substantially more flexibility to recover shape details such as self-occlusions, dents and holes, which are not visible in the object silhouette.

We propose a fundamentally novel approach to real-time visual odometry for a monocular camera. It allows to benefit from the simplicity and accuracy of dense tracking - which does not depend on visual features - while running in real-time on a CPU. The key idea is to continuously estimate a semi-dense inverse depth map for the current frame, which in turn is used to track the motion of the camera using dense image alignment. More specifically, we estimate the depth of all pixels which have a non-negligible image gradient. Each estimate is represented as a Gaussian probability distribution over the inverse depth. We propagate this information over time, and update it with new measurements as new images arrive. In terms of tracking accuracy and computational speed, the proposed method compares favorably to both state-of-the-art dense and feature-based visual odometry and SLAM algorithms. As our method runs in real-time on a CPU, it is of large practical value for robotics and augmented reality applications.

While total variation is among the most popular regularizers for variational problems, its extension to functions with values in a manifold is an open problem. In this paper, we propose the first algorithm to solve such problems which applies to arbitrary Riemannian manifolds. The key idea is to reformulate the variational problem as a multilabel optimization problem with an infinite number of labels. This leads to a hard optimization problem which can be approximately solved using convex relaxation techniques. The framework can be easily adapted to different manifolds including spheres and three-dimensional rotations, and allows to obtain accurate solutions even with a relatively coarse discretization. With numerous examples we demonstrate that the proposed framework can be applied to variational models that incorporate chromaticity values, normal fields, or camera trajectories.

We propose a convex multilabel framework for image sequence segmentation which allows to impose proportion priors on object parts in order to preserve their size ratios across multiple images. The key idea is that for strongly deformable objects such as a gymnast the size ratio of respective regions (head versus torso, legs versus full body, etc.) is typically preserved. We propose different ways to impose such priors in a Bayesian framework for image segmentation. We show that near-optimal solutions can be computed using convex relaxation techniques. Extensive qualitative and quantitative evaluations demonstrate that the proportion priors allow for highly accurate segmentations, avoiding seeping-out of regions and preserving semantically relevant small-scale structures such as hands or feet. They naturally apply to multiple object instances such as players in sports scenes, and they can relate different objects instead of object parts, e.g. organs in medical imaging. The algorithm is efficient and easily parallelized leading to proportion-consistent segmentations at runtimes around one second.

We consider a parametrized relaxation of the widely adopted quadratic assignment problem (QAP) formulation for minimum distortion correspondence between deformable shapes. In order to control the accuracy/sparsity trade-off we introduce a weighting parameter on the combination of two existing relaxations, namely spectral and game-theoretic. This leads to the introduction of the elastic net penalty function into shape matching problems. In combination with an efficient algorithm to project onto the elastic net ball, we obtain an approach for deformable shape matching with controllable sparsity. Experiments on a standard benchmark confirm the effectiveness of the approach.

We propose a method to generate highly detailed, textured 3D models of large environments from RGB-D sequences. Our system runs in real-time on a standard desktop PC with a state-of-the-art graphics card. To reduce the memory consumption, we fuse the acquired depth maps and colors in a multi-scale octree representation of a signed distance function. To estimate the camera poses, we construct a pose graph and use dense image alignment to determine the relative pose between pairs of frames. We add edges between nodes when we detect loop-closures and optimize the pose graph to correct for long-term drift. Our implementation is highly parallelized on graphics hardware to achieve real-time performance. More specifically, we can reconstruct, store, and continuously update a colored 3D model of an entire corridor of nine rooms at high levels of detail in real-time on a single GPU with 2.5GB.

In this work we propose a novel method to include a connectivity prior into image segmentation that is based on a binary labeling of a directed graph, in this case a geodesic shortest path tree. Specifically we make two contributions: First, we construct a geodesic shortest path tree with a distance measure that is related to the image data and the bending energy of each path in the tree. Second, we include a connectivity prior in our segmentation model, that allows to segment not only a single elongated structure, but instead a whole connected branching tree. Because both our segmentation model and the connectivity constraint are convex a global optimal solution can be found. To this end, we generalize a recent primal-dual algorithm for continuous convex optimization to an arbitrary graph structure. To validate our method we present results on data from medical imaging in angiography and retinal blood vessel segmentation.

In this paper we present a method for automatic video segmentation of RGB-D video streams provided by combined colour and depth sensors like the Microsoft Kinect. To this end, we combine position and normal information from the depth sensor with colour information to compute temporally stable, depth-adaptive superpixels and combine them into a graph of strand-like spatiotemporal, depth-adaptive supervoxels. We use spectral graph clustering on the supervoxel graph to partition it into spatiotemporal segments. Experimental evaluation on several challenging scenarios demonstrates that our two-layer RGB-D video segmentation technique produces excellent video segmentation results.

The goal of our work is to provide a fast and accurate method to estimate the camera motion from RGB-D images. Our approach registers two consecutive RGB-D frames directly upon each other by minimizing the photometric error. We estimate the camera motion using non-linear minimization in combination with a coarse-to-fine scheme. To allow for noise and outliers in the image data, we propose to use a robust error function that reduces the influence of large residuals. Furthermore, our formulation allows for the inclusion of a motion model which can be based on prior knowledge, temporal filtering, or additional sensors like an IMU. Our method is attractive for robots with limited computational resources as it runs in real-time on a single CPU core and has a small, constant memory footprint. In an extensive set of experiments carried out both on a benchmark dataset and synthetic data, we demonstrate that our approach is more accurate and robust than previous methods. We provide our software under an open source license.

In this paper, we propose a dense visual SLAM method for RGB-D cameras that minimizes both the photometric and the depth error over all pixels. In contrast to sparse, feature-based methods, this allows us to better exploit the available information in the image data which leads to higher pose accuracy. Furthermore, we propose an entropy-based similarity measure for keyframe selection and loop closure detection. From all successful matches, we build up a graph that we optimize using the g2o framework. We evaluated our approach extensively on publicly available benchmark datasets, and found that it performs well in scenes with low texture as well as low structure. In direct comparison to several state-of-the-art methods, our approach yields a significantly lower trajectory error. We release our software as open-source.

In this paper, we present an approach that allows a quadrocopter to follow a person and to recognize simple gestures using an onboard depth camera. This enables novel applications such as hands-free filming and picture taking. The problem of tracking a person with an onboard camera however is highly challenging due to the self-motion of the platform. To overcome this problem, we stabilize the depth image by warping it to a virtual-static camera, using the estimated pose of the quadrocopter obtained from vision and inertial sensors using an Extended Kalman filter. We show that such a stabilized depth video is well suited to use with existing person trackers such as the OpenNI tracker. Using this approach, the quadrocopter not only obtains the position and orientation of the tracked person, but also the full body pose - which can then for example be used to recognize hand gestures to control the quadrocopter's behaviour. We implemented a small set of example commands (“follow me”, “take picture”, “land”), and generate corresponding motion commands. We demonstrate the practical performance of our approach in an extensive set of experiments with a quadrocopter. Although our current system is limited to indoor environments and small motions due to the restrictions of the used depth sensor, it indicates that there is large potential for such applications in the near future.

We propose a method for interactive multilabel segmentation which explicitly takes into account the spatial variation of color distributions. To this end, we estimate a joint distribution over color and spatial location using a generalized Parzen density estimator applied to each user scribble. In this way, we obtain a likelihood for observing certain color values at a spatial coordinate. This likelihood is then incorporated in a Bayesian MAP estimation approach to multiregion segmentation which in turn is optimized using recently developed convex relaxation techniques. These guarantee global optimality for the two-region case (foreground/background) and solutions of bounded optimality for the multiregion case. We show results on the GrabCut benchmark, the recently published Graz benchmark, and on the Berkeley segmentation database which exceed previous approaches such as GrabCut, the Random Walker, Santner's approach, TV-Seg, and interactive graph cuts in accuracy. Our results demonstrate that taking into account the spatial variation of color models leads to drastic improvements for interactive image segmentation.

Multilabel problems are of fundamental importance in computer vision and image analysis. Yet, finding global minima of the associated energies is typically a hard computational challenge. Recently, progress has been made by reverting to spatially continuous formulations of respective problems and solving the arising convex relaxation globally. In practice this leads to solutions which are either optimal or within an a posteriori bound of the optimum. Unfortunately, in previous methods, both run time and memory requirements scale linearly in the total number of labels, making these methods very inefficient and often not applicable to problems with higher dimensional label spaces. In this paper, we propose a reduction technique for the case that the label space is a continuous product space and the regularizer is separable, i.e., a sum of regularizers for each dimension of the label space. In typical real-world labeling problems, the resulting convex relaxation requires orders of magnitude less memory and computation time than previous methods. This enables us to apply it to large-scale problems like optic flow, stereo with occlusion detection, segmentation into a very large number of regions, and joint denoising and local noise estimation. Experiments show that despite the drastic gain in performance, we do not arrive at less accurate solutions than the original relaxation. Using the novel method, we can for the first time efficiently compute solutions to the optic flow functional which are within provable bounds (typically 5%) of the global optimum.

We propose a novel algorithmic solution for estimating a three-dimensional model of an object observed in a single image. Based on a minimal user input, the algorithm interactively determines the objects' silhouette and subsequently computes a silhouette-consistent 3D model which is precisely the globally minimal surface with user-specified volume. In contrast to a recently published approach to single view reconstruction, the proposed algorithm does not constrain the resolution in the depth-direction, it assures the global optimum and is faster by about an order of magnitude. Experiments demonstrate that plausible high-resolution 3D models can be generated in fractions of a second and compare favorably with other methods.

We propose the first tractable convex formulation of the vectorial Mumford-Shah functional which allows to compute high-quality solutions independent of the initialization. To this end, we generalize recently introduced convex formulations for scalar functionals to the vector-valued scenario in such a way that discontinuities in the different color channels preferably coincide. Furthermore, we propose an efficient solution which makes the overall optimization problem as tractable as in the scalar-valued case. Numerous experimental comparisons with the naive channel-wise approach, with the well-known Ambrosio-Tortorelli approximation, and with the classical total variation confirm the advantages of the proposed relaxation for contrast-preserving and edge-enhancing regularization.

We present an approach to simultaneous localization and mapping (SLAM) for RGB-D cameras like the Microsoft Kinect. Our system concurrently estimates the trajectory of a hand-held Kinect and generates a dense 3D model of the environment. We present the key features of our approach and evaluate its performance thoroughly on a recently published dataset, including a large set of sequences of different scenes with varying camera speeds and illumination conditions. In particular, we evaluate the accuracy, robustness, and processing time for three different feature descriptors (SIFT, SURF, and ORB). The experiments demonstrate that our system can robustly deal with difficult data in common indoor scenarios while being fast enough for online operation. Our system is fully available as open-source.

In this paper, we present a generalized framework for robustly operating previously unknown cabinets in kitchen environments. Our framework consists of the following four components: (1) a module for detecting both Lambertian and non-Lambertian (i.e. specular) handles, (2) a module for opening and closing novel cabinets using impedance control and for learning their kinematic models, (3) a module for storing and retrieving information about these objects in the map, and (4) a module for reliably operating cabinets of which the kinematic model is known. The presented work is the result of a collaboration of three PR2 beta sites. We rigorously evaluated our approach on 29 cabinets in five real kitchens located at our institutions. These kitchens contained 13 drawers, 12 doors, 2 refrigerators and 2 dishwashers. We evaluated the overall performance of detecting the handle of a novel cabinet, operating it and storing its model in a semantic map. We found that our approach was successful in 51.9% of all 104 trials. With this work, we contribute a well-tested building block of open-source software for future robotic service applications.

In this paper, we describe a system that enables a low-cost quadrocopter coupled with a ground-based laptop to navigate autonomously in previously unknown and GPS-denied environments. Our system consists of three components: a monocular SLAM system, an extended Kalman filter for data fusion and state estimation and a PID controller to generate steering commands. Next to a working system, the main contribution of this paper is a novel, closed-form solution to estimate the absolute scale of the generated visual map from inertial and altitude measurements. In an extensive set of experiments, we demonstrate that our system is able to navigate in previously unknown environments at absolute scale without requiring artificial markers or external sensors. Furthermore, we show (1) its robustness to temporary loss of visual tracking and significant delays in the communication process, (2) the elimination of odometry drift as a result of the visual SLAM system and (3) accurate, scale-aware pose estimation and navigation.

In this paper, we present a novel benchmark for the evaluation of RGB-D SLAM systems. We recorded a large set of image sequences from a Microsoft Kinect with highly accurate and time-synchronized ground truth camera poses from a motion capture system. The sequences contain both the color and depth images in full sensor resolution (640 × 480) at video frame rate (30 Hz). The ground-truth trajectory was obtained from a motion-capture system with eight high-speed tracking cameras (100 Hz). The dataset consists of 39 sequences that were recorded in an office environment and an industrial hall. The dataset covers a large variety of scenes and camera motions. We provide sequences for debugging with slow motions as well as longer trajectories with and without loop closures. Most sequences were recorded from a handheld Kinect with unconstrained 6-DOF motions but we also provide sequences from a Kinect mounted on a Pioneer 3 robot that was manually navigated through a cluttered indoor environment. To stimulate the comparison of different approaches, we provide automatic evaluation tools both for the evaluation of drift of visual odometry systems and the global pose error of SLAM systems. The benchmark website [1] contains all data, detailed descriptions of the scenes, specifications of the data formats, sample code, and evaluation tools.

In this paper, we consider the problem of tracking human motion with a 22-DOF kinematic model from depth images. In contrast to existing approaches, our system naturally scales to multiple sensors. The motivation behind our approach, termed Multiple Depth Camera Approach (MDCA), is that by using several cameras, we can significantly improve the tracking quality and reduce ambiguities as for example caused by occlusions. By fusing the depth images of all available cameras into one joint point cloud, we can seamlessly incorporate the available information from multiple sensors into the pose estimation. To track the high-dimensional human pose, we employ state-of-the-art annealed particle filtering and partition sampling. We compute the particle likelihood based on the truncated signed distance of each observed point to a parameterized human shape model. We apply a coarse-to-fine scheme to recognize a wide range of poses to initialize the tracker. In our experiments, we demonstrate that our approach can accurately track human motion in real-time (15Hz) on a GPGPU. In direct comparison to two existing trackers (OpenNI, Microsoft Kinect SDK), we found that our approach is significantly more robust for unconstrained motions and under (partial) occlusions.

BACKGROUND: The enteric pathogen Salmonella is the causative agent of the majority of food-borne bacterial poisonings. Resent research revealed that colonization of plants by Salmonella is an active infection process. Salmonella changes the metabolism and adjust the plant host by suppressing the defense mechanisms. In this report we developed an automatic algorithm to quantify the symptoms caused by Salmonella infection on Arabidopsis. RESULTS: The algorithm is designed to attribute image pixels into one of the two classes: healthy and unhealthy. The task is solved in three steps. First, we perform segmentation to divide the image into foreground and background. In the second step, a support vector machine (SVM) is applied to predict the class of each pixel belonging to the foreground. And finally, we do refinement by a neighborhood-check in order to omit all falsely classified pixels from the second step. The developed algorithm was tested on infection with the non-pathogenic E. coli and the plant pathogen Pseudomonas syringae and used to study the interaction between plants and Salmonella wild type and T3SS mutants. We proved that T3SS mutants of Salmonella are unable to suppress the plant defenses. Results obtained through the automatic analyses were further verified on biochemical and transcriptome levels. CONCLUSION: This report presents an automatic pixel-based classification method for detecting "unhealthy" regions in leaf images. The proposed method was compared to existing method and showed a higher accuracy. We used this algorithm to study the impact of the human pathogenic bacterium Salmonella Typhimurium on plants immune system. The comparison between wild type bacteria and T3SS mutants showed similarity in the infection process in animals and in plants. Plant epidemiology is only one possible application of the proposed algorithm, it can be easily extended to other detection tasks, which also rely on color information, or even extended to other features.

Bridging the gap between low-level and high-level image analysis has been a central challenge in computer vision throughout the last decades. In this article I will point out a number of recent developments in low-level image analysis which open up new possibilities to bring together concepts of high-level and low-level vision. The key observation is that numerous multi‐label optimization problems can nowadays be efficiently solved in a near-optimal manner, using either graph-theoretic algorithms or convex relaxation techniques. Moreover, higher-level semantic knowledge can be learned and imposed on the basis of such multi‐label formulations.

We propose a probabilistic formulation of joint silhouette extraction and 3D reconstruction given a series of calibrated 2D images. Instead of segmenting each image separately in order to construct a 3D surface consistent with the estimated silhouettes, we compute the most probable 3D shape that gives rise to the observed color information. The probabilistic framework, based on Bayesian inference, enables robust 3D reconstruction by optimally taking into account the contribution of all views. We solve the arising maximum a posteriori shape inference in a globally optimal manner by convex relaxation techniques in a spatially continuous representation. For an interactively provided user input in the form of scribbles specifying foreground and background regions, we build corresponding color distributions as multivariate Gaussians and find a volume occupancy that best fits to this data in a variational sense. Compared to classical methods for silhouette-based multiview reconstruction, the proposed approach does not depend on initialization and enjoys significant resilience to violations of the model assumptions due to background clutter, specular reflections, and camera sensor perturbations. In experiments on several real-world data sets, we show that exploiting a silhouette coherency criterion in a multiview setting allows for dramatic improvements of silhouette quality over independent 2D segmentations without any significant increase of computational efforts. This results in more accurate visual hull estimation, needed by a multitude of image-based modeling approaches. We made use of recent advances in parallel computing with a GPU implementation of the proposed method generating reconstructions on volume grids of more than 20 million voxels in up to 4.41 seconds.

We describe a convex relaxation for a family of problems of minimal perimeter partitions. The minimization of the relaxed problem can be tackled numerically: we describe an algorithm and show some results. In most cases, our relaxed problem finds a correct numerical approximation of the optimal solution: we give some arguments to explain why it should be so and also discuss some situations where it fails.

Several ways to generalize scalar total variation to vector-valued functions have been proposed in the past. In this paper, we give a detailed analysis of a variant we denote by $\text{TV}_J$, which has not been previously explored as a regularizer. The contributions of the manuscript are twofold: on the theoretical side, we show that $\text{TV}_J$ can be derived from the generalized Jacobians from geometric measure theory. Thus, within the context of this theory, $\text{TV}_J$ is the most natural form of a vectorial total variation. As an important feature, we derive how $\text{TV}_J$ can be written as the support functional of a convex set in $\mathcal{L}^2$. This property allows us to employ fast and stable minimization algorithms to solve inverse problems. The analysis also shows that in contrast to other total variation regularizers for color images, the proposed one penalizes across a common edge direction for all channels, which is a major theoretical advantage. Our practical contribution consist of an extensive experimental section, where we compare the performance of a number of provable convergent algorithms for inverse problems with our proposed regularizer. In particular, we show in experiments for denoising, deblurring, superresolution, and inpainting that its use leads to a significantly better restoration of color images, both visually and quantitatively. Source code for all algorithms employed in the experiments is provided online.

We consider the problem of decomposing a video sequence into a superposition of (a given number of) moving layers. For this problem, we propose an energy minimization approach based on the coding cost. Our contributions affect both the model (what is minimized) and the algorithmic side (how it is minimized). The novelty of the coding-cost model is the inclusion of a refined model of the image formation process, known as super resolution. This accounts for camera blur and area averaging arising in a physically plausible image formation process. It allows us to extract sharp high-resolution layers from the video sequence. The algorithmic framework is based on an alternating minimization scheme and includes the following innovations. 1) A video labeling, we optimize the layer domains. This allows to regularize the shapes of the layers and a very elegant handling of occlusions. 2) We present an efficient parallel algorithm for extracting super-resolved layers based on TV filtering.

We introduce a novel type of total variation regularizer, TVS1, for cyclic structures such as angles or hue values. The method handles the periodicity of values in a simple and consistent way and is invariant to value shifts. The regularizer is integrated in a recent functional lifting framework which allows for arbitrary nonconvex data terms. Results are superior and more natural than with the simple total variation without special care about wrapping interval end points. In addition we propose an equivalent formulation which can be minimized with the same time and memory efficiency as the standard total variation.

In this work we present a novel method for tracking an un known number of objects with a single camera system in real time. The proposed algorithm is based on high-accuracy optical flow and finite set statistics. In this framework the target state is treated as a random vector and the number of possible objects as a random number, which has to be estimated correctly. We are able to deal with false alarms, clutter and object spawning. Since possible objects can appear or disappear in the scene we propose a probability model for these events, in order to obtain stable results in the case of missing detections. Additionally, we show how track labeling, based on color and state information, can improve the results. Since the method partly relies on color information, it can handle partial occlusion and is invariant to rotation and scaling. We verify the theoretical results on various scenes.

We introduce a spatially dense variational approach to estimate the calibration of multiple cameras in the context of 3D reconstruction. We propose a relaxation scheme which allows to transform the original photometric error into a geometric one, thereby decoupling the problems of dense matching and camera calibration. In both quantitative and qualitative experiments, we demonstrate that the proposed decoupling scheme allows for robust and accurate estimation of camera parameters. In particular, the presented dense camera calibration formulation leads to substantial improvements both in the reconstructed 3D geometry and in the super-resolution texture estimation.

We introduce the novel continuous regularizer total curvature (TC) for images u: Ω → ℝ. It is defined as the Menger-Melnikov curvature of the Radon measure |Du|, which can be understood as a measure theoretic formulation of curvature mathematically related to mean curvature. The functional is not convex, therefore we define a convex relaxation which yields a close approximation. Similar to the total variation, the relaxation can be written as the support functional of a convex set, which means that there are stable and efficient minimization algorithms available when it is used as a regularizer in image processing problems. Our current implementation can handle general inverse problems, inpainting and segmentation. We demonstrate in experiments and comparisons how the regularizer performs in practice.

Convex relaxation techniques have become a popular approach to image segmentation as they allow to compute solutions independent of initialization to a variety of image segmentation problems. In this paper, we will show that shape priors in terms of moment constraints can be imposed within the convex optimization framework, since they give rise to convex constraints. In particular, the lower-order moments correspond to the overall volume, the centroid, and the variance or covariance of the shape and can be easily imposed in interactive segmentation methods. Respective constraints can be imposed as hard constraints or soft constraints. Quantitative segmentation studies on a variety of images demonstrate that the user can easily impose such constraints with a few mouse clicks, giving rise to substantial improvements of the resulting segmentation, and reducing the average segmentation error from 12% to 0:35%. GPU-based computation times of around 1 second allow for interactive segmentation.

We propose a novel framework for imposing label ordering constraints in multilabel optimization. In particular, label jumps can be penalized differently depending on the jump direction. In contrast to the recently proposed MRF-based approaches, the proposed method arises from the viewpoint of spatially continuous optimization. It unifies and generalizes previous approaches to label ordering constraints: Firstly, it provides a common solution to three different problems which are otherwise solved by three separate approaches [4, 10, 14]. We provide an exact characterization of the penalization functions expressible with our approach. Secondly, we show that it naturally extends to three and higher dimensions of the image domain. Thirdly, it allows novel applications, such as the convex shape prior. Despite this generality, our model is easily adjustable to various label layouts and is also easy to implement. On a number of experiments we show that it works quite well, producing solutions comparable and superior to those obtained with previous approaches.

The multi-label problem is of fundamental importance to computer vision, yet finding global minima of the associated energies is very hard and usually impossible in practice. Recently, progress has been made using continuous formulations of the multi-label problem and solving a convex relaxation globally, thereby getting a solution with optimality bounds. In this work, we develop a novel framework for continuous convex relaxations, where the label space is a continuous product space. In this setting, we can combine the memory efficient product relaxation of [9] with the much tighter relaxation of [5], which leads to solutions closer to the global optimum. Furthermore, the new setting allows us to formulate more general continuous regularizers, which can be freely combined in the different label dimensions. We also improve upon the relaxation of the products in the data term of [9], which removes the need for artificial smoothing and allows the use of exact solvers.

We propose a novel method for computing a geometrically consistent and spatially dense matching between two 3D shapes. Rather than mapping points to points we match infinitesimal surface patches while preserving the geometric structures. In this spirit we consider matchings as diffeomorphisms between the objects' surfaces which are by definition geometrically consistent. Based on the observation that such diffeomorphisms can be represented as closed and continuous surfaces in the product space of the two shapes we are led to a minimal surface problem in this product space. The proposed discrete formulation describes the search space with linear constraints. Computationally, our approach leads to a binary linear program whose relaxed version can be solved efficiently in a globally optimal manner. As cost function for matching, we consider a thin shell energy, measuring the physical energy necessary to deform one shape into the other. Experimental results demonstrate that the proposed LP relaxation allows to compute highquality matchings which reliably put into correspondence articulated 3D shapes. Moreover a quantitative evaluation shows improvements over existing works.

Abstract We study an algorithmic framework for computing an elastic orientation‐preserving matching of non‐rigid 3D shapes. We outline an Integer Linear Programming formulation whose relaxed version can be minimized globally in polynomial time. Because of the high number of optimization variables, the key algorithmic challenge lies in efficiently solving the linear program. We present a performance analysis of several Linear Programming algorithms on our problem. Furthermore, we introduce a multiresolution strategy which allows the matching of higher resolution models.

We propose a convex formulation for silhouette and stereo fusion in 3D reconstruction from multiple images. The key idea is to show that the reconstruction problem can be cast as one of minimizing a convex functional, where the exact silhouette consistency is imposed as convex constraints that restrict the domain of feasible functions. As a consequence, we can retain the original stereo-weighted surface area as a cost functional without heuristic modifications of this energy by balloon terms or other strategies, yet still obtain meaningful (non-empty) reconstructions which are guaranteed to be silhouette-consistent. We prove that the proposed convex relaxation approach provides solutions that lie within a bound of the optimal solution. Compared to existing alternatives, the proposed method does not depend on initialization and leads to a simpler and more robust numerical scheme for imposing silhouette consistency obtained by projection onto convex sets. We show that this projection can be solved exactly using an efficient algorithm. We propose a parallel implementation of the resulting convex optimization problem on a graphics card. Given a photo-consistency map and a set of image silhouettes, we are able to compute highly accurate and silhouette-consistent reconstructions for challenging real-world data sets. In particular, experimental results demonstrate that the proposed silhouette constraints help to preserve fine-scale details of the reconstructed shape. Computation times depend on the resolution of the input imagery and vary between a few seconds and a couple of minutes for all experiments in this paper.

Traditional optical flow algorithms rely on consecutive short-exposed images. In this work, we make use of an additional long-exposed image for motion field estimation. Long-exposed images integrate motion information directly in the form of motion-blur. With this additional information, more robust and accurate motion fields can be estimated. In addition, the moment of occlusion can be determined. Considering the basic signal-theoretical problem in motion field estimation, we exploit the fact that long-exposed images integrate motion information to prevent temporal aliasing. A suitable image formation model relates the long-exposed image to preceding and succeeding short-exposed images in terms of dense 2D motion and per-pixel occlusion/disocclusion timings. Based on our image formation model, we describe a practical variational algorithm to estimate the motion field not only for visible image regions but also for regions getting occluded. Results for synthetic as well as real-world scenes demonstrate the validity of the approach.

We present the first ratio-based image segmentation method that allows imposing curvature regularity of the region boundary. Our approach is a generalization of the ratio framework pioneered by Jermyn and Ishikawa so as to allow penalty functions that take into account the local curvature of the curve. The key idea is to cast the segmentation problem as one of finding cyclic paths of minimal ratio in a graph where each graph node represents a line segment. Among ratios whose discrete counterparts can be globally minimized with our approach, we focus in particular on the elastic ratio [Formula: see text] that depends, given an image I, on the oriented boundary C of the segmented region candidate. Minimizing this ratio amounts to finding a curve, neither small nor too curvy, through which the brightness flux is maximal. We prove the existence of minimizers for this criterion among continuous curves with mild regularity assumptions. We also prove that the discrete minimizers provided by our graph-based algorithm converge, as the resolution increases, to continuous minimizers. In contrast to most existing segmentation methods with computable and meaningful, i.e., nondegenerate, global optima, the proposed approach is fully unsupervised in the sense that it does not require any kind of user input such as seed nodes. Numerical experiments demonstrate that curvature regularity allows substantial improvement of the quality of segmentations. Furthermore, our results allow drawing conclusions about global optima of a parameterization-independent version of the snakes functional: the proposed algorithm allows determining parameter values where the functional has a meaningful solution and simultaneously provides the corresponding global solution.

We analyze a previously unexplored generalization of the scalar total variation to vector-valued functions, which is motivated by geometric measure theory. A complete mathematical characterization is given, which proves important invariance properties as well as existence of solutions of the vectorial ROF model. As an important feature, there exists a dual formulation for the proposed vectorial total variation, which leads to a fast and stable minimization algorithm. The main difference to previous approaches with similar properties is that we penalize across a common edge direction for all channels, which is a major theoretical advantage. Experiments show that this leads to a significantly better restoration of color edges in practice.

In this paper, we propose the combined use of complementary concepts for 3D tracking: region fitting on one side and dense optical flow as well as tracked SIFT features on the other. Both concepts are chosen such that they can compensate for the shortcomings of each other. While tracking by the object region can prevent the accumulation of errors, optical flow and SIFT can handle larger transformations. Whereas segmentation works best in case of homogeneous objects, optical flow computation and SIFT tracking rely on sufficiently structured objects. We show that a sensible combination yields a general tracking system that can be applied in a large variety of scenarios without the need to manually adjust weighting parameters.

We propose a combinatorial solution to determine the optimal elastic matching of a deformable template to an image. The central idea is to cast the optimal matching of each template point to a corresponding image pixel as a problem of finding a minimum cost cyclic path in the three-dimensional product space spanned by the template and the input image. We introduce a cost functional associated with each cycle, which consists of three terms: a data fidelity term favoring strong intensity gradients, a shape consistency term favoring similarity of tangent angles of corresponding points, and an elastic penalty for stretching or shrinking. The functional is normalized with respect to the total length to avoid a bias toward shorter curves. Optimization is performed by Lawler's Minimum Ratio Cycle algorithm parallelized on state-of-the-art graphics cards. The algorithm provides the optimal segmentation and point correspondence between template and segmented curve in computation times that are essentially linear in the number of pixels. To the best of our knowledge, this is the only existing globally optimal algorithm for real-time tracking of deformable shapes.

We propose an algorithmic framework for computing global solutions of variational models with convex regularity terms that permit quite arbitrary data terms. While the minimization of variational problems with convex data and regularity terms is straightforward (using, for example, gradient descent), this is no longer trivial for functionals with nonconvex data terms. Using the theoretical framework of calibrations, the original variational problem can be written as the maximum flux of a particular vector field going through the boundary of the subgraph of the unknown function. Upon relaxation this formulation turns the problem into a convex problem, although in a higher dimension. In order to solve this problem, we propose a fast primal-dual algorithm which significantly outperforms existing algorithms. In experimental results we show the application of our method to outlier filtering of range images and disparity estimation in stereo images using a variety of convex regularity terms.

TV regularization is an L1 penalization of the flow gradient magnitudes, and due to the tendency of the L1 norm to favor sparse solutions (i.e. lots of ‘zeros’), the fill-in effect caused by the regularizer leads to piecewise constant solutions in weakly textured areas. This effect, known as ‘staircasing’ in a 1D setting, can be reduced significantly by using a quadratic penalization for small gradient magnitudes while sticking to linear penalization for larger magnitudes to maintain the discontinuity preserving properties known from TV. A comparison of isotropic TV and isotropic Huber regularity is shown in Fig. 1 by means of rendering the disparities u1 of the Dimetrodon dataset. The color coded flow (cf. Fig. 1(a)) is superimposed as texture. Based on the two observations that motion discontinuities often occur along object boundaries and that in turn object boundaries often coincide

We introduce a convex relaxation framework to optimally minimize continuous surface ratios. The key idea is to minimize the continuous surface ratio by solving a sequence of convex optimization problems. We show that such minimal ratios are superior to traditionally used minimal surface formulations in that they do not suffer from a shrinking bias and no longer require the choice of a regularity parameter. The absence of a shrinking bias in the minimal ratio model is proven analytically. Furthermore we demonstrate that continuous ratio optimization can be applied to derive a new algorithm for reconstructing three-dimensional silhouette-consistent objects from multiple views. Experimental results confirm that our approach allows to accurately reconstruct deep concavities even without the specification of tuning parameters.

In this work we propose a convex relaxation approach for computing minimal partitions. Our approach is based on rewriting the minimal partition problem (also known as Potts model) in terms of a primal dual Total Variation functional. We show that the Potts prior can be incorporated by means of convex constraints on the dual variables. For minimization we propose an efficient primal dual projected gradient algorithm which also allows a fast implementation on parallel hardware. Although our approach does not guarantee to find global minimizers of the Potts model we can give a tight bound on the energy between the computed solution and the true minimizer. Furthermore we show that our relaxation approach dominates recently proposed relaxations. As a consequence, our approach allows to compute solutions closer to the true minimizer. For many practical problems we even find the global minimizer. We demonstrate the excellent performance of our approach on several multi-label image segmentation and stereo problems.

We present a fast graph cut algorithm for planar graphs. It is based on the graph theoretical work and leads to an efficient method that we apply on shape matching and image segmentation. In contrast to currently used methods in computer vision, the presented approach provides an upper bound for its runtime behavior that is almost linear. In particular, we are able to match two different planar shapes of N points in O(N2log N) and segment a given image of N pixels in O(N log N). We present two experimental benchmark studies which demonstrate that the presented method is also in practice faster than previously proposed graph cut methods: On planar shape matching and image segmentation we observe a speed-up of an order of magnitude, depending on resolution.

We study the scenario of a multiview setting, where several calibrated views of a textured object with known surface geometry are available. The objective is to estimate a diffuse texture map as precisely as possible. A superresolution image formation model based on the camera properties leads to a total variation energy for the desired texture map, which can be recovered as the minimizer of the functional by solving the Euler-Lagrange equation on the surface. The PDE is transformed to planar texture space via an automatically created conformal atlas, where it can be solved using total variation deblurring. The proposed approach allows to recover a high-resolution, high-quality texture map even from lower-resolution photographs, which is of interest for a variety of image-based modeling applications.

In this work we revisit the Mumford-Shah functional, one of the most studied variational approaches to image segmentation. The contribution of this paper is to propose an algorithm which allows to minimize a convex relaxation of the Mumford-Shah functional obtained by functional lifting. The algorithm is an efficient primal-dual projection algorithm for which we prove convergence. In contrast to existing algorithms for minimizing the full Mumford-Shah this is the first one which is based on a convex relaxation. As a consequence the computed solutions are independent of the initialization. Experimental results confirm that the proposed algorithm determines smooth approximations while preserving discontinuities of the underlying signal.

We consider a class of region-based energies for image segmentation and inpainting which combine region integrals with curvature regularity of the region boundary. To minimize such energies, we formulate an integer linear program which jointly estimates regions and their boundaries. Curvature regularity is imposed by respective costs on pairs of adjacent boundary segments. By solving the associated linear programming relaxation and thresholding the solution one obtains an approximate solution to the original integer problem. To our knowledge this is the first approach to impose curvature regularity in region-based formulations in a manner that is independent of initialization and allows to compute a bound on the optimal energy. In a variety of experiments on segmentation and inpainting, we demonstrate the advantages of higher-order regularity. Moreover, we demonstrate that for most experiments the optimality gap is smaller than 2% of the global optimum. For many instances we are even able to compute the global optimum.

We propose an algorithm for large displacement optical flow estimation which does not require the commonly used coarse-to-fine warping strategy. It is based on a quadratic relaxation of the optical flow functional which decouples data term and regularizer in such a way that the non-linearized variational problem can be solved by an alternation of two globally optimal steps, one imposing optimal data consistency, the other imposing discontinuity-preserving regularity of the flow field. Experimental results confirm that the proposed algorithmic implementation outperforms the traditional warping strategy, in particular for the case of large displacements of small scale structures.

The accurate estimation of motion in image sequences is of central importance to numerous computer vision applications. Most competitive algorithms compute flow fields by minimizing an energy made of a data and a regularity term. To date, the best performing methods rely on rather simple purely geometric regularizes favoring smooth motion. In this paper, we revisit regularization and show that appropriate adaptive regularization substantially improves the accuracy of estimated motion fields. In particular, we systematically evaluate regularizes which adoptively favor rigid body motion (if supported by the image data) and motion field discontinuities that coincide with discontinuities of the image structure. The proposed algorithm relies on sequential convex optimization, is real-time capable and outperforms all previously published algorithms by more than one average rank on the Middlebury optic flow benchmark.

We propose a polynomial-time algorithm for segmentation and (open) boundary estimation which takes into account a series of user-specified attraction points. In contrast to existing algorithms which impose that the segmenting boundary passes through these points, our algorithm allows an imprecision in the user input. An energy minimization approach imposes that the segmenting boundary optimally passes along high-contrast edges in such a way that at least one point along the computed boundary is as close as possible to any given attraction point. In this sense, the user input can be seen as a soft constraint. We prove that the resulting optimization problem is NP-hard. We prove that in the case that the user attraction points are ordered, then optimal solutions can be computed in polynomial time using a shortest path formulation in an appropriately constructed four-dimensional graph spanned by the image pixels, a set of tangent angles and the user attraction points. Experimental results on a variety of images demonstrate that good quality segmentations can be obtained with a few imprecise user clicks.

We propose a general technique for modeling the visible road surface in front of a vehicle. The common assumption of a planar road surface is often violated in reality. A workaround proposed in the literature is the use of a piecewise linear or quadratic function to approximate the road surface. Our approach is based on representing the road surface as a general parametric B-spline curve. The surface parameters are tracked over time using a Kalman filter. The surface parameters are estimated from stereo measurements in the free space. To this end, we adopt a recently proposed road-obstacle segmentation algorithm to include disparity measurements and the B-spline road-surface representation. Experimental results in planar and undulating terrain verify the increase in free-space availability and accuracy using a flexible B-spline for road-surface modeling.

We propose an efficient polynomial time algorithm to match an elastically deforming shape to an image. It is based on finding a globally optimal geodesic in the product space spanned by the image and the prior contour. To this end a branch-and-bound scheme is combined with shortest path techniques. We compare this algorithm with a recently proposed ratio minimization approach. While we show that generally the ratio is the better model, for many instances the two perform similarly. We identify a class of problems where the proposed method is likely to be faster. 1 Introduction and Related Work For decades researchers have striven to develop machine vision algorithms which can compete with or even outperform the human visual system. Despite many efforts this remains a challenging problem. The human visual system makes heavily use of prior world knowledge. As a consequence

Interactive object extraction is an important part in any image editing software. We present a two step segmentation algorithm that first obtains a binary segmentation and then applies matting on the border regions to obtain a smooth alpha channel. The proposed segmentation algorithm is based on the minimization of the Geodesic Active Contour energy. A fast Total Variation minimization algorithm is used to find the globally optimal solution. We show how user interaction can be incorporated and outline an efficient way to exploit color information. A novel matting approach, based on energy minimization, is presented. Experimental evaluations are discussed, and the algorithm is compared to state of the art object extraction algorithms. The GPU based binaries are available online.

In this work, we introduce a novel implicit representation of shape which is based on assigning to each pixel a probability that this pixel is inside the shape. This probabilistic representation of shape resolves two important drawbacks of alternative implicit shape representations such as the level set method: Firstly, the space of shapes is convex in the sense that arbitrary convex combinations of a set of shapes again correspond to a valid shape. Secondly, we prove that the introduction of shape priors into variational image segmentation leads to functionals which are convex with respect to shape deformations. For a large class of commonly considered (spatially continuous) functionals, we prove that - under mild regularity assumptions - segmentation and tracking with statistical shape priors can be performed in a globally optimal manner. In experiments on tracking a walking person through a cluttered scene we demonstrate the advantage of global versus local optimality.

This work deals with modeling and markerless tracking of athletes interacting with sports gear. In contrast to classical markerless tracking, the interaction with sports gear comes along with joint movement restrictions due to additional constraints: while humans can generally use all their joints, interaction with the equipment imposes a coupling between certain joints. A cyclist who performs a cycling pattern is one example: The feet are supposed to stay on the pedals, which are again restricted to move along a circular trajectory in 3D-space. In this paper, we present a markerless motion capture system that takes the lower-dimensional pose manifold into account by modeling the motion restrictions via soft constraints during pose optimization. Experiments with two different models, a cyclist and a snowboarder, demonstrate the applicability of the method. Moreover, we present motion capture results for challenging outdoor scenes including shadows and strong illumination changes.

We introduce a novel energy minimization method to decompose a video into a set of super-resolved moving layers. The proposed energy corresponds to the cost of coding the sequence. It consists of a data term and two terms imposing regularity of the geometry and the intensity of each layer. In contrast to existing motion layer methods, we perform graph cut optimization in the (dual) layer space to determine which layer is visible at which video position. In particular, we show how arising higher-order terms can be accounted for by a generalization of alpha expansions. Moreover, our model accurately captures long-term temporal consistency. To the best of our knowledge, this is the first work which aims at modeling details of the image formation process (such as camera blur and downsampling) in the context of motion layer decomposition. The experimental results demonstrate that energy minimization leads to a reconstruction of a video in terms of a superposition of multiple high-resolution motion layers.

Most algorithms for real-time tracking of deformable shapes provide sub-optimal solutions for a suitable energy minimization task: The search space is typically considered too large to allow for globally optimal solutions. In this paper we show that - under reasonable constraints on the object motion - one can guarantee global optimality while maintaining real-time requirements. The problem is cast as finding the optimal cycle in a graph spanned by the prior template and the image. The underlying combinatorial algorithm is implemented on state-of- the-art graphics hardware. Solutions on FPGAs are conceivable. Experimental results demonstrate long-term tracking of cars in real-time, while coping with challenging weather conditions. In particular, we show that the proposed tracking algorithm is highly robust to illumination changes and that it outperforms local tracking methods such as the level set method.

While global methods for matching shapes to images have recently been proposed, so far research has focused on small deformations of a fixed template. In this paper we present the first global method able to pixel-accurately match non-rigidly deformable shapes across images at amenable run-times. By finding cycles of optimal ratio in a four-dimensional graph - spanned by the image, the prior shape and a set of rotation angles - we simultaneously compute a segmentation of the image plane, a matching of points on the template to points on the segmenting boundary, and a decomposition of the template into a set of deformable parts. In particular, the interpretation of the shape template as a collection of an a priori unknown number of deformable parts - an important aspect of higher-level shape representations - emerges as a byproduct of our matching algorithm. On real-world data of running people and walking animals, we demonstrate that the proposed method can match strongly deformed shapes, even in cases where simple shape measures and optic flow methods fail.

This paper contributes two novel techniques in the context of image restoration by nonlocal filtering. First, we introduce an efficient implementation of the nonlocal means filter based on arranging the data in a cluster tree. The structuring of data allows for a fast and accurate preselection of similar patches. In contrast to previous approaches, the preselection is based on the same distance measure as used by the filter itself. It allows for large speedups, especially when the search for similar patches covers the whole image domain, i.e., when the filter is truly nonlocal. However, also in the windowed version of the filter, the cluster tree approach compares favorably to previous techniques in respect of quality versus computational cost. Second, we suggest an iterative version of the filter that is derived from a variational principle and is designed to yield nontrivial steady states. It reveals to be particularly useful in order to restore regular, textured patterns.

The introduction of statistical shape knowledge into level set based segmentation methods was shown to improve the segmentation of familiar structures in the presence of noise, clutter or partial occlusions. While most work has been focused on shape priors which are constant in time, it is clear that when tracking deformable shapes certain silhouettes may become more or less likely over time. In fact, the deformations of familiar objects such as the silhouettes of a walking person are often characterized by pronounced temporal correlations. In this paper, we propose a nonlinear dynamical shape prior for level set based image segmentation. Specifically, we propose to approximate the temporal evolution of the eigenmodes of the level set function by means of a mixture of autoregressive models. We detail how such shape priors "with memory" can be integrated into a variational framework for level set segmentation. As an application, we experimentally validate that the nonlinear dynamical prior drastically improves the tracking of a person walking in different directions, despite large amounts of clutter and noise.

The matching of planar shapes can be cast as a problem of finding the shortest path through a graph spanned by the two shapes, where the nodes of the graph encode the local similarity of respective points on each contour. While this problem can be solved using dynamic time warping, the complete search over the initial correspondence leads to cubic runtime in the number of sample points. In this paper, we cast the shape matching problem as one of finding the shortest circular path on a torus. We propose an algorithm to determine this shortest cycle which has provably sub-cubic runtime. Numerical experiments demonstrate that the proposed algorithm provides faster shape matching than previous methods. As an application, we show that it allows to efficiently compute a clustering of a shape data base.

So far global optimization techniques have been developed independently for the tasks of shape matching and image segmentation. In this paper we show that both tasks can in fact be solved simultaneously using global optimization. By computing cycles of minimal ratio in a large graph spanned by the product of the input image and a shape template, we are able to compute globally optimal segmentations of the image which are similar to a familiar shape and located in places of strong gradient. The presented approach is translation-invariant and robust to local and global scaling and rotation of the given shape. We show how it can be extended to incorporate invariance to similarity transformations. The particular structure of the graph allows for run-time and memory efficient implementations. Highly parallel implementations on graphics cards allow to produce globally optimal solutions in a few seconds only.

While the majority of competitive image segmentation methods are based on energy minimization, only few allow to efficiently determine globally optimal solutions. A graph-theoretic algorithm for finding globally optimal segmentations is given by the minimum ratio cycles, first applied to segmentation by Jermyn and Ishikawa (2001). In this paper we show that the class of image segmentation problems solvable by minimum ratio cycles is significantly larger than previously considered. In particular, they allow for the introduction of higher-order regularity of the region boundary. The key idea is to introduce an extended graph representation, where each node of the graph represents an image pixel as well as the orientation of the incoming line segment. With each graph edge representing a pair of adjacent line segments, edge weights can depend on the curvature. This way arbitrary positive functions of curvature can be introduced into globally optimal segmentation by minimum ratio cycles. In numerous experiments we demonstrate that compared to length-regularity the integration of curvature-regularity will drastically improve segmentation results. Moreover, we show an interesting relation to the snakes functional: minimum ratio cycles provide a way to find one of the few cases where the snakes functional has a meaningful global minimum.

The introduction of prior knowledge has greatly enhanced numerous purely low-level driven image processing algorithms. In this work, we focus on the problem of nonrigid image registration. A number of powerful registration criteria have been developed in the last decade, most prominently the criterion of maximum mutual information. Although this criterion provides for good registration results in many applications, it remains a purely low-level criterion. As a consequence, registration results will deteriorate once this low-level information is corrupted, due to noise, partial occlusions or missing image structure. In this paper, we will develop a Bayesian framework that allows to impose statistically learned prior knowledge about the joint intensity distribution into image registration methods. The prior is given by a kernel density estimate on the space of joint intensity distributions computed from a representative set of pre-registered image pairs. This nonparametric prior accurately models previously learned intensity relations between various image modalities and slice locations. Experimental results demonstrate that the resulting registration process is more robust to missing low-level information as it favors intensity correspondences statistically consistent with the learned intensity distributions.

In recent years, researchers have proposed introducing statistical shape knowledge into level set-based segmentation methods in order to cope with insufficient low-level information. While these priors were shown to drastically improve the segmentation of familiar objects, so far the focus has been on statistical shape priors which are static in time. Yet, in the context of tracking deformable objects, it is clear that certain silhouettes (such as those of a walking person) may become more or less likely over time. In this paper, we tackle the challenge of learning dynamical statistical models for implicitly represented shapes. We show how these can be integrated as dynamical shape priors in a Bayesian framework for level set-based image sequence segmentation. We assess the effect of such shape priors "with memory" on the tracking of familiar deformable objects in the presence of noise and occlusion. We show comparisons between dynamical and static shape priors, between models of pure deformation and joint models of deformation and transformation, and we quantitatively evaluate the segmentation accuracy as a function of the noise level and of the camera frame rate. Our experiments demonstrate that level set-based segmentation and tracking can be strongly improved by exploiting the temporal correlations among consecutive silhouettes which characterize deforming shapes.

For shapes represented as closed planar contours, we introduce a class of functionals which are invariant with respect to the Euclidean group and which are obtained by performing integral operations. While such integral invariants enjoy some of the desirable properties of their differential counterparts, such as locality of computation (which allows matching under occlusions) and uniqueness of representation (asymptotically), they do not exhibit the noise sensitivity associated with differential quantities and, therefore, do not require presmoothing of the input shape. Our formulation allows the analysis of shapes at multiple scales. Based on integral invariants, we define a notion of distance between shapes. The proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other; its computation results in optimal point correspondence as an intermediate step. Numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts, missing parts and noise. As a quantitative analysis, we report matching scores for shape retrieval from a database.

Based on a geometric interpretation of the optic flow constraint equation, we propose a conditional probability on the spatio-temporal image gradient. We consistently derive a variational approach for the segmentation of the image domain into regions of homogeneous motion. The proposed energy functional extends the Mumford-Shah functional from gray value segmentation to motion segmentation. It depends on the spatio-temporal image gradient calculated from only two consecutive images of an image sequence. Moreover, it depends on motion vectors for a set of regions and a boundary separating these regions. In contrast to most alternative approaches, the problems of motion estimation and motion segmentation are jointly solved by minimizing a single functional. Numerical evaluation with both explicit and implicit (level set based) representations of the boundary shows the strengths and limitations of our approach.

We propose a variational method for segmenting image sequences into spatiotemporal domains of homogeneous motion. To this end, we formulate the problem of motion estimation in the framework of Bayesian inference, using a prior which favors domain boundaries of minimal surface area. We derive a cost functional which depends on a surface in space-time separating a set of motion regions, as well as a set of vectors modeling the motion in each region. We propose a multiphase level set formulation of this functional, in which the surface and the motion regions are represented implicitly by a vector-valued level set function. Joint minimization of the proposed functional results in an eigenvalue problem for the motion model of each region and in a gradient descent evolution for the separating interface. Numerical results on real-world sequences demonstrate that minimization of a single cost functional generates a segmentation of space-time into multiple motion regions.

We address the problem of segmenting a sequence of images of natural scenes into disjoint regions that are characterized by constant spatio-temporal statistics. We model the spatio-temporal dynamics in each region by Gauss-Markov models, and infer the model parameters as well as the boundary of the regions in a variational optimization framework. Numerical results demonstrate that - in contrast to purely texture-based segmentation schemes - our method is effective in segmenting regions that differ in their dynamics even when spatial statistics are identical.

We introduce a novel optimization method based on semidefinite programming relaxations to the field of computer vision and apply it to the combinatorial problem of minimizing quadratic functionals in binary decision variables subject to linear constraints. The approach is (tuning) parameter-free and computes high-quality combinatorial solutions using interior-point methods (convex programming) and a randomized hyperplane technique. Apart from a symmetry condition, no assumptions (such as metric pairwise interactions) are made with respect to the objective criterion. As a consequence, the approach can be applied to a wide range of problems. Applications to unsupervised partitioning, figure-ground discrimination, and binary restoration are presented along with extensive ground-truth experiments. From the viewpoint of relaxation of the underlying combinatorial problem, we show the superiority of our approach to relaxations based on spectral graph theory and prove performance bounds.

Field models provide an elegant mathematical framework to analyze large-scale patterns of neural activity. On the microscopic level, these models are usually based on either a firing-rate picture or integrate-and-fire dynamics. This article shows that in spite of the large conceptual differences between the two types of dynamics, both generate closely related plane-wave solutions. Furthermore, for a large group of models, estimates about the network connectivity derived from the speed of these plane waves only marginally depend on the assumed class of microscopic dynamics. We derive quantitative results about this phenomenon and discuss consequences for the interpretation of experimental data.