The field of computer graphics was revolutionized by models such as NeRF and 3D Gaussian Splatting, displacing triangles as the dominant representation for photogrammetry. In this paper, we argue for a triangle comeback. We develop a differentiable renderer that directly optimizes triangles via end-to-end gradients. We achieve this by rendering each triangle as differentiable splats, combining the efficiency of triangles with the adaptive density of representations based on independent primitives. Compared to popular 2D and 3D Gaussian Splatting methods, our approach achieves competitive rendering and convergence speed, and demonstrates high visual quality. On the Mip-NeRF360 dataset, our method outperforms concurrent nonvolumetric primitives in visual fidelity and achieves higher perceptual quality than the state-of-the-art Zip-NeRF on indoor scenes. Triangles are simple, compatible with standard graphics stacks and GPU hardware, and highly efficient. Our results highlight the efficiency and effectiveness of triangle-based representations for high-quality novel view synthesis. Triangles bring us closer to mesh-based optimization by combining classical computer graphics with modern differentiable rendering frameworks. The project page is https://trianglesplatting.github.io/

We introduce HiT, a novel hierarchical neural field representation for 3D shapes that learns general hierarchies in a coarse-to-fine manner across different shape categories in an unsupervised setting. Our key contribution is a hierarchical transformer (HIT), where each level learns parent–child relationships of the tree hierarchy using a compressed codebook. This codebook enables the network to automatically identify common substructures across potentially diverse shape categories. Unlike previous works that constrain the task to a fixed hierarchical structure (e.g., binary), we impose no such restriction, except for limiting the total number of nodes at each tree level. This flexibility allows our method to infer the hierarchical structure directly from data, over multiple shape categories, and representing more general and complex hierarchies than prior approaches. When trained at scale with a reconstruction loss, our model captures meaningful containment relationships between parent and child nodes. We demonstrate its effectiveness through an unsupervised shape segmentation task over all 55 ShapeNet categories, where our method successfully segments shapes into multiple levels of granularity. Project Page: aditya-vora.github.io/HiT/

We present a novel approach to large-scale point cloud surface reconstruction by developing an efficient framework that converts an irregular point cloud into a signed distance field (SDF). Our backbone builds upon recent transformer-based architectures (i.e. PointTransformerV3), that serializes the point cloud into a locality-preserving sequence of tokens. We efficiently predict the SDF value at a point by aggregating nearby tokens, where fast approximate neighbors can be retrieved thanks to the serialization. We serialize the point cloud at different levels/scales, and non-linearly aggregate a feature to predict the SDF value. We show that aggregating across multiple scales is critical to overcome the approximations introduced by the serialization (i.e. false negatives in the neighborhood). Our frameworks sets the new state-of-the-art in terms of accuracy and efficiency (better or similar performance with half the latency of the best prior method, coupled with a simpler implementation), particularly on outdoor datasets where sparse-grid methods have shown limited performance.

Numerous works have recently integrated 3D camera control into foundational text-to-video models, but the resulting camera control is often imprecise, and video generation quality suffers. In this work, we analyze camera motion from a first principles perspective, uncovering insights that enable precise 3D camera manipulation without compromising synthesis quality. First, we determine that motion induced by camera movements in videos is low-frequency in nature. This motivates us to adjust train and test pose conditioning schedules, accelerating training convergence while improving visual and motion quality. Then, by probing the representations of an unconditional video diffusion transformer, we observe that they implicitly perform camera pose estimation under the hood, and only a sub-portion of their layers contain the camera information. This suggested us to limit the injection of camera conditioning to a subset of the architecture to prevent interference with other video features, leading to a 4× reduction of training parameters, improved training speed, and 10% higher visual quality. Finally, we complement the typical dataset for camera control learning with a curated dataset of 20K diverse, dynamic videos with stationary cameras. This helps the model distinguish between camera and scene motion and improves the dynamics of generated pose-conditioned videos. We compound these findings to design the Advanced 3D Camera Control (AC3D) architecture, the new state-of-the-art model for generative video modeling with camera control.

We introduce the Pose and Illumination agnostic Anomaly Detection (PIAD) problem, a generalization of pose-agnostic anomaly detection (PAD). Being illumination agnostic is critical, as it relaxes the assumption that training data for an object has to be acquired in the same light configuration of the query images that we want to test. Moreover, even if the object is placed within the same capture environment, being illumination agnostic implies that we can relax the assumption that the relative pose between environment light and query object has to match the one in the training data. We introduce a new dataset to study this problem, containing both synthetic and real-world examples, propose a new baseline for PIAD, and demonstrate how our baseline provides state-of-the-art results in both PAD and PIAD, not only in the new proposed dataset, but also in existing datasets that were designed for the simpler PAD problem. Project page: https://kaichen-yang.github.io/piad/.

There has been extensive progress in the reconstruction and generation of 4D scenes from monocular casually-captured video. While these tasks rely heavily on known camera poses, the problem of finding such poses using structure-from-motion (SfM) often depends on robustly separating static from dynamic parts of a video. The lack of a robust solution to this problem limits the performance of SfM camera-calibration pipelines. We propose a novel approach to video-based motion segmentation to identify the components of a scene that are moving w.r.t. a fixed world frame. Our simple but effective iterative method, RoMo, combines optical flow and epipolar cues with a pre-trained video segmentation model. It outperforms unsupervised baselines for motion segmentation as well as supervised baselines trained from synthetic data. More importantly, the combination of an off-the-shelf SfM pipeline with our segmentation masks establishes a new state-of-the-art on camera calibration for scenes with dynamic content, outperforming existing methods by a substantial margin.

Research on differentiable scene representations is consistently moving towards more efficient, real-time models. Recently, this has led to the popularization of splatting methods, which eschew the traditional ray-based rendering of radiance fields in favor of rasterization. This has yielded a significant improvement in rendering speeds due to the efficiency of rasterization algorithms and hardware, but has come at a cost: the approximations that make rasterization efficient also make implementation of light transport phenomena like reflection and refraction much more difficult. We propose a novel scene representation which avoids these approximations, but keeps the efficiency and reconstruction quality of splatting by leveraging a decades-old efficient volumetric mesh ray tracing algorithm which has been largely overlooked in recent computer vision research. The resulting model, which we name Radiant Foam, achieves rendering speed and quality comparable to Gaussian Splatting, without the constraints of rasterization. Unlike ray traced Gaussian models that use hardware ray tracing acceleration, our method requires no special hardware or APIs beyond the standard features of a programmable GPU.

3D Gaussian splatting (3DGS) is a popular radiance field method, with many application-specific extensions. Most variants rely on the same core algorithm: depth-sorting of Gaussian splats then rasterizing in primitive order. This ensures correct alpha compositing, but can cause rendering artifacts due to built-in approximations. Moreover, for a fixed representation, sorted rendering offers little control over render cost and visual fidelity. For example, and counter-intuitively, rendering a lower-resolution image is not necessarily faster. In this work, we address the above limitations by combining 3D Gaussian splatting with stochastic rasterization. Concretely, we leverage an unbiased Monte Carlo estimator of the volume rendering equation. This removes the need for sorting, and allows for accurate 3D blending of overlapping Gaussians. The number of Monte Carlo samples further imbues 3DGS with a way to trade off computation time and quality. We implement our method using OpenGL shaders, enabling efficient rendering on modern GPU hardware. At a reasonable visual quality, our method renders more than four times faster than sorted rasterization.

Segmenting an object in a video presents significant challenges. Each pixel must be accurately labeled, and these labels must remain consistent across frames. The difficulty increases when the segmentation is with arbitrary granularity, meaning the number of segments can vary arbitrarily, and masks are defined based on only one or a few sample images. In this paper, we address this issue by employing a pre-trained text to image diffusion model supplemented with an additional tracking mechanism. We demonstrate that our approach can effectively manage various segmentation scenarios and outperforms state-of-the-art alternatives. The project page is available at https://segment-me-in-time.github.io/

Modern text-to-video synthesis models demonstrate coherent, photorealistic generation of complex videos from a text description. However, most existing models lack fine-grained control over camera movement, which is critical for downstream applications related to content creation, visual effects, and 3D vision. Recently, new methods demonstrate the ability to generate videos with controllable camera poses---these techniques leverage pre-trained U-Net-based diffusion models that explicitly disentangle spatial and temporal generation. Still, no existing approach enables camera control for new, transformer-based video diffusion models that process spatial and temporal information jointly. Here, we propose to tame video transformers for 3D camera control using a ControlNet-like conditioning mechanism that incorporates spatiotemporal camera embeddings based on Plucker coordinates. The approach demonstrates state-of-the-art performance for controllable video generation after fine-tuning on the RealEstate10K dataset. To the best of our knowledge, our work is the first to enable camera control for transformer-based video diffusion models.

We present 4DiM, a cascaded diffusion model for 4D novel view synthesis (NVS), supporting generation with arbitrary camera trajectories and timestamps, in natural scenes, conditioned on one or more images. With a novel architecture and sampling procedure, we enable training on a mixture of 3D (with camera pose), 4D (pose+time) and video (time but no pose) data, which greatly improves generalization to unseen images and camera pose trajectories over prior works which generally operate in limited domains (e.g., object centric). 4DiM is the first-ever NVS method with intuitive metric-scale camera pose control enabled by our novel calibration pipeline for structure-from-motion-posed data. Experiments demonstrate that 4DiM outperforms prior 3D NVS models both in terms of image fidelity and pose alignment, while also enabling the generation of scene dynamics. 4DiM provides a general framework for a variety of tasks including single-image-to-3D, two-image-to-video (interpolation and extrapolation), and pose-conditioned video-to-video translation, which we illustrate qualitatively on a variety of scenes. See https://4d-diffusion.github.io for video samples.

Recent advances in radiance fields and novel view synthesis enable creation of realistic digital twins from photographs. However, current methods struggle with flat, texture-less surfaces, creating uneven and semi-transparent reconstructions, due to an ill-conditioned photometric reconstruction objective. Surface reconstruction methods solve this issue but sacrifice visual quality. We propose a novel hybrid 2D/3D representation that jointly optimizes constrained planar (2D) Gaussians for modeling flat surfaces and freeform (3D) Gaussians for the rest of the scene. Our end-to-end approach dynamically detects and refines planar regions, improving both visual fidelity and geometric accuracy. It achieves state-of-the-art depth estimation on ScanNet++ and ScanNetv2, and excels at mesh extraction without overfitting to a specific camera model, showing its effectiveness in producing high-quality reconstruction of indoor scenes.

Three-dimensional Gaussian Splatting (3DGS) is a promising technique for 3D reconstruction, offering efficient training and rendering speeds, making it suitable for real-time applications. However, current methods require highly controlled environments–no moving people or wind-blown elements, and consistent lighting–to meet the interview consistency assumption of 3DGS. This makes reconstruction of real-world captures problematic. We present SpotLessSplats, an approach that leverages pre-trained and general-purpose features coupled with robust optimization to effectively ignore transient distractors. Our method achieves state-of-the-art reconstruction quality both visually and quantitatively, on casual captures.

Recent breakthroughs in text-to-4D generation rely on pre-trained text-to-image and text-to-video models to generate dynamic 3D scenes. However, current text-to-4D methods face a three-way tradeoff between the quality of scene appearance, 3D structure, and motion. For example, text-to-image models and their 3D-aware variants are trained on internet-scale image datasets and can be used to produce scenes with realistic appearance and 3D structure—but no motion. Text-to-video models are trained on relatively smaller video datasets and can produce scenes with motion, but poorer appearance and 3D structure. While these models have complementary strengths, they also have opposing weaknesses, making it difficult to combine them in a way that alleviates this three-way tradeoff. Here, we introduce hybrid score distillation sampling, an alternating optimization procedure that blends supervision signals from multiple pre-trained diffusion models and incorporates benefits of each for high-fidelity text-to-4D generation. Using hybrid SDS, we demonstrate synthesis of 4D scenes with compelling appearance, 3D structure, and motion.

We introduce pixelSplat, a feed-forward model that learns to reconstruct 3D radiance fields parameterized by 3D Gaussian primitives from pairs of images. Our model features real-time and memory-efficient rendering for scalable training as well as fast 3D reconstruction at inference time. To overcome local minima inherent to sparse and locally supported representations, we predict a dense probability distribution over 3D and sample Gaussian means from that probability distribution. We make this sampling operation differentiable via a reparameterization trick, allowing us to back-propagate gradients through the Gaussian splatting representation. We benchmark our method on wide-baseline novel view synthesis on the real-world RealEstate10k and ACID datasets, where we outperform state-of-the-art light field transformers and accelerate rendering by 2.5 orders of magnitude while reconstructing an interpretable and ed-itable 3D radiance field. Additional materials can be found on the project website.11dcharatan.github.io/pixelsplat

Neural Radiance Fields (NeRFs) have shown promise in applications like view synthesis and depth estimation, but learning from multiview images faces inherent uncertain-ties. Current methods to quantify them are either heuristic or computationally demanding. We introduce Bayes'Rays, a post-hoc framework to evaluate uncertainty in any pre-trained NeRF without modifying the training process. Our method establishes a volumetric uncertainty field using spa-tial perturbations and a Bayesian Laplace approximation. We derive our algorithm statistically and show its superior performance in key metrics and applications. More results available at: https://bayesrays.github.io

Unsupervised learning of keypoints and landmarks has seen significant progress with the help of modern neural network architectures, but performance is yet to match the supervised counterpart, making their practicability questionable. We leverage the emergent knowledge within text-to-image diffusion models, towards more robust unsupervised keypoints. Our core idea is to find text embeddings that would cause the generative model to consistently attend to compact regions in images (i.e. keypoints). To do so, we simply optimize the text embedding such that the cross-attention maps within the denoising network are localized as Gaussians with small standard deviations. We validate our performance on multiple datasets: the CelebA, CUB-200-2011, Tai-Chi-HD, DeepFashion, and Human3.6m datasets. We achieve significantly improved accuracy, sometimes even outperforming supervised ones, particularly for data that is non-aligned and less curated. Our code is publicly available at the project page.

We present an approach to accelerate Neural Field training by efficiently selecting sampling locations. While Neural Fields have recently become popular, it is often trained by uniformly sampling the training domain, or through handcrafted heuristics. We show that improved convergence and final training quality can be achieved by a soft mining technique based on importance sampling: rather than either considering or ignoring a pixel completely, we weigh the corresponding loss by a scalar. To implement our idea we use Langevin Monte-Carlo sampling. We show that by doing so, regions with higher error are being selected more frequently, leading to more than 2x improvement in convergence speed. The code and related resources for this study are publicly available at project page.

Neural fields have emerged as a powerful and broadly applicable method for representing signals. However, in contrast to classical discrete digital signal processing, the portfolio of tools to process such representations is still severely limited and restricted to Euclidean domains. In this paper, we address this problem by showing how a prob-abilistic re-interpretation of neural fields can enable their training and inference processes to become “filter-aware”. The formulation we propose not only merges training and filtering in an efficient way, but also generalizes beyond the familiar Euclidean coordinate spaces to the more general set of smooth manifolds and convolutions induced by the actions of Lie groups. We demonstrate how this framework can enable novel integrations of signal processing techniques for neural field applications on both Euclidean do-mains, such as images and audio, as well as non-Euclidean domains, such as rotations and rays. A noteworthy benefit of our method is its applicability. Our method can be sum-marized as primarily a modification of the loss function, and in most cases does not require changes to the network ar-chitecture or the inference process.

Largely due to their implicit nature, neural fields lack a direct mechanism for filtering, as Fourier analysis from discrete signal processing is not directly applicable to these representations. Effective filtering of neural fields is critical to enable level-of-detail processing in downstream applications, and support operations that involve sampling the field on regular grids (e.g. marching cubes). Existing methods that attempt to decompose neural fields in the frequency domain either resort to heuristics or require extensive modifications to the neural field architecture. We show that via a simple modification, one can obtain neural fields that are low-pass filtered, and in turn show how this can be exploited to obtain a frequency decomposition of the entire signal. We demonstrate the validity of our technique by investigating level-of-detail reconstruction, and showing how coarser representations can be computed effectively. Source code is available at https://theialab.github.io/banf

While 3D Gaussian Splatting has recently become popular for neural rendering, current methods rely on carefully engineered cloning and splitting strategies for placing Gaussians, which does not always generalize and may lead to poor-quality renderings. For many real-world scenes this leads to their heavy dependence on good initializations. In this work, we rethink the set of 3D Gaussians as a random sample drawn from an underlying probability distribution describing the physical representation of the scene—in other words, Markov Chain Monte Carlo (MCMC) samples. Under this view, we show that the 3D Gaussian updates can be converted as Stochastic Gradient Langevin Dynamics (SGLD) update by simply introducing noise. We then rewrite the densification and pruning strategies in 3D Gaussian Splatting as simply a deterministic state transition of MCMC samples, removing these heuristics from the framework. To do so, we revise the ‘cloning’ of Gaussians into a relocalization scheme that approximately preserves sample probability. To encourage efficient use of Gaussians, we introduce an L1-regularizer on the Gaussians. On various standard evaluation scenes, we show that our method provides improved rendering quality, easy control over the number of Gaussians, and robustness to initialization. The project website is available at https://3dgs-mcmc.github.io/.

Neural Radiance Fields (NeRFs) have demonstrated amazing ability to synthesize images of 3D scenes from novel views. However, they rely upon specialized volumetric rendering algorithms based on ray marching that are mismatched to the capabilities of widely deployed graphics hardware. This paper introduces a new NeRF representation based on textured polygons that can synthesize novel images efficiently with standard rendering pipelines. The NeRF is represented as a set of polygons with textures representing binary opacities and feature vectors. Traditional rendering of the polygons with a z-buffer yields an image with features at every pixel, which are interpreted by a small, view-dependent MLP running in a fragment shader to produce a final pixel color. This approach enables NeRFs to be rendered with the traditional polygon rasterization pipeline, which provides massive pixel-level parallelism, achieving interactive frame rates on a wide range of compute platforms, including mobile phones. Project page: https://mobile-nerf.github.io

Generating faithful visualizations of human faces requires capturing both coarse and fine-level details of the face geometry and appearance. Existing methods are either data-driven, requiring an extensive corpus of data not publicly accessible to the research community, or fail to capture fine details because they rely on geometric face models that cannot represent fine-grained details in texture with a mesh discretization and linear deformation designed to model only a coarse face geometry. We introduce a method that bridges this gap by drawing inspiration from traditional computer graphics techniques. Unseen expressions are modeled by blending appearance from a sparse set of extreme poses. This blending is performed by measuring local volumetric changes in those expressions and locally reproducing their appearance whenever a similar expression is performed at test time. We show that our method generalizes to unseen expressions, adding fine-grained effects on top of smooth volumetric deformations of a face, and demonstrate how it generalizes beyond faces.

Traditional 3D scene understanding approaches rely on labeled 3D datasets to train a model for a single task with supervision. We propose OpenScene, an alternative approach where a model predicts dense features for 3D scene points that are co-embedded with text and image pixels in CLIP feature space. This zero-shot approach enables task-agnostic training and open-vocabulary queries. For example, to perform SOTA zero-shot 3D semantic segmentation it first infers CLIP features for every 3D point and later classifies them based on similarities to embeddings of arbitrary class labels. More interestingly, it enables a suite of open-vocabulary scene understanding applications that have never been done before. For example, it allows a user to enter an arbitrary text query and then see a heat map indicating which parts of a scene match. Our approach is effective at identifying objects, materials, affordances, activities, and room types in complex 3D scenes, all using a single model trained without any labeled 3D data.

Neural radiance fields (NeRF) excel at synthesizing new views given multi-view, calibrated images of a static scene. When scenes include distractors, which are not persistent during image capture (moving objects, lighting variations, shadows), artifacts appear as view-dependent effects or ‘floaters’. To cope with distractors, we advocate a form of robust estimation for NeRF training, modeling distractors in training data as outliers of an optimization problem. Our method successfully removes outliers from a scene and improves upon our baselines, on synthetic and real-world scenes. Our technique is simple to incorporate in modern NeRF frameworks, with few hyper-parameters. It does not assume a priori knowledge of the types of distractors, and is instead focused on the optimization problem rather than pre-processing or modeling transient objects. More results at https://robustnerf.github.io/public.

Camera pose estimation is a key step in standard 3D reconstruction pipelines that operate on a dense set of images of a single object or scene. However, methods for pose estimation often fail when only a few images are available because they rely on the ability to robustly identify and match visual features between image pairs. While these methods can work robustly with dense camera views, capturing a large set of images can be time-consuming or impractical. We propose SparsePose for recovering accurate camera poses given a sparse set of wide-baseline images (fewer than 10). The method learns to regress initial camera poses and then iteratively refine them after training on a large-scale dataset of objects (Co3D: Common Objects in 3D). SparsePose significantly outperforms conventional and learning-based baselines in recovering accurate camera rotations and translations. We also demonstrate our pipeline for high-fidelity 3D reconstruction using only 5–9 images of an object. Project webpage: https://sparsepose.github.io/

This paper presents an end-to-end neural mapping method for camera localization, encoding a whole scene into a grid of latent codes, with which a Transformer-based auto-decoder regresses 3D coordinates of query pixels. State-of-the-art camera localization methods require each scene to be stored as a 3D point cloud with per-point features, which takes several gigabytes of storage per scene. While compression is possible, the performance drops significantly at high compression rates. NeuMap achieves extremely high compression rates with minimal performance drop by using 1) learnable latent codes to store scene information and 2) a scene-agnostic Transformer-based auto-decoder to infer coordinates for a query pixel. The scene-agnostic network design also learns robust matching priors by training with large-scale data, and further allows us to just optimize the codes quickly for a new scene while fixing the network weights. Extensive evaluations with five benchmarks show that NeuMap outperforms all the other coordinate regression methods significantly and reaches similar performance as the feature matching methods while having a much smaller scene representation size. For example, NeuMap achieves 39.1% accuracy in Aachen night benchmark with only 6MB of data, while other compelling methods require 100MB or a few gigabytes and fail completely under high compression settings. The codes are available at https://github.com/Tangshitao/NeuMap.

Neural fields have rapidly been adopted for representing 3D signals, but their application to more classical 2D image-processing has been relatively limited. In this paper, we consider one of the most important operations in image processing: upsampling. In deep learning, learnable upsampling layers have extensively been used for single image super-resolution. We propose to parameterize upsampling kernels as neural fields. This parameterization leads to a compact architecture that obtains a 40-fold reduction in the number of parameters when compared with competing arbitrary-scale super-resolution architectures. When upsampling images of size 256×256 we show that our architecture is 2x-10x more efficient than competing arbitrary-scale super-resolution architectures, and more efficient than sub-pixel convolutions when instantiated to a single-scale model. In the general setting, these gains grow polynomially with the square of the target scale. We validate our method on standard benchmarks showing such efficiency gains can be achieved without sacrifices in super-resolution performance. https://cuf-paper.github.io

In this work, we introduce CC3D, a conditional generative model that synthesizes complex 3D scenes conditioned on 2D semantic scene layouts, trained using single-view images. Different from most existing 3D GANs that limit their applicability to aligned single objects, we focus on generating complex scenes with multiple objects, by modeling the compositional nature of 3D scenes. By devising a 2D layout-based approach for 3D synthesis and implementing a new 3D field representation with a stronger geometric inductive bias, we have created a 3D GAN that is both efficient and of high quality, while allowing for a more controllable generation process. Our evaluations on synthetic 3D-FRONT and real-world KITTI-360 datasets demonstrate that our model generates scenes of improved visual and geometric quality in comparison to previous works.

We introduce a technique for pairwise registration of neural fields that extends classical optimization-based local registration (i.e. ICP) to operate on Neural Radiance Fields (NeRF)-neural 3D scene representations trained from collections of calibrated images. NeRF does not decompose illumination and color, so to make registration invariant to illumination, we introduce the concept of a “surface field” - a field distilled from a pre-trained NeRF model that measures the likelihood of a point being on the surface of an object. We then cast nerf2nerf registration as a robust optimization that iteratively seeks a rigid transformation that aligns the surface fields of the two scenes. We evaluate the effectiveness of our technique by introducing a dataset of pre-trained NeRF scenes - our synthetic scenes enable quantitative evaluations and comparisons to classical registration techniques, while our real scenes demonstrate the validity of our technique in real-world scenarios. Additional results available at: https://nerf2nerf.github.io

Text-to-image diffusion models are now capable of generating images that are often indistinguishable from real images. To generate such images, these models must understand the semantics of the objects they are asked to generate. In this work we show that, without any training, one can leverage this semantic knowledge within diffusion models to find semantic correspondences – locations in multiple images that have the same semantic meaning. Specifically, given an image, we optimize the prompt embeddings of these models for maximum attention on the regions of interest. These optimized embeddings capture semantic information about the location, which can then be transferred to another image. By doing so we obtain results on par with the strongly supervised state of the art on the PF-Willow dataset and significantly outperform (20.9% relative for the SPair-71k dataset) any existing weakly- or unsupervised method on PF-Willow, CUB-200 and SPair-71k datasets.

While deep learning techniques have become extremely popular for solving a broad range of optimization problems, methods to enforce hard constraints during optimization, particularly on deep neural networks, remain underdeveloped. Inspired by the rich literature on meshless interpolation and its extension to spectral collocation methods in scientific computing, we develop a series of approaches for enforcing hard constraints on neural fields, which we refer to as Constrained Neural Fields (CNF). The constraints can be specified as a linear operator applied to the neural field and its derivatives. We also design specific model representations and training strategies for problems where standard models may encounter difficulties, such as conditioning of the system, memory consumption, and capacity of the network when being constrained. Our approaches are demonstrated in a wide range of real-world applications. Additionally, we develop a framework that enables highly efficient model and constraint specification, which can be readily applied to any downstream task where hard constraints need to be explicitly satisfied during optimization.

We introduce a method for instance proposal generation for 3D point clouds. Existing techniques typically directly regress proposals in a single feed-forward step, leading to inaccurate estimation. We show that this serves as a critical bottleneck, and propose a method based on iterative bilateral filtering with learned kernels. Following the spirit of bilateral filtering, we consider both the deep feature embeddings of each point, as well as their locations in the 3D space. We show via synthetic experiments that our method brings drastic improvements when generating instance proposals for a given point of interest. We further validate our method on the challenging ScanNet benchmark, achieving the best instance segmentation performance amongst the sub-category of top-down methods.

Polygonal meshes are ubiquitous, but have only played a relatively minor role in the deep learning revolution. State-of-the-art neural generative models for 3D shapes learn implicit functions and generate meshes via expensive iso-surfacing. We overcome these challenges by employing a classical spatial data structure from computer graphics, Binary Space Partitioning (BSP), to facilitate 3D learning. The core operation of BSP involves recursive subdivision of 3D space to obtain convex sets. By exploiting this property, we devise BSP-Net, a network that learns to represent a 3D shape via convex decomposition without supervision. The network is trained to reconstruct a shape using a set of convexes obtained from a BSP-tree built over a set of planes, where the planes and convexes are both defined by learned network weights. BSP-Net directly outputs polygonal meshes from the inferred convexes. The generated meshes are watertight, compact (i.e., low-poly), and well suited to represent sharp geometry. We show that the reconstruction quality by BSP-Net is competitive with those from state-of-the-art methods while using much fewer primitives.We also explore variations to BSP-Net including using a more generic decoder for reconstruction, more general primitives than planes, as well as training a generative model with variational auto-encoders.

Data is the driving force of machine learning, with the amount and quality of training data often being more important for the performance of a system than architecture and training details. But collecting, processing and annotating real data at scale is difficult, expensive, and frequently raises additional privacy, fairness and legal concerns. Synthetic data is a powerful tool with the potential to address these shortcomings: 1) it is cheap 2) supports rich ground-truth annotations 3) offers full control over data and 4) can circumvent or mitigate problems regarding bias, privacy and licensing. Unfortunately, software tools for effective data generation are less mature than those for architecture design and training, which leads to fragmented generation efforts. To address these problems we introduce Kubric, an open-source Python framework that interfaces with PyBullet and Blender to generate photo-realistic scenes, with rich annotations, and seamlessly scales to large jobs distributed over thousands of machines, and generating TBs of data. We demonstrate the effectiveness of Kubric by presenting a series of 13 different generated datasets for tasks ranging from studying 3D NeRF models to optical flow estimation. We release Kubric, the used assets, all of the generation code, as well as the rendered datasets for reuse and modification.

We extend neural 3D representations to allow for intu-itive and interpretable user control beyond novel view ren-dering (i. e. camera control). We allow the user to annotate which part of the scene one wishes to control with just a small number of mask annotations in the training images. Our key idea is to treat the attributes as latent variables that are regressed by the neural network given the scene en-coding. This leads to afew-shot learning framework, where attributes are discovered automatically by the framework, when annotations are not provided. We apply our method to various scenes with different types of controllable attributes (e.g. expression control on human faces, or state control in movement of inanimate objects). Overall, we demonstrate, to the best of our knowledge, for the first time novel view and novel attribute re-rendering of scenes from a single video.

We present Panoptic Neural Fields (PNF), an object-aware neural scene representation that decomposes a scene into a set of objects (things) and background (stuff). Each object is represented by an oriented 3D bounding box and a multi-layer perceptron (MLP) that takes position, direction, and time and outputs density and radiance. The background stuff is represented by a similar MLP that additionally outputs semantic labels. Each object MLPs are instance-specific and thus can be smaller and faster than previous object-aware approaches, while still leveraging category-specific priors incorporated via meta-learned initialization. Our model builds a panoptic radiance field representation of any scene from just color images. We use off-the-shelf algorithms to predict camera poses, object tracks, and 2D image semantic segmentations. Then we jointly optimize the MLP weights and bounding box parameters using analysis-by-synthesis with self-supervision from color images and pseudo-supervision from predicted semantic segmentations. During experiments with real-world dynamic scenes, we find that our model can be used effectively for several tasks like novel view synthesis, 2D panoptic segmentation, 3D scene editing, and multiview depth prediction.

We present a method for learning a generative 3D model based on neural radiance fields, trained solely from data with only single views of each object. While generating realistic images is no longer a difficult task, producing the corresponding 3D structure such that they can be rendered from different views is non-trivial. We show that, unlike existing methods, one does not need multi-view data to achieve this goal. Specifically, we show that by reconstructing many images aligned to an approximate canonical pose with a single network conditioned on a shared latent space, you can learn a space of radiance fields that models shape and appearance for a class of objects. We demonstrate this by training models to reconstruct object categories using datasets that contain only one view of each subject without depth or geometry information. Our experiments show that we achieve state-of-the-art results in novel view synthesis and high-quality results for monocular depth prediction. https://lolnerf.github.io.

The goal of this work is to perform 3D reconstruction and novel view synthesis from data captured by scanning platforms commonly deployed for world mapping in urban outdoor environments (e.g., Street View). Given a sequence of posed RGB images and lidar sweeps acquired by cameras and scanners moving through an outdoor scene, we produce a model from which 3D surfaces can be extracted and novel RGB images can be synthesized. Our approach extends Neural Radiance Fields, which has been demonstrated to synthesize realistic novel images for small scenes in controlled settings, with new methods for leveraging asynchronously captured lidar data, for addressing exposure variation between captured images, and for leveraging predicted image segmentations to supervise densities on rays pointing at the sky. Each of these three extensions provides significant performance improvements in experiments on Street View data. Our system produces state-of-the-art 3D surface reconstructions and synthesizes higher quality novel views in comparison to both traditional methods (e.g. COLMAP) and recent neural representations (e.g. Mip-NeRF).

A classical problem in computer vision is to infer a 3D scene representation from few images that can be used to render novel views at interactive rates. Previous work focuses on reconstructing pre-defined 3D representations, e.g. textured meshes, or implicit representations, e.g. radiance fields, and often requires input images with precise camera poses and long processing times for each novel scene. In this work, we propose the Scene Representation Transformer (SRT), a method which processes posed or unposed RGB images of a new area, infers a “set-latent scene representation ”, and synthesises novel views, all in a single feed-forward pass. To calculate the scene representation, we propose a generalization of the Vision Transformer to sets of images, enabling global information integration, and hence 3D reasoning. An efficient decoder transformer parameterizes the light field by attending into the scene representation to render novel views. Learning is supervised end-to-end by minimizing a novel-view reconstruction error. We show that this method outperforms recent baselines in terms of PSNR and speed on synthetic datasets, including a new dataset created for the paper. Further, we demonstrate that SRT scales to support interactive visualization and semantic segmentation of real-world outdoor environments using Street View imagery.

In the era of deep learning, human pose estimation from multiple cameras with unknown calibration has received little attention to date. We show how to train a neural model to perform this task with high precision and minimal latency overhead. The proposed model takes into account joint location uncertainty due to occlusion from multiple views, and requires only 2D keypoint data for training. Our method outperforms both classical bundle adjustment and weakly-supervised monocular 3D baselines on the well-established Human3.6M dataset, as well as the more challenging in-the-wild Ski-Pose PTZ dataset.

We present Neural Descriptor Fields (NDFs), an object representation that encodes both points and relative poses between an object and a target (such as a robot gripper or a rack used for hanging) via category-level descriptors. We employ this representation for object manipulation, where given a task demonstration, we want to repeat the same task on a new object instance from the same category. We propose to achieve this objective by searching (via optimization) for the pose whose descriptor matches that observed in the demonstration. NDFs are conveniently trained in a self-supervised fashion via a 3D auto-encoding task that does not rely on expert-labeled keypoints. Further, NDFs are SE(3)-equivariant, guaranteeing performance that generalizes across all possible 3D object translations and rotations. We demonstrate learning of manipulation tasks from few (∼5-10) demonstrations both in simulation and on a real robot. Our performance generalizes across both object instances and 6-DoF object poses, and significantly outperforms a recent baseline that relies on 2D descriptors. Project website: https://yilundu.github.io/ndf/

Given a monocular video, segmenting and decoupling dynamic objects while recovering the static environment is a widely studied problem in machine intelligence. Existing solutions usually approach this problem in the image domain, limiting their performance and understanding of the environment. We introduce Decoupled Dynamic Neural Radiance Field (D^2NeRF), a self-supervised approach that takes a monocular video and learns a 3D scene representation which decouples moving objects, including their shadows, from the static background. Our method represents the moving objects and the static background by two separate neural radiance fields with only one allowing for temporal changes. A naive implementation of this approach leads to the dynamic component taking over the static one as the representation of the former is inherently more general and prone to overfitting. To this end, we propose a novel loss to promote correct separation of phenomena. We further propose a shadow field network to detect and decouple dynamically moving shadows. We introduce a new dataset containing various dynamic objects and shadows and demonstrate that our method can achieve better performance than state-of-the-art approaches in decoupling dynamic and static 3D objects, occlusion and shadow removal, and image segmentation for moving objects. Project page: https://d2nerf.github.io/

We introduce neural dual contouring (NDC), a new data-driven approach to mesh reconstruction based on dual contouring (DC). Like traditional DC, it produces exactly one vertex per grid cell and one quad for each grid edge intersection, a natural and efficient structure for reproducing sharp features. However, rather than computing vertex locations and edge crossings with hand-crafted functions that depend directly on difficult-to-obtain surface gradients, NDC uses a neural network to predict them. As a result, NDC can be trained to produce meshes from signed or unsigned distance fields, binary voxel grids, or point clouds (with or without normals); and it can produce open surfaces in cases where the input represents a sheet or partial surface. During experiments with five prominent datasets, we find that NDC, when trained on one of the datasets, generalizes well to the others. Furthermore, NDC provides better surface reconstruction accuracy, feature preservation, output complexity, triangle quality, and inference time in comparison to previous learned (e.g., neural marching cubes, convolutional occupancy networks) and traditional (e.g., Poisson) methods. Code and data are available at https://github.com/czq142857/NDC.

We propose a deep network that can be trained to tackle image reconstruction and classification problems that involve detection of multiple object instances, without any supervision regarding their whereabouts. The network learns to extract the most significant K patches, and feeds these patches to a task-specific network – e.g., auto-encoder or classifier – to solve a domain specific problem. The challenge in training such a network is the non-differentiable top-K selection process. To address this issue, we lift the training optimization problem by treating the result of top-K selection as a slack variable, resulting in a simple, yet effective, multi-stage training. Our method is able to learn to detect recurring structures in the training dataset by learning to reconstruct images. It can also learn to localize structures when only knowledge on the occurrence of the object is provided, and in doing so it outperforms the state-of-the-art. Code available at https://github.com/ubc-vision/mist

With the advent of Neural Radiance Fields (NeRF), neural networks can now render novel views of a 3D scene with quality that fools the human eye. Yet, generating these images is very computationally intensive, limiting their applicability in practical scenarios. In this paper, we propose a technique based on spatial decomposition capable of mitigating this issue. Our key observation is that there are diminishing returns in employing larger (deeper and/or wider) networks. Hence, we propose to spatially decompose a scene and dedicate smaller networks for each decomposed part. When working together, these networks can render the whole scene. This allows us near-constant inference time regardless of the number of decomposed parts. Moreover, we show that a Voronoi spatial decomposition is preferable for this purpose, as it is provably compatible with the Painter’s Algorithm for efficient and GPU-friendly rendering. Our experiments show that for real-world scenes, our method provides up to 3× more efficient inference than NeRF (with the same rendering quality), or an improvement of up to 1.0 dB in PSNR (for the same inference cost).

Invariance and equivariance to the rotation group have been widely discussed in the 3D deep learning community for pointclouds. Yet most proposed methods either use complex mathematical tools that may limit their accessibility, or are tied to specific input data types and network architectures. In this paper, we introduce a general framework built on top of what we call Vector Neuron representations for creating SO (3) -equivariant neural networks for pointcloud processing. Extending neurons from 1D scalars to 3D vectors, our vector neurons enable a simple mapping of SO (3) actions to latent spaces thereby providing a framework for building equivariance in common neural operations – including linear layers, non-linearities, pooling, and normalizations. Due to their simplicity, vector neurons are versatile and, as we demonstrate, can be incorporated into diverse network architecture backbones, allowing them to process geometry inputs in arbitrary poses. Despite its simplicity, our method performs comparably well in accuracy and generalization with other more complex and specialized state-of-the-art methods on classification and segmentation tasks. We also show for the first time a rotation equivariant reconstruction network. Source code is available at https://github.com/FlyingGiraffe/vnn.

We propose a novel framework for finding correspondences in images based on a deep neural network that, given two images and a query point in one of them, finds its correspondence in the other. By doing so, one has the option to query only the points of interest and retrieve sparse correspondences, or to query all points in an image and obtain dense mappings. Importantly, in order to capture both local and global priors, and to let our model relate between image regions using the most relevant among said priors, we realize our network using a transformer. At inference time, we apply our correspondence network by recursively zooming in around the estimates, yielding a multiscale pipeline able to provide highly-accurate correspondences. Our method significantly outperforms the state of the art on both sparse and dense correspondence problems on multiple datasets and tasks, ranging from wide-baseline stereo to optical flow, without any retraining for a specific dataset. We commit to releasing data, code, and all the tools necessary to train from scratch and ensure reproducibility.

Capsule networks aim to parse images into a hierarchy of objects, parts and relations. While promising, they remain limited by an inability to learn effective low level part descriptions. To address this issue we propose a way to learn primary capsule encoders that detect atomic parts from a single image. During training we exploit motion as a powerful perceptual cue for part definition, with an expressive decoder for part generation within a layered image model with occlusion. Experiments demonstrate robust part discovery in the presence of multiple objects, cluttered backgrounds, and occlusion. The learned part decoder is shown to infer the underlying shape masks, effectively filling in occluded regions of the detected shapes. We evaluate FlowCapsules on unsupervised part segmentation and unsupervised image classification.

We propose a self-supervised capsule architecture for 3D point clouds. We compute capsule decompositions of objects through permutation-equivariant attention, and self-supervise the process by training with pairs of randomly rotated objects. Our key idea is to aggregate the attention masks into semantic keypoints, and use these to supervise a decomposition that satisfies the capsule invariance/equivariance properties. This not only enables the training of a semantically consistent decomposition, but also allows us to learn a canonicalization operation that enables object-centric reasoning. To train our neural network we require neither classification labels nor manually-aligned training datasets. Yet, by learning an object-centric representation in a self-supervised manner, our method outperforms the state-of-the-art on 3D point cloud reconstruction, canonicalization, and unsupervised classification.

Polygonal meshes are ubiquitous in the digital 3D domain, yet they have only played a minor role in the deep learning revolution. Leading methods for learning generative models of shapes rely on implicit functions, and generate meshes only after expensive iso-surfacing routines. To overcome these challenges, we are inspired by a classical spatial data structure from computer graphics, Binary Space Partitioning (BSP), to facilitate 3D learning. The core ingredient of BSP is an operation for recursive subdivision of space to obtain convex sets. By exploiting this property, we devise BSP-Net, a network that learns to represent a 3D shape via convex decomposition. Importantly, BSP-Net is unsupervised since no convex shape decompositions are needed for training. The network is trained to reconstruct a shape using a set of convexes obtained from a BSP-tree built on a set of planes. The convexes inferred by BSP-Net can be easily extracted to form a polygon mesh, without any need for iso-surfacing. The generated meshes are compact (i.e., low-poly) and well suited to represent sharp geometry; they are guaranteed to be watertight and can be easily parameterized. We also show that the reconstruction quality by BSP-Net is competitive with state-of-the-art methods while using much fewer primitives. Code is available at https://github.com/czq142857/BSP-NET-original.

Any solid object can be decomposed into a collection of convex polytopes (in short, convexes). When a small number of convexes are used, such a decomposition can be thought of as a piece-wise approximation of the geometry. This decomposition is fundamental in computer graphics, where it provides one of the most common ways to approximate geometry, for example, in real-time physics simulation. A convex object also has the property of being simultaneously an explicit and implicit representation: one can interpret it explicitly as a mesh derived by computing the vertices of a convex hull, or implicitly as the collection of half-space constraints or support functions. Their implicit representation makes them particularly well suited for neural network training, as they abstract away from the topology of the geometry they need to represent. However, at testing time, convexes can also generate explicit representations - polygonal meshes - which can then be used in any downstream application. We introduce a network architecture to represent a low dimensional family of convexes. This family is automatically derived via an auto-encoding process. We investigate the applications of this architecture including automatic convex decomposition, image to 3D reconstruction, and part-based shape retrieval.

Many problems in computer vision require dealing with sparse, unordered data in the form of point clouds. Permutation-equivariant networks have become a popular solution - they operate on individual data points with simple perceptrons and extract contextual information with global pooling. This can be achieved with a simple normalization of the feature maps, a global operation that is unaffected by the order. In this paper, we propose Attentive Context Normalization (ACN), a simple yet effective technique to build permutation-equivariant networks robust to outliers. Specifically, we show how to normalize the feature maps with weights that are estimated within the network, excluding outliers from this normalization. We use this mechanism to leverage two types of attention: local and global - by combining them, our method is able to find the essential data points in high-dimensional space in order to solve a given task. We demonstrate through extensive experiments that our approach, which we call Attentive Context Networks (ACNe), provides a significant leap in performance compared to the state-of-the-art on camera pose estimation, robust fitting, and point cloud classification under noise and outliers. Source code: https://github.com/vcg-uvic/acne.

We describe a novel approach for compressing truncated signed distance fields (TSDF) stored in 3D voxel grids, and their corresponding textures. To compress the TSDF, our method relies on a block-based neural network architecture trained end-to-end, achieving state-of-the-art rate-distortion trade-off. To prevent topological errors, we losslessly com- press the signs of the TSDF, which also upper bounds the reconstruction error by the voxel size. To compress the corresponding texture, we designed a fast block-based UV parameterization, generating coherent texture maps that can be effectively compressed using existing video compression algorithms. We demonstrate the performance of our algo- rithms on two 4D performance capture datasets, reducing bitrate by 66% for the same distortion, or alternatively re- ducing the distortion by 50% for the same bitrate, compared to the state-of-the-art.

We introduce an end-to-end learnable technique to robustly identify feature edges in 3D point cloud data. We represent these edges as a collection of parametric curves (i.e.,~lines, circles, and B-splines). Accordingly, our deep neural network, coined PIE-NET, is trained for parametric inference of edges. The network relies on a "region proposal" architecture, where a first module proposes an over-complete collection of edge and corner points, and a second module ranks each proposal to decide whether it should be considered. We train and evaluate our method on the ABC dataset, a large dataset of CAD models, and compare our results to those produced by traditional (non-learning) processing pipelines, as well as a recent deep learning based edge detector (EC-NET). Our results significantly improve over the state-of-the-art from both a quantitative and qualitative standpoint.

We present a generative model for stroke-based drawing tasks which is able to model complex free-form structures. While previous approaches rely on sequence-based models for drawings of basic objects or handwritten text, we propose a model that treats drawings as a collection of strokes that can be composed into complex structures such as diagrams (e.g., flow-charts). At the core of the approach lies a novel auto-encoder that projects variable-length strokes into a latent space of fixed dimension. This representation space allows a relational model, operating in latent space, to better capture the relationship between strokes and to predict subsequent strokes. We demonstrate qualitatively and quantitatively that our proposed approach is able to model the appearance of individual strokes, as well as the compositional structure of larger diagram drawings. Our approach is suitable for interactive use cases such as auto-completing diagrams. We make code and models publicly available at https://eth-ait.github.io/cose.

We present ShapeFlow, a flow-based model for learning a deformation space for entire classes of 3D shapes with large intra-class variations. ShapeFlow allows learning a multi-template deformation space that is agnostic to shape topology, yet preserves fine geometric details. Different from a generative space where a latent vector is directly decoded into a shape, a deformation space decodes a vector into a continuous flow that can advect a source shape towards a target. Such a space naturally allows the disentanglement of geometric style (coming from the source) and structural pose (conforming to the target). We parametrize the deformation between geometries as a learned continuous flow field via a neural network and show that such deformations can be guaranteed to have desirable properties, such as bijectivity, freedom from self-intersections, or volume preservation. We illustrate the effectiveness of this learned deformation space for various downstream applications, including shape generation via deformation, geometric style transfer, unsupervised learning of a consistent parameterization for entire classes of shapes, and shape interpolation.

Volumetric (4D) performance capture is fundamental for AR/VR content generation. Whereas previous work in 4D performance capture has shown impressive results in studio settings, the technology is still far from being accessible to a typical consumer who, at best, might own a single RGBD sensor. Thus, in this work, we propose a method to synthesize free viewpoint renderings using a single RGBD camera. The key insight is to leverage previously seen “calibration” images of a given user to extrapolate what should be rendered in a novel viewpoint from the data available in the sensor. Given these past observations from multiple viewpoints, and the current RGBD image from a fixed view, we propose an end-to-end framework that fuses both these data sources to generate novel renderings of the performer. We demonstrate that the method can produce high fidelity images, and handle extreme changes in subject pose and camera viewpoints. We also show that the system generalizes to performers not seen in the training data. We run exhaustive experiments demonstrating the effectiveness of the proposed semi-parametric model (i.e. calibration images available to the neural network) compared to other state of the art machine learned solutions. Further, we compare the method with more traditional pipelines that employ multi-view capture. We show that our framework is able to achieve compelling results, with substantially less infrastructure than previously required.

We propose a novel image sampling method for differentiable image transformation in deep neural networks. The sampling schemes currently used in deep learning, such as Spatial Transformer Networks, rely on bilinear interpolation, which performs poorly under severe scale changes, and more importantly, results in poor gradient propagation. This is due to their strict reliance on direct neighbors. Instead, we propose to generate random auxiliary samples in the vicinity of each pixel in the sampled image, and create a linear approximation with their intensity values. We then use this approximation as a differentiable formula for the transformed image. We demonstrate that our approach produces more representative gradients with a wider basin of convergence for image alignment, which leads to considerable performance improvements when training networks for registration and classification tasks. This is not only true under large downsampling, but also when there are no scale changes. We compare our approach with multi-scale sampling and show that we outperform it. We then demonstrate that our improvements to the sampler are compatible with other tangential improvements to Spatial Transformer Networks and that it further improves their performance.

Abstract We present an incremental Voronoi vertex labelling algorithm for approximating contours, medial axes and dominant points (high curvature points) from 2D point sets. Though there exist many number of algorithms for reconstructing curves, medial axes or dominant points, a unified framework capable of approximating all the three in one place from points is missing in the literature. Our algorithm estimates the normals at each sample point through poles (farthest Voronoi vertices of a sample point) and uses the estimated normals and the corresponding tangents to determine the spatial locations (inner or outer) of the Voronoi vertices with respect to the original curve. The vertex classification helps to construct a piece‐wise linear approximation to the object boundary. We provide a theoretical analysis of the algorithm for points non‐uniformly (ε‐sampling) sampled from simple, closed, concave and smooth curves. The proposed framework has been thoroughly evaluated for its usefulness using various test data. Results indicate that even sparsely and non‐uniformly sampled curves with outliers or collection of curves are faithfully reconstructed by the proposed algorithm.

Abstract The medial axis transform has applications in numerous fields including visualization, computer graphics, and computer vision. Unfortunately, traditional medial axis transformations are usually brittle in the presence of outliers, perturbations and/or noise along the boundary of objects. To overcome this limitation, we introduce a new formulation of the medial axis transform which is naturally robust in the presence of these artefacts. Unlike previous work which has approached the medial axis from a computational geometry angle, we consider it from a numerical optimization perspective. In this work, we follow the definition of the medial axis transform as ‘the set of maximally inscribed spheres’. We show how this definition can be formulated as a least squares relaxation where the transform is obtained by minimizing a continuous optimization problem. The proposed approach is inherently parallelizable by performing independent optimization of each sphere using Gauss–Newton, and its least‐squares form allows it to be significantly more robust compared to traditional computational geometry approaches. Extensive experiments on 2D and 3D objects demonstrate that our method provides superior results to the state of the art on both synthetic and real‐data.

We present an autonomous scanning approach which allows multiple robots to perform collaborative scanning for dense 3D reconstruction of unknown indoor scenes. Our method plans scanning paths for several robots, allowing them to efficiently coordinate with each other such that the collective scanning coverage and reconstruction quality is maximized while the overall scanning effort is minimized. To this end, we define the problem as a dynamic task assignment and introduce a novel formulation based on Optimal Mass Transport (OMT). Given the currently scanned scene, a set of task views are extracted to cover scene regions which are either unknown or uncertain. These task views are assigned to the robots based on the OMT optimization. We then compute for each robot a smooth path over its assigned tasks by solving an approximate traveling salesman problem. In order to showcase our algorithm, we implement a multi-robot auto-scanning system. Since our method is computationally efficient, we can easily run it in real time on commodity hardware, and combine it with online RGB-D reconstruction approaches. In our results, we show several real-world examples of large indoor environments; in addition, we build a benchmark with a series of carefully designed metrics for quantitatively evaluating multi-robot autoscanning. Overall, we are able to demonstrate high-quality scanning results with respect to reconstruction quality and scanning efficiency, which significantly outperforms existing multi-robot exploration systems.

We present a novel technique to relight images of human faces by learning a model of facial reflectance from a database of 4D reflectance field data of several subjects in a variety of expressions and viewpoints. Using our learned model, a face can be relit in arbitrary illumination environments using only two original images recorded under spherical color gradient illumination. The output of our deep network indicates that the color gradient images contain the information needed to estimate the full 4D reflectance field, including specular reflections and high frequency details. While capturing spherical color gradient illumination still requires a special lighting setup, reduction to just two illumination conditions allows the technique to be applied to dynamic facial performance capture. We show side-by-side comparisons which demonstrate that the proposed system outperforms the state-of-the-art techniques in both realism and speed.

Real time non-rigid reconstruction pipelines are extremely computationally expensive and easily saturate the highest end GPUs currently available. This requires careful strategic choices to be made about a set of highly interconnected parameters that divide up the limited compute. At the same time, offline systems, prove the value of increasing voxel resolution, more iterations, and higher frame rates. To this end, we demonstrate a set of remarkably simple but effective modifications to these algorithms that significantly reduce the average per-frame computation cost allowing these parameters to be increased. Specifically, we divide the depth stream into sub-frames and fusion-frames, disabling both model accumulation (fusion) and non-rigid alignment (model tracking) on the former. Instead, we efficiently track point correspondences across neighboring sub-frames. We then leverage these correspondences to initialize the standard non-rigid alignment to a fusion-frame where data can then be accumulated into the model. As a result, compute resources in the modified non-rigid reconstruction pipeline can be immediately re-purposed to increase voxel resolution, use more iterations or to increase the frame rate. To demonstrate the latter, we leverage recent high frame rate depth algorithms to build a novel “twin” sensor consisting of a low-res/highfps sub-frame camera and a second low-fps/high-res fusion camera.

The advent of consumer depth cameras has incited the development of a new cohort of algorithms tackling challenging computer vision problems. The primary reason is that depth provides direct geometric information that is largely invariant to texture and illumination. As such, substantial progress has been made in human and object pose estimation, 3D reconstruction and simultaneous localization and mapping. Most of these algorithms naturally benefit from the ability to accurately track the pose of an object or scene of interest from one frame to the next. However, commercially available depth sensors (typically running at 30fps) can allow for large inter-frame motions to occur that make such tracking problematic. A high frame rate depth camera would thus greatly ameliorate these issues, and further increase the tractability of these computer vision problems. Nonetheless, the depth accuracy of recent systems for high-speed depth estimation [Fanello et al. 2017b] can degrade at high frame rates. This is because the active illumination employed produces a low SNR and thus a high exposure time is required to obtain a dense accurate depth image. Furthermore in the presence of rapid motion, longer exposure times produce artifacts due to motion blur, and necessitates a lower frame rate that introduces large inter-frame motion that often yield tracking failures. In contrast, this paper proposes a novel combination of hardware and software components that avoids the need to compromise between a dense accurate depth map and a high frame rate. We document the creation of a full 3D capture system for high speed and quality depth estimation, and demonstrate its advantages in a variety of tracking and reconstruction tasks. We extend the state of the art active stereo algorithm presented in Fanello et al. [2017b] by adding a space-time feature in the matching phase. We also propose a machine learning based depth refinement step that is an order of magnitude faster than traditional postprocessing methods. We quantitatively and qualitatively demonstrate the benefits of the proposed algorithms in the acquisition of geometry in motion. Our pipeline executes in 1.1ms leveraging modern GPUs and off-the-shelf cameras and illumination components. We show how the sensor can be employed in many different applications, from [non-]rigid reconstructions to hand/face tracking. Further, we show many advantages over existing state of the art depth camera technologies beyond framerate, including latency, motion artifacts, multi-path errors, and multi-sensor interference.

We introduce a realtime compression architecture for 4D performance capture that is two orders of magnitude faster than current state-of-the-art techniques, yet achieves comparable visual quality and bitrate. We note how much of the algorithmic complexity in traditional 4D compression arises from the necessity to encode geometry using an explicit model (i.e. a triangle mesh). In contrast, we propose an encoder that leverages an implicit representation (namely a Signed Distance Function) to represent the observed geometry, as well as its changes through time. We demonstrate how SDFs, when defined over a small local region (i.e. a block), admit a low-dimensional embedding due to the innate geometric redundancies in their representation. We then propose an optimization that takes a Truncated SDF (i.e. a TSDF), such as those found in most rigid/non-rigid reconstruction pipelines, and efficiently projects each TSDF block onto the SDF latent space. This results in a collection of low entropy tuples that can be effectively quantized and symbolically encoded. On the decoder side, to avoid the typical artifacts of block-based coding, we also propose a variational optimization that compensates for quantization residuals in order to penalize unsightly discontinuities in the decompressed signal. This optimization is expressed in the SDF latent embedding, and hence can also be performed efficiently. We demonstrate our compression/decompression architecture by realizing, to the best of our knowledge, the first system for streaming a real-time captured 4D performance on consumer-level networks.

We present a robust algorithm for personalizing a sphere-mesh tracking model to a user from a collection of depth measurements. Our core contribution is to demonstrate how simple geometric reasoning can be exploited to build a shape-space, and how its performance is comparable to shape-spaces constructed from datasets of carefully calibrated models. We achieve this goal by first re-parameterizing the geometry of the tracking template, and introducing a multi-stage calibration optimization. Our novel parameterization decouples the degrees of freedom for pose and shape, resulting in improved convergence properties. Our analytically differentiable multi-stage calibration pipeline optimizes for the model in the natural low-dimensional space of local anisotropic scalings, leading to an effective solution that can be easily embedded in other tracking/calibration algorithms. Compared to existing sphere-mesh calibration algorithms, quantitative experiments assess our algorithm possesses a larger convergence basin, and our personalized models allows to perform motion tracking with superior accuracy.

Abstract The area of surface reconstruction has seen substantial progress in the past two decades. The traditional problem addressed by surface reconstruction is to recover the digital representation of a physical shape that has been scanned, where the scanned data contain a wide variety of defects. While much of the earlier work has been focused on reconstructing a piece‐wise smooth representation of the original shape, recent work has taken on more specialized priors to address significantly challenging data imperfections, where the reconstruction can take on different representations—not necessarily the explicit geometry. We survey the field of surface reconstruction, and provide a categorization with respect to priors, data imperfections and reconstruction output. By considering a holistic view of surface reconstruction, we show a detailed characterization of the field, highlight similarities between diverse reconstruction techniques and provide directions for future work in surface reconstruction.

Implicit models can be combined by using composition operators; functions that determine the resulting shape. Recently, gradient-based composition operators have been used to express a variety of behaviours including smooth transitions, sharp edges, contact surfaces, bulging, or any combinations. The problem for designers is that building new operators is a complex task that requires specialized technical knowledge. In this work, we introduce an automatic method for deriving a gradient-based implicit operator from 2D drawings that prototype the intended visual behaviour. To solve this inverse problem, in which a shape defines a function, we introduce a general template for implicit operators. A user's sketch is interpreted as samples in the 3D operator's domain. We fit the template to the samples with a non-rigid registration approach. The process works at interactive rates and can accommodate successive refinements by the user. The final result can be applied to 3D surfaces as well as to 2D shapes. Our method is able to replicate the effect of any blending operator presented in the literature, as well as generating new ones such as non-commutative operators. We demonstrate the usability of our method with examples in font-design, collision-response modeling, implicit skinning, and complex shape design.

We present a new algorithm for real-time hand tracking on commodity depth-sensing devices. Our method does not require a user-specific calibration session, but rather learns the geometry as the user performs live in front of the camera, thus enabling seamless virtual interaction at the consumer level. The key novelty in our approach is an online optimization algorithm that jointly estimates pose and shape in each frame, and determines the uncertainty in such estimates. This knowledge allows the algorithm to integrate per-frame estimates over time, and build a personalized geometric model of the captured user. Our approach can easily be integrated in state-of-the-art continuous generative motion tracking software. We provide a detailed evaluation that shows how our approach achieves accurate motion tracking for real-time applications, while significantly simplifying the workflow of accurate hand performance capture. We also provide quantitative evaluation datasets at http://gfx.uvic.ca/datasets/handy

Abstract Given a shape, a skeleton is a thin centered structure which jointly describes the topology and the geometry of the shape. Skeletons provide an alternative to classical boundary or volumetric representations, which is especially effective for applications where one needs to reason about, and manipulate, the structure of a shape. These skeleton properties make them powerful tools for many types of shape analysis and processing tasks. For a given shape, several skeleton types can be defined, each having its own properties, advantages, and drawbacks. Similarly, a large number of methods exist to compute a given skeleton type, each having its own requirements, advantages, and limitations. While using skeletons for two‐dimensional (2D) shapes is a relatively well covered area, developments in the skeletonization of three‐dimensional (3D) shapes make these tasks challenging for both researchers and practitioners. This survey presents an overview of 3D shape skeletonization. We start by presenting the definition and properties of various types of 3D skeletons. We propose a taxonomy of 3D skeletons which allows us to further analyze and compare them with respect to their properties. We next overview methods and techniques used to compute all described 3D skeleton types, and discuss their assumptions, advantages, and limitations. Finally, we describe several applications of 3D skeletons, which illustrate their added value for different shape analysis and processing tasks.

Modern systems for real-time hand tracking rely on a combination of discriminative and generative approaches to robustly recover hand poses. Generative approaches require the specification of a geometric model. In this paper, we propose a the use of sphere-meshes as a novel geometric representation for real-time generative hand tracking. How tightly this model fits a specific user heavily affects tracking precision. We derive an optimization to non-rigidly deform a template model to fit the user data in a number of poses. This optimization jointly captures the user's static and dynamic hand geometry, thus facilitating high-precision registration. At the same time, the limited number of primitives in the tracking template allows us to retain excellent computational performance. We confirm this by embedding our models in an open source real-time registration algorithm to obtain a tracker steadily running at 60Hz. We demonstrate the effectiveness of our solution by qualitatively and quantitatively evaluating tracking precision on a variety of complex motions. We show that the improved tracking accuracy at high frame-rate enables stable tracking of extended and complex motion sequences without the need for per-frame re-initialization. To enable further research in the area of high-precision hand tracking, we publicly release source code and evaluation datasets.

Abstract We present a robust method for capturing articulated hand motions in realtime using a single depth camera. Our system is based on a realtime registration process that accurately reconstructs hand poses by fitting a 3D articulated hand model to depth images. We register the hand model using depth, silhouette, and temporal information. To effectively map low‐quality depth maps to realistic hand poses, we regularize the registration with kinematic and temporal priors, as well as a data‐driven prior built from a database of realistic hand poses. We present a principled way of integrating such priors into our registration optimization to enable robust tracking without severely restricting the freedom of motion. A core technical contribution is a new method for computing tracking correspondences that directly models occlusions typical of single‐camera setups. To ensure reproducibility of our results and facilitate future research, we fully disclose the source code of our implementation.

We present a new algorithm for computational caustic design. Our algorithm solves for the shape of a transparent object such that the refracted light paints a desired caustic image on a receiver screen. We introduce an optimal transport formulation to establish a correspondence between the input geometry and the unknown target shape. A subsequent 3D optimization based on an adaptive discretization scheme then finds the target surface from the correspondence map. Our approach supports piecewise smooth surfaces and non-bijective mappings, which eliminates a number of shortcomings of previous methods. This leads to a significantly richer space of caustic images, including smooth transitions, singularities of infinite light density, and completely black areas. We demonstrate the effectiveness of our approach with several simulated and fabricated examples.

Abstract Rigid registration of two geometric data sets is essential in many applications, including robot navigation, surface reconstruction, and shape matching. Most commonly, variants of the Iterative Closest Point (ICP) algorithm are employed for this task. These methods alternate between closest point computations to establish correspondences between two data sets, and solving for the optimal transformation that brings these correspondences into alignment. A major difficulty for this approach is the sensitivity to outliers and missing data often observed in 3D scans. Most practical implementations of the ICP algorithm address this issue with a number of heuristics to prune or reweight correspondences. However, these heuristics can be unreliable and difficult to tune, which often requires substantial manual assistance. We propose a new formulation of the ICP algorithm that avoids these difficulties by formulating the registration optimization using sparsity inducing norms. Our new algorithm retains the simple structure of the ICP algorithm, while achieving superior registration results when dealing with outliers and incomplete data. The complete source code of our implementation is provided at http://lgg.epfl.ch/sparseicp .

Abstract Inspired by recent developments in contraction‐based curve skeleton extraction, we formulate the skeletonization problem via mean curvature flow (MCF). While the classical application of MCF is surface fairing, we take advantage of its area‐minimizing characteristic to drive the curvature flow towards the extreme so as to collapse the input mesh geometry and obtain a skeletal structure. By analyzing the differential characteristics of the flow, we reveal that MCF locally increases shape anisotropy. This justifies the use of curvature motion for skeleton computation, and leads to the generation of what we call “mean curvature skeletons”. To obtain a stable and efficient discretization, we regularize the surface mesh by performing local remeshing via edge splits and collapses. Simplifying mesh connectivity throughout the motion leads to more efficient computation and avoids numerical instability arising from degeneracies in the triangulation. In addition, the detection of collapsed geometry is facilitated by working with simplified mesh connectivity and monitoring potential non‐manifold edge collapses. With topology simplified throughout the flow, minimal post‐processing is required to convert the collapsed geometry to a curve. Formulating skeletonization via MCF allows us to incorporate external energy terms easily, resulting in a constrained flow. We define one such energy term using the Voronoi medial skeleton and obtain a medially centred curve skeleton. We call the intermediate results of our skeletonization motion meso‐skeletons ; these consist of a mixture of curves and surface sheets as appropriate to the local 3D geometry they capture.

Abstract Classical approaches to shape correspondence base their computation purely on the properties, in particular geometric similarity, of the shapes in question. Their performance still falls far short of that of humans in challenging cases where corresponding shape parts may differ significantly in geometry or even topology. We stipulate that in these cases, shape correspondence by humans involves recognition of the shape parts where prior knowledge on the parts would play a more dominant role than geometric similarity. We introduce an approach to part correspondence which incorporates prior knowledge imparted by a training set of pre‐segmented, labeled models and combines the knowledge with content‐driven analysis based on geometric similarity between the matched shapes. First, the prior knowledge is learned from the training set in the form of per‐label classifiers. Next, given two query shapes to be matched, we apply the classifiers to assign a probabilistic label to each shape face. Finally, by means of a joint labeling scheme, the probabilistic labels are used synergistically with pairwise assignments derived from geometric similarity to provide the resulting part correspondence. We show that the incorporation of knowledge is especially effective in dealing with shapes exhibiting large intra‐class variations. We also show that combining knowledge and content analyses outperforms approaches guided by either attribute alone.

Abstract Objects with many concavities are difficult to acquire using laser scanners. The highly concave areas are hard to access by a scanner due to occlusions by other components of the object. The resulting point scan typically suffers from large amounts of missing data. Methods that use surface‐based priors rely on local surface estimates and perform well only when filling small holes. When the holes become large, the reconstruction problem becomes severely under‐constrained, which necessitates the use of additional reconstruction priors. In this paper, we introduce weak volumetric priors which assume that the volume of a shape varies smoothly and that each point cloud sample is visible from outside the shape. Specifically, the union of view‐rays given by the scanner implicitly carves the exterior volume, while volumetric smoothness regularizes the internal volume. We incorporate these priors into a surface evolution framework where a new energy term defined by volumetric smoothness is introduced to handle large amount of missing data. We demonstrate the effectiveness of our method on objects exhibiting deep concavities, and show its general applicability over a broader spectrum of geometric scenario.

We present an algorithm for curve skeleton extraction via Laplacian-based contraction. Our algorithm can be applied to surfaces with boundaries, polygon soups, and point clouds. We develop a contraction operation that is designed to work on generalized discrete geometry data, particularly point clouds, via local Delaunay triangulation and topological thinning. Our approach is robust to noise and can handle moderate amounts of missing data, allowing skeleton-based manipulation of point clouds without explicit surface reconstruction. By avoiding explicit reconstruction, we are able to perform skeleton-driven topology repair of acquired point clouds in the presence of large amounts of missing data. In such cases, automatic surface reconstruction schemes tend to produce incorrect surface topology. We show that the curve skeletons we extract provide an intuitive and easy-to-manipulate structure for effective topology modification, leading to more faithful surface reconstruction.

Abstract We introduce the notion of consensus skeletons for non‐rigid space‐time registration of a deforming shape. Instead of basing the registration on point features, which are local and sensitive to noise, we adopt the curve skeleton of the shape as a global and descriptive feature for the task. Our method uses no template and only assumes that the skeletal structure of the captured shape remains largely consistent over time. Such an assumption is generally weaker than those relying on large overlap of point features between successive frames, allowing for more sparse acquisition across time. Building our registration framework on top of the low‐dimensional skeleton‐time structure avoids heavy processing of dense point or volumetric data, while skeleton consensusization provides robust handling of incompatibilities between per‐frame skeletons. To register point clouds from all frames, we deform them by their skeletons, mirroring the skeleton registration process, to jump‐start a non‐rigid ICP. We present results for non‐rigid space‐time registration under sparse and noisy spatio‐temporal sampling, including cases where data was captured from only a single view.

We present an algorithm for curve skeleton extraction from imperfect point clouds where large portions of the data may be missing. Our construction is primarily based on a novel notion of generalized rotational symmetry axis (ROSA) of an oriented point set. Specifically, given a subset S of oriented points, we introduce a variational definition for an oriented point that is most rotationally symmetric with respect to S . Our formulation effectively utilizes normal information to compensate for the missing data and leads to robust curve skeleton computation over regions of a shape that are generally cylindrical. We present an iterative algorithm via planar cuts to compute the ROSA of a point cloud. This is complemented by special handling of non-cylindrical joint regions to obtain a centered, topologically clean, and complete 1D skeleton. We demonstrate that quality curve skeletons can be extracted from a variety of shapes captured by incomplete point clouds. Finally, we show how our algorithm assists in shape completion under these challenges by developing a skeleton-driven point cloud completion scheme.

While many 3D objects exhibit various forms of global symmetries, prominent intrinsic symmetries which exist only on parts of an object are also well recognized. Such partial symmetries are often seen as more natural than a global one, even when the symmetric parts are under complex pose. We introduce an algorithm to extract partial intrinsic reflectional symmetries (PIRS) of a 3D shape. Given a closed 2-manifold mesh, we develop a voting scheme to obtain an intrinsic reflectional symmetry axis (IRSA) transform, which is a scalar field over the mesh that accentuates prominent IRSAs of the shape. We then extract a set of explicit IRSA curves on the shape based on a refined measure of local reflectional symmetry support along a curve. The iterative refinement procedure combines IRSA-induced region growing and region-constrained symmetry support refinement to improve accuracy and address potential issues arising from rotational symmetries in the shape. We show how the extracted IRSA curves can be incorporated into a conventional mesh segmentation scheme so that the implied symmetry cues can be utilized to obtain more meaningful results. We also demonstrate the use of IRSA curves for symmetry-driven part repair.

Abstract Non‐rigid 3D shape correspondence is a fundamental and difficult problem. Most applications which require a correspondence rely on manually selected markers. Without user assistance, the performances of existing automatic correspondence methods depend strongly on a good initial shape alignment or shape prior, and they generally do not tolerate large shape variations. We present an automatic feature correspondence algorithm capable of handling large, non‐rigid shape variations, as well as partial matching. This is made possible by leveraging the power of state‐of‐the‐art mesh deformation techniques and relying on a combinatorial tree traversal for correspondence search. The search is deformation‐driven, prioritized by a self‐distortion energy measured on meshes deformed according to a given correspondence. We demonstrate the ability of our approach to naturally match shapes which differ in pose, local scale, part decomposition, and geometric detail through numerous examples.