Structure from Motion (SfM) is a fundamental computer vision problem which has not been well handled by deep learning. One of the promising solutions is to apply explicit structural constraint, e.g., 3D cost volume, into the neural network. Obtaining accurate camera poses from images alone can be challenging, especially with complicated environmental factors. Existing methods usually assume accurate camera poses from GT or other methods, which is unrealistic in practice and additional sensors are needed. In this work, we design a physical driven architecture, namely DeepSFM, inspired by traditional Bundle Adjustment, which consists of two cost volume based architectures to iteratively refine depth and pose. The explicit constraints on both depth and pose, when combined with the learning components, bring merit from both traditional BA and emerging deep learning technology. To speed up the learning and inference efficiency, we apply the Gated Recurrent Units (GRUs)-based depth and pose update modules with coarse to fine cost volumes on the iterative refinements. In addition, with the extended residual depth prediction module, our model can be adapted to dynamic scenes effectively. Extensive experiments on various datasets show that our model achieves state-of-the-art performance with superior robustness against challenging inputs.

We study the problem of shape generation in 3D mesh representation from a small number of color images with or without camera poses. While many previous works learn to hallucinate the shape directly from priors, we adopt to further improve the shape quality by leveraging cross-view information with a graph convolution network. Instead of building a direct mapping function from images to 3D shape, our model learns to predict series of deformations to improve a coarse shape iteratively. Inspired by traditional multiple view geometry methods, our network samples nearby area around the initial mesh's vertex locations and reasons an optimal deformation using perceptual feature statistics built from multiple input images. Extensive experiments show that our model produces accurate 3D shapes that are not only visually plausible from the input perspectives, but also well aligned to arbitrary viewpoints. With the help of physically driven architecture, our model also exhibits generalization capability across different semantic categories, and the number of input images. Model analysis experiments show that our model is robust to the quality of the initial mesh and the error of camera pose, and can be combined with a differentiable renderer for test-time optimization.

Subspace clustering has been extensively studied from the hypothesis-and-test, algebraic, and spectral clustering-based perspectives. Most assume that only a single type/class of subspace is present. Generalizations to multiple types are non-trivial, plagued by challenges such as choice of types and numbers of models, sampling imbalance and parameter tuning. In many real world problems, data may not lie perfectly on a linear subspace and hand designed linear subspace models may not fit into these situations. In this work, we formulate the multi-type subspace clustering problem as one of learning non-linear subspace filters via deep multi-layer perceptrons (mlps). The response to the learnt subspace filters serve as the feature embedding that is clustering-friendly, i.e., points of the same clusters will be embedded closer together through the network. For inference, we apply K-means to the network output to cluster the data. Experiments are carried out on synthetic data and real world motion segmentation problems, producing state-of-the-art results.

In this paper, we propose an end-to-end deep learning architecture that generates 3D triangular meshes from single color images. Restricted by the nature of prevalent deep learning techniques, the majority of previous works represent 3D shapes in volumes or point clouds. However, it is non-trivial to convert these representations to compact and ready-to-use mesh models. Unlike the existing methods, our network represents 3D shapes in meshes, which are essentially graphs and well suited for graph-based convolutional neural networks. Leveraging perceptual features extracted from an input image, our network produces the correct geometry by progressively deforming an ellipsoid. To make the whole deformation procedure stable, we adopt a coarse-to-fine strategy, and define various mesh/surface related losses to capture properties of various aspects, which benefits producing the visually appealing and physically accurate 3D geometry. In addition, our model by nature can be adapted to objects in specific domains, e.g., human faces, and be easily extended to learn per-vertex properties, e.g., color. Extensive experiments show that our method not only qualitatively produces the mesh model with better details, but also achieves the higher 3D shape estimation accuracy compared against the state-of-the-arts.

Many real-world video sequences cannot be conveniently categorized as general or degenerate; in such cases, imposing a false dichotomy in using the fundamental matrix or homography model for motion segmentation on video sequences would lead to difficulty. Even when we are confronted with a general scene-motion, the fundamental matrix approach as a model for motion segmentation still suffers from several defects, which we discuss in this paper. The full potential of the fundamental matrix approach could only be realized if we judiciously harness information from the simpler homography model. From these considerations, we propose a multi-model spectral clustering framework that synergistically combines multiple models (homography and fundamental matrix) together. We show that the performance can be substantially improved in this way. For general motion segmentation tasks, the number of independently moving objects is often unknown a priori and needs to be estimated from the observations. This is referred to as model selection and it is essentially still an open research problem. In this work, we propose a set of model selection criteria balancing data fidelity and model complexity. We perform extensive testing on existing motion segmentation datasets with both segmentation and model selection tasks, achieving state-of-the-art performance on all of them; we also put forth a more realistic and challenging dataset adapted from the KITTI benchmark, containing real-world effects such as strong perspectives and strong forward translations not seen in the traditional datasets.

We present Uncertainty-aware Cascaded Stereo Network (UCS-Net) for 3D reconstruction from multiple RGB images. Multi-view stereo (MVS) aims to reconstruct fine-grained scene geometry from multi-view images. Previous learning-based MVS methods estimate per-view depth using plane sweep volumes (PSVs) with a fixed depth hypothesis at each plane; this requires densely sampled planes for high accuracy, which is impractical for high-resolution depth because of limited memory. In contrast, we propose adaptive thin volumes (ATVs); in an ATV, the depth hypothesis of each plane is spatially varying, which adapts to the uncertainties of previous per-pixel depth predictions. Our UCS-Net has three stages: the first stage processes a small PSV to predict low-resolution depth; two ATVs are then used in the following stages to refine the depth with higher resolution and higher accuracy. Our ATV consists of only a small number of planes with low memory and computation costs; yet, it efficiently partitions local depth ranges within learned small uncertainty intervals. We propose to use variance-based uncertainty estimates to adaptively construct ATVs; this differentiable process leads to reasonable and fine-grained spatial partitioning. Our multi-stage framework progressively sub-divides the vast scene space with increasing depth resolution and precision, which enables reconstruction with high completeness and accuracy in a coarse-to-fine fashion. We demonstrate that our method achieves superior performance compared with other learning-based MVS methods on various challenging datasets.

We present a new deep point cloud rendering pipeline through multi-plane projections. The input to the network is the raw point cloud of a scene and the output are image or image sequences from a novel view or along a novel camera trajectory. Unlike previous approaches that directly project features from 3D points onto 2D image domain, we propose to project these features into a layered volume of camera frustum. In this way, the visibility of 3D points can be automatically learnt by the network, such that ghosting effects due to false visibility check as well as occlusions caused by noise interferences are both avoided successfully. Next, the 3D feature volume is fed into a 3D CNN to produce multiple planes of images w.r.t. the space division in the depth directions. The multi-plane images are then blended based on learned weights to produce the final rendering results. Experiments show that our network produces more stable renderings compared to previous methods, especially near the object boundaries. Moreover, our pipeline is robust to noisy and relatively sparse point cloud for a variety of challenging scenes.

Depth from a monocular video can enable billions of devices and robots with a single camera to see the world in 3D. In this paper, we present a model for video depth estimation, which consists of a flow-to-depth layer, a camera pose refinement module, and a depth fusion network. Given optical flow and camera poses, our flow-to-depth layer generates depth proposals and their corresponding confidence maps by explicitly solving an epipolar geometry optimization problem. Our flow-to-depth layer is differentiable, and thus we can refine camera poses by maximizing the aggregated confidence in the camera pose refinement module. Our depth fusion network can utilize the target frame, depth proposals, and confidence maps inferred from different neighboring frames to produce the final depth map. Furthermore, the depth fusion network can additionally take the depth proposals generated by other methods to further improve the results. The experiments on three public datasets show that our approach outperforms state-of-the-art depth estimation methods, and has reasonable crossdataset generalization ability: our model trained on KITTI still performs well on the unseen Waymo dataset.

Physically based rendering has been widely used to generate photo-realistic images, which greatly impacts industry by providing appealing rendering, such as for entertainment and augmented reality, and academia by serving large scale high-fidelity synthetic training data for data hungry methods like deep learning. However, physically based rendering heavily relies on ray-tracing, which can be computational expensive in complicated environment and hard to parallelize. In this paper, we propose an end-to-end deep learning based approach to generate physically based rendering efficiently. Our system consists of two stacked neural networks, which effectively simulates the physical behavior of the rendering process and produces photo-realistic images. The first network, namely shading network, is designed to predict the optimal shading image from surface normal, depth and illumination; the second network, namely composition network, learns to combine the predicted shading image with the reflectance to generate the final result. Our approach is inspired by intrinsic image decomposition, and thus it is more physically reasonable to have shading as intermediate supervision. Extensive experiments show that our approach is robust to noise thanks to a modified perceptual loss and even outperforms the physically based rendering systems in complex scenes given a reasonable time budget.

Convolutional networks for single-view object reconstruction have shown impressive performance and have become a popular subject of research. All existing techniques are united by the idea of having an encoder-decoder network that performs non-trivial reasoning about the 3D structure of the output space. In this work, we set up two alternative approaches that perform image classification and retrieval respectively. These simple baselines yield better results than state-of-the-art methods, both qualitatively and quantitatively. We show that encoder-decoder methods are statistically indistinguishable from these baselines, thus indicating that the current state of the art in single-view object reconstruction does not actually perform reconstruction but image classification. We identify aspects of popular experimental procedures that elicit this behavior and discuss ways to improve the current state of research.

We study the problem of shape generation in 3D mesh representation from a few color images with known camera poses. While many previous works learn to hallucinate the shape directly from priors, we resort to further improving the shape quality by leveraging cross-view information with a graph convolutional network. Instead of building a direct mapping function from images to 3D shape, our model learns to predict series of deformations to improve a coarse shape iteratively. Inspired by traditional multiple view geometry methods, our network samples nearby area around the initial mesh's vertex locations and reasons an optimal deformation using perceptual feature statistics built from multiple input images. Extensive experiments show that our model produces accurate 3D shape that are not only visually plausible from the input perspectives, but also well aligned to arbitrary viewpoints. With the help of physically driven architecture, our model also exhibits generalization capability across different semantic categories, number of input images, and quality of mesh initialization.

Interactive image segmentation is characterized by multimodality. When the user clicks on a door, do they intend to select the door or the whole house? We present an end-to-end learning approach to interactive image segmentation that tackles this ambiguity. Our architecture couples two convolutional networks. The first is trained to synthesize a diverse set of plausible segmentations that conform to the user's input. The second is trained to select among these. By selecting a single solution, our approach retains compatibility with existing interactive segmentation interfaces. By synthesizing multiple diverse solutions before selecting one, the architecture is given the representational power to explore the multimodal solution space. We show that the proposed approach outperforms existing methods for interactive image segmentation, including prior work that applied convolutional networks to this problem, while being much faster.

Many real-world sequences cannot be conveniently categorized as general or degenerate; in such cases, imposing a false dichotomy in using the fundamental matrix or homography model for motion segmentation would lead to difficulty. Even when we are confronted with a general scene-motion, the fundamental matrix approach as a model for motion segmentation still suffers from several defects, which we discuss in this paper. The full potential of the fundamental matrix approach could only be realized if we judiciously harness information from the simpler homography model. From these considerations, we propose a multi-view spectral clustering framework that synergistically combines multiple models together. We show that the performance can be substantially improved in this way. We perform extensive testing on existing motion segmentation datasets, achieving state-of-the-art performance on all of them; we also put forth a more realistic and challenging dataset adapted from the KITTI benchmark, containing real-world effects such as strong perspectives and strong forward translations not seen in the traditional datasets.

We present a learning-based approach to computing solutions for certain NP-hard problems. Our approach combines deep learning techniques with useful algorithmic elements from classic heuristics. The central component is a graph convolutional network that is trained to estimate the likelihood, for each vertex in a graph, of whether this vertex is part of the optimal solution. The network is designed and trained to synthesize a diverse set of solutions, which enables rapid exploration of the solution space via tree search. The presented approach is evaluated on four canonical NP-hard problems and five datasets, which include benchmark satisfiability problems and real social network graphs with up to a hundred thousand nodes. Experimental results demonstrate that the presented approach substantially outperforms recent deep learning work, and performs on par with highly optimized state-of-the-art heuristic solvers for some NP-hard problems. Experiments indicate that our approach generalizes across datasets, and scales to graphs that are orders of magnitude larger than those used during training.

While clustering has been well studied in the past decade, model selection has drawn much less attention due to the difficulty of the problem. In this paper, we address both problems in a joint manner by recovering an ideal affinity tensor from an imperfect input. By taking into account the relationship of the affinities induced by the cluster structures, we are able to significantly improve the affinity input, such as repairing those entries corrupted by gross outliers. More importantly, the recovered ideal affinity tensor also directly indicates the number of clusters and their membership, thus solving the model selection and clustering jointly. To enforce the requisite global consistency in the affinities demanded by the cluster structure, we impose a number of constraints, specifically, among others, the tensor should be low rank and sparse, and it should obey what we call the rank-1 sum constraint. To solve this highly non-smooth and non-convex problem, we exploit the mathematical structures, and express the original problem in an equivalent form amenable for numerical optimization and convergence analysis. To scale to large problem sizes, we also propose an alternative formulation, so that those problems can be efficiently solved via stochastic optimization in an online fashion. We evaluate our algorithm with different applications to demonstrate its superiority, and show it can adapt to a large variety of settings.

Estimating the number of clusters remains a difficult model selection problem. We consider this problem in the domain where the affinity relations involve groups of more than two nodes. Building on the previous formulation for the pairwise affinity case, we exploit the mathematical structures in the higher order case. We express the original minimal-rank and positive semi-definite (PSD) constraints in a form amenable for numerical implementation, as the original constraints are either intractable or even undefined in general in the higher order case. To scale to large problem sizes, we also propose an alternative formulation, so that it can be efficiently solved via stochastic optimization in an online fashion. We evaluate our algorithm with different applications to demonstrate its superiority, and show it can adapt to varying levels of unbalancedness of clusters.

Recently sparse representation has been applied to visual tracking by modeling the target appearance using a sparse approximation over the template set. However, this approach is limited by the high computational cost of the ℓ1-norm minimization involved, which also impacts on the amount of particle samples that we can have. This paper introduces a basic constraint on the self-representation of the target set. The sparsity pattern in the self-representation allows us to recover the “sparse coefficients” of the candidate samples by some small-scale ℓ2-norm minimization; this results in a fast tracking algorithm. It also leads to a principled dictionary update mechanism which is crucial for good performance. Experiments on a recently released benchmark with 50 challenging video sequences show significant runtime efficiency and tracking accuracy achieved by the proposed algorithm.

We present a method to jointly estimate scene depth and recover the clear latent image from a foggy video sequence. In our formulation, the depth cues from stereo matching and fog information reinforce each other, and produce superior results than conventional stereo or defogging algorithms. We first improve the photo-consistency term to explicitly model the appearance change due to the scattering effects. The prior matting Laplacian constraint on fog transmission imposes a detail-preserving smoothness constraint on the scene depth. We further enforce the ordering consistency between scene depth and fog transmission at neighboring points. These novel constraints are formulated together in an MRF framework, which is optimized iteratively by introducing auxiliary variables. The experiment results on real videos demonstrate the strength of our method.

While clustering has been well studied in the past decade, model selection has drawn less attention. This paper addresses both problems in a joint manner with an indicator matrix formulation, in which the clustering cost is penalized by a Frobenius inner product term and the group number estimation is achieved by a rank minimization. As affinity graphs generally contain positive edge values, a sparsity term is further added to avoid the trivial solution. Rather than adopting the conventional convex relaxation approach wholesale, we represent the original problem more faithfully by taking full advantage of the particular structure present in the optimization problem and solving it efficiently using the Alternating Direction Method of Multipliers. The highly constrained nature of the optimization provides our algorithm with the robustness to deal with the varying and often imperfect input affinity matrices arising from different applications and different group numbers. Evaluations on the synthetic data as well as two real world problems show the superiority of the method across a large variety of settings.

Given a pair of videos having a common action, our goal is to simultaneously segment this pair of videos to extract this common action. As a preprocessing step, we first remove background trajectories by a motion-based figure ground segmentation. To remove the remaining background and those extraneous actions, we propose the trajectory co saliency measure, which captures the notion that trajectories recurring in all the videos should have their mutual saliency boosted. This requires a trajectory matching process which can compare trajectories with different lengths and not necessarily spatiotemporally aligned, and yet be discriminative enough despite significant intra-class variation in the common action. We further leverage the graph matching to enforce geometric coherence between regions so as to reduce feature ambiguity and matching errors. Finally, to classify the trajectories into common action and action outliers, we formulate the problem as a binary labeling of a Markov Random Field, in which the data term is measured by the trajectory co-saliency and the smoothness term is measured by the spatiotemporal consistency between trajectories. To evaluate the performance of our framework, we introduce a dataset containing clips that have animal actions as well as human actions. Experimental results show that the proposed method performs well in common action extraction.

This paper addresses real-world challenges in the motion segmentation problem, including perspective effects, missing data, and unknown number of motions. It first formulates the 3-D motion segmentation from two perspective views as a subspace clustering problem, utilizing the epipolar constraint of an image pair. It then combines the point correspondence information across multiple image frames via a collaborative clustering step, in which tight integration is achieved via a mixed norm optimization scheme. For model selection, we propose an over-segment and merge approach, where the merging step is based on the property of the ell_1-norm of the mutual sparse representation of two over-segmented groups. The resulting algorithm can deal with incomplete trajectories and perspective effects substantially better than state-of-the-art two-frame and multi-frame methods. Experiments on a 62-clip dataset show the significant superiority of the proposed idea in both segmentation accuracy and model selection.

This paper presents a new system level framework for Diminished Reality, leveraging for the first time both the appearance and 3D information provided by large photo collections on the Internet. Recent computer vision techniques have made it possible to automatically reconstruct 3-D structure-from-motion points from large and unordered photo collections. Using these point clouds and a prior provided by GPS, reasonably accurate 6 degree of freedom camera poses can be obtained, thus allowing localization. Once the camera (and hence the user) is correctly localized, photos depicting scenes visible from the user's viewpoint can be used to remove unwanted objects indicated by the user in the video sequences. Existing methods based on texture synthesis bring undesirable artifacts and video inconsistency when the background is heterogeneous; the task is rendered even harder for these methods when the background contains complex structures. On the other hand, methods based on plane warping fail when the background has arbitrary shape. Unlike these methods, our algorithm copes with these problems by making use of internet photos, registering them in 3D space and obtaining the 3D scene structure in an offline process. We carefully design the various components during the online phase so as to meet both speed and quality requirements of the task. Experiments on real data collected demonstrate the superiority of our system.

We present a two-level approach for height map estimation from single images, aiming at restoring brick and stone relief(BSR) from their rubbing images in a visually plausible manner. In our approach, the base relief of the low frequency component is estimated automatically with a partial differential equation (PDE)-based mesh deformation scheme. A few vertices near the central area of the object region are selected and assigned with heights estimated by an erosion-based contour map. These vertices together with object boundary vertices, boundary normals as well as the partial differential properties of the mesh are taken as constraints to deform the mesh by minimizing a least-squares error functional. The high frequency detail is estimated directly from rubbing images automatically or optionally with minimal interactive processing. The final height map for a restored BSR is obtained by blending height maps of the base relief and high frequency detail. We demonstrate that our method can not only successfully restore several BSR maps from their rubbing images, but also restore some relief-like surfaces from photographic images.