Optical flow estimation via steered-L1 norm

Global variational methods for estimating optical flow are among the best performing methods due to the subpixel accuracy and the ‘fill-in’ effect they provide. The fill-in effect allows optical flow displacements to be estimated even in low and untextured areas of the image. The estimation of such displacements are induced by the smoothness term. The L1 norm provides a robust regularisation term for the optical flow energy function with a very good performance for edge-preserving. However this norm suffers from several issues, among these is the isotropic nature of this norm which reduces the fill-in effect and eventually the accuracy of estimation in areas near motion boundaries. In this paper we propose an enhancement to the L1 norm that improves the fill-in effect for this smoothness term. In order to do this we analyse the structure tensor matrix and use its eigenvectors to steer the smoothness term into components that are ‘orthogonal to’ and ‘aligned with’ image structures. This is done in primal-dual formulation. Results show a reduced end-point error and improved accuracy compared to the conventional L1 norm

Optical flow estimation via steered-L1 norm

Global variational methods for estimating optical flow are among the best performing methods due to the subpixel accuracy and the ‘fill-in’ effect they provide. The fill-in effect allows optical flow displacements to be estimated even in low and untextured areas of the image. The estimation of such displacements are induced by the smoothness term. The L1 norm provides a robust regularisation term for the optical flow energy function with a very good performance for edge-preserving. However this norm suffers from several issues, among these is the isotropic nature of this norm which reduces the fill-in effect and eventually the accuracy of estimation in areas near motion boundaries. In this paper we propose an enhancement to the L1 norm that improves the fill-in effect for this smoothness term. In order to do this we analyse the structure tensor matrix and use its eigenvectors to steer the smoothness term into components that are ‘orthogonal to’ and ‘aligned with’ image structures. This is done in primal-dual formulation. Results show a reduced end-point error and improved accuracy compared to the conventional L1 norm

Robust Subspace Estimation via Low-Rank and Sparse Decomposition and Applications in Computer Vision

PhDRecent advances in robust subspace estimation have made dimensionality reduction and noise and outlier suppression an area of interest for research, along with continuous improvements in computer vision applications. Due to the nature of image and video signals that need a high dimensional representation, often storage, processing, transmission, and analysis of such signals is a difficult task. It is therefore desirable to obtain a low-dimensional representation for such signals, and at the same time correct for corruptions, errors, and outliers, so that the signals could be readily used for later processing. Major recent advances in low-rank modelling in this context were initiated by the work of Cand`es et al. [17] where the authors provided a solution for the long-standing problem of decomposing a matrix into low-rank and sparse components in a Robust Principal Component Analysis (RPCA) framework. However, for computer vision applications RPCA is often too complex, and/or may not yield desirable results. The low-rank component obtained by the RPCA has usually an unnecessarily high rank, while in certain tasks lower dimensional representations are required. The RPCA has the ability to robustly estimate noise and outliers and separate them from the low-rank component, by a sparse part. But, it has no mechanism of providing an insight into the structure of the sparse solution, nor a way to further decompose the sparse part into a random noise and a structured sparse component that would be advantageous in many computer vision tasks. As videos signals are usually captured by a camera that is moving, obtaining a low-rank component by RPCA becomes impossible. In this thesis, novel Approximated RPCA algorithms are presented, targeting different shortcomings of the RPCA. The Approximated RPCA was analysed to identify the most time consuming RPCA solutions, and replace them with simpler yet tractable alternative solutions. The proposed method is able to obtain the exact desired rank for the low-rank component while estimating a global transformation to describe camera-induced motion. Furthermore, it is able to decompose the sparse part into a foreground sparse component, and a random noise part that contains no useful information for computer vision processing. The foreground sparse component is obtained by several novel structured sparsity-inducing norms, that better encapsulate the needed pixel structure in visual signals. Moreover, algorithms for reducing complexity of low-rank estimation have been proposed that achieve significant complexity reduction without sacrificing the visual representation of video and image information. The proposed algorithms are applied to several fundamental computer vision tasks, namely, high efficiency video coding, batch image alignment, inpainting, and recovery, video stabilisation, background modelling and foreground segmentation, robust subspace clustering and motion estimation, face recognition, and ultra high definition image and video super-resolution. The algorithms proposed in this thesis including batch image alignment and recovery, background modelling and foreground segmentation, robust subspace clustering and motion segmentation, and ultra high definition image and video super-resolution achieve either state-of-the-art or comparable results to existing methods

Unsupervised Learning from Shollow to Deep

Machine learning plays a pivotal role in most state-of-the-art systems in many application research domains. With the rising of deep learning, massive labeled data become the solution of feature learning, which enables the model to learn automatically. Unfortunately, the trained deep learning model is hard to adapt to other datasets without fine-tuning, and the applicability of machine learning methods is limited by the amount of available labeled data. Therefore, the aim of this thesis is to alleviate the limitations of supervised learning by exploring algorithms to learn good internal representations, and invariant feature hierarchies from unlabelled data. Firstly, we extend the traditional dictionary learning and sparse coding algorithms onto hierarchical image representations in a principled way. To achieve dictionary atoms capture additional information from extended receptive fields and attain improved descriptive capacity, we present a two-pass multi-resolution cascade framework for dictionary learning and sparse coding. This cascade method allows collaborative reconstructions at different resolutions using only the same dimensional dictionary atoms. The jointly learned dictionary comprises atoms that adapt to the information available at the coarsest layer, where the support of atoms reaches a maximum range, and the residual images, where the supplementary details refine progressively a reconstruction objective. Our method generates flexible and accurate representations using only a small number of coefficients, and is efficient in computation. In the following work, we propose to incorporate the traditional self-expressiveness property into deep learning to explore better representation for subspace clustering. This architecture is built upon deep auto-encoders, which non-linearly map the input data into a latent space. Our key idea is to introduce a novel self-expressive layer between the encoder and the decoder to mimic the ``self-expressiveness'' property that has proven effective in traditional subspace clustering. Being differentiable, our new self-expressive layer provides a simple but effective way to learn pairwise affinities between all data points through a standard back-propagation procedure. Being nonlinear, our neural-network based method is able to cluster data points having complex (often nonlinear) structures. However, Subspace clustering algorithms are notorious for their scalability issues because building and processing large affinity matrices are demanding. We propose two methods to tackle this problem. One method is based on $k$-Subspace Clustering, where we introduce a method that simultaneously learns an embedding space along subspaces within it to minimize a notion of reconstruction error, thus addressing the problem of subspace clustering in an end-to-end learning paradigm. This in turn frees us from the need of having an affinity matrix to perform clustering. The other way starts from using a feed forward network to replace the spectral clustering and learn the affinities of each data from "self-expressive" layer. We introduce the Neural Collaborative Subspace Clustering, where it benefits from a classifier which determines whether a pair of points lies on the same subspace under supervision of "self-expressive" layer. Essential to our model is the construction of two affinity matrices, one from the classifier and the other from a notion of subspace self-expressiveness, to supervise training in a collaborative scheme. In summary, we make constributions on how to perform the unsupervised learning in several tasks in this thesis. It starts from traditional sparse coding and dictionary learning perspective in low-level vision. Then, we exploit how to incorporate unsupervised learning in convolutional neural networks without label information and make subspace clustering to large scale dataset. Furthermore, we also extend the clustering on dense prediction task (saliency detection)

Salient Objects in Clutter

This paper identifies and addresses a serious design bias of existing salient object detection (SOD) datasets, which unrealistically assume that each image should contain at least one clear and uncluttered salient object. This design bias has led to a saturation in performance for state-of-the-art SOD models when evaluated on existing datasets. However, these models are still far from satisfactory when applied to real-world scenes. Based on our analyses, we propose a new high-quality dataset and update the previous saliency benchmark. Specifically, our dataset, called Salient Objects in Clutter~\textbf{(SOC)}, includes images with both salient and non-salient objects from several common object categories. In addition to object category annotations, each salient image is accompanied by attributes that reflect common challenges in common scenes, which can help provide deeper insight into the SOD problem. Further, with a given saliency encoder, e.g., the backbone network, existing saliency models are designed to achieve mapping from the training image set to the training ground-truth set. We, therefore, argue that improving the dataset can yield higher performance gains than focusing only on the decoder design. With this in mind, we investigate several dataset-enhancement strategies, including label smoothing to implicitly emphasize salient boundaries, random image augmentation to adapt saliency models to various scenarios, and self-supervised learning as a regularization strategy to learn from small datasets. Our extensive results demonstrate the effectiveness of these tricks. We also provide a comprehensive benchmark for SOD, which can be found in our repository: https://github.com/DengPingFan/SODBenchmark.Comment: 349 references, 20 pages, survey 201 models, benchmark 100 models. Online benchmark: https://github.com/DengPingFan/SODBenchmar

Robust low-dimensional structure learning for big data and its applications

Ph.DDOCTOR OF PHILOSOPH

Depth Estimation Using 2D RGB Images

Single image depth estimation is an ill-posed problem. That is, it is not mathematically possible to uniquely estimate the 3rd dimension (or depth) from a single 2D image. Hence, additional constraints need to be incorporated in order to regulate the solution space. As a result, in the first part of this dissertation, the idea of constraining the model for more accurate depth estimation by taking advantage of the similarity between the RGB image and the corresponding depth map at the geometric edges of the 3D scene is explored. Although deep learning based methods are very successful in computer vision and handle noise very well, they suffer from poor generalization when the test and train distributions are not close. While, the geometric methods do not have the generalization problem since they benefit from temporal information in an unsupervised manner. They are sensitive to noise, though. At the same time, explicitly modeling of a dynamic scenes as well as flexible objects in traditional computer vision methods is a big challenge. Considering the advantages and disadvantages of each approach, a hybrid method, which benefits from both, is proposed here by extending traditional geometric models’ abilities to handle flexible and dynamic objects in the scene. This is made possible by relaxing geometric computer vision rules from one motion model for some areas of the scene into one for every pixel in the scene. This enables the model to detect even small, flexible, floating debris in a dynamic scene. However, it makes the optimization under-constrained. To change the optimization from under-constrained to over-constrained while maintaining the model’s flexibility, ”moving object detection loss” and ”synchrony loss” are designed. The algorithm is trained in an unsupervised fashion. The primary results are in no way comparable to the current state of the art. Because the training process is so slow, it is difficult to compare it to the current state of the art. Also, the algorithm lacks stability. In addition, the optical flow model is extremely noisy and naive. At the end, some solutions are suggested to address these issues

Robust motion segmentation with subspace constraints

Motion segmentation is an important task in computer vision with many applications such as dynamic scene understanding and multi-body structure from motion. When the point correspondences across frames are given, motion segmentation can be addressed as a subspace clustering problem under an affine camera model. In the first two parts of this thesis, we target the general subspace clustering problem and propose two novel methods, namely Efficient Dense Subspace Clustering (EDSC) and the Robust Shape Interaction Matrix (RSIM) method. Instead of following the standard compressive sensing approach, in EDSC we formulate subspace clustering as a Frobenius norm minimization problem, which inherently yields denser connections between data points. While in the noise-free case we rely on the self-expressiveness of the observations, in the presence of noise we recover a clean dictionary to represent the data. Our formulation lets us solve the subspace clustering problem efficiently. More specifically, for outlier-free observations, the solution can be obtained in closed-form, and in the presence of outliers, we solve the problem by performing a series of linear operations. Furthermore, we show that our Frobenius norm formulation shares the same solution as the popular nuclear norm minimization approach when the data is free of any noise. In RSIM, we revisit the Shape Interaction Matrix (SIM) method, one of the earliest approaches for motion segmentation (or subspace clustering), and reveal its connections to several recent subspace clustering methods. We derive a simple, yet effective algorithm to robustify the SIM method and make it applicable to real-world scenarios where the data is corrupted by noise. We validate the proposed method by intuitive examples and justify it with the matrix perturbation theory. Moreover, we show that RSIM can be extended to handle missing data with a Grassmannian gradient descent method. The above subspace clustering methods work well for motion segmentation, yet they require that point trajectories across frames are known {\it a priori}. However, finding point correspondences is in itself a challenging task. Existing approaches tackle the correspondence estimation and motion segmentation problems separately. In the third part of this thesis, given a set of feature points detected in each frame of the sequence, we develop an approach which simultaneously performs motion segmentation and finds point correspondences across the frames. We formulate this problem in terms of Partial Permutation Matrices (PPMs) and aim to match feature descriptors while simultaneously encouraging point trajectories to satisfy subspace constraints. This lets us handle outliers in both point locations and feature appearance. The resulting optimization problem is solved via the Alternating Direction Method of Multipliers (ADMM), where each subproblem has an efficient solution. In particular, we show that most of the subproblems can be solved in closed-form, and one binary assignment subproblem can be solved by the Hungarian algorithm. Obtaining reliable feature tracks in a frame-by-frame manner is desirable in applications such as online motion segmentation. In the final part of the thesis, we introduce a novel multi-body feature tracker that exploits a multi-body rigidity assumption to improve tracking robustness under a general perspective camera model. A conventional approach to addressing this problem would consist of alternating between solving two subtasks: motion segmentation and feature tracking under rigidity constraints for each segment. This approach, however, requires knowing the number of motions, as well as assigning points to motion groups, which is typically sensitive to motion estimates. By contrast, we introduce a segmentation-free solution to multi-body feature tracking that bypasses the motion assignment step and reduces to solving a series of subproblems with closed-form solutions. In summary, in this thesis, we exploit the powerful subspace constraints and develop robust motion segmentation methods in different challenging scenarios where the trajectories are either given as input, or unknown beforehand. We also present a general robust multi-body feature tracker which can be used as the first step of motion segmentation to get reliable trajectories