Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio

Robust Principal Component Analysis on Graphs

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA solves the first issue with a sparse penalty term. The second issue can be handled with the matrix factorization model, which is however non-convex. Besides, PCA based clustering can also be enhanced by using a graph of data similarity. In this article, we introduce a new model called "Robust PCA on Graphs" which incorporates spectral graph regularization into the Robust PCA framework. Our proposed model benefits from 1) the robustness of principal components to occlusions and missing values, 2) enhanced low-rank recovery, 3) improved clustering property due to the graph smoothness assumption on the low-rank matrix, and 4) convexity of the resulting optimization problem. Extensive experiments on 8 benchmark, 3 video and 2 artificial datasets with corruptions clearly reveal that our model outperforms 10 other state-of-the-art models in its clustering and low-rank recovery tasks

Learning Robust and Discriminative Manifold Representations for Pattern Recognition

Face and object recognition find applications in domains such as biometrics, surveillance and human computer interaction. An important component in any recognition pipeline is to learn pertinent image representations that will help the system to discriminate one image class from another. These representations enable the system to learn a discriminative function that can classify a wide range of images. In practical situations, the images acquired are often corrupted with occlusions and noise. Thus, a robust and discriminative learning is necessary for good classification performance. This thesis explores two scenarios where robust and discriminative manifold representations help recognize face and object images. On one hand learning robust manifold projections enables the system to adapt to images across different domains including cases with noise and occlusions. And on the other hand learning discriminative manifold representations aid in image set comparison. The first contribution of this thesis is a robust approach to visual domain adaptation by learning a subspace with L1 principal component analysis (PCA) and L1 Grassmannian with applications to object and face recognition. Mapping data from different domains on a low dimensional subspace through PCA is a common step in subspace based unsupervised domain adaptation. Subspaces extracted by PCA are prone to be affected by outliers that lead to noisy projections. A robust subspace learning through L1-PCA helps in improving performance. The proposed approach was tested on the office, Caltech - 256, Yale-A and AT&T datasets. Results indicate the improvement of classification accuracy for face and object recognition task. The second contribution of this thesis is a biologically motivated manifold learning framework for image set classification by independent component analysis (ICA) for Grassmann manifolds. It has been discovered that the simple cells in the visual cortex learn spatially localized image representations. Similar representations can be learnt using ICA. Motivated by the manifold hypothesis, a Grassmann manifold is learnt using the independent components which enables compact representation through linear subspaces. The efficacy of the proposed approach is demonstrated for image set classification on face and object recognition datasets such as AT&T, extended Yale, labelled faces in the wild and ETH - 80

Efficient Sparse Coding in Early Sensory Processing: Lessons from Signal Recovery

Sensory representations are not only sparse, but often overcomplete: coding units significantly outnumber the input units. For models of neural coding this overcompleteness poses a computational challenge for shaping the signal processing channels as well as for using the large and sparse representations in an efficient way. We argue that higher level overcompleteness becomes computationally tractable by imposing sparsity on synaptic activity and we also show that such structural sparsity can be facilitated by statistics based decomposition of the stimuli into typical and atypical parts prior to sparse coding. Typical parts represent large-scale correlations, thus they can be significantly compressed. Atypical parts, on the other hand, represent local features and are the subjects of actual sparse coding. When applied on natural images, our decomposition based sparse coding model can efficiently form overcomplete codes and both center-surround and oriented filters are obtained similar to those observed in the retina and the primary visual cortex, respectively. Therefore we hypothesize that the proposed computational architecture can be seen as a coherent functional model of the first stages of sensory coding in early vision