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

Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds

Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in Euclidean spaces. With the aim of building a bridge between the two realms, we address the problem of sparse coding and dictionary learning over the space of linear subspaces, which form Riemannian structures known as Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into the space of symmetric matrices by an isometric mapping. This in turn enables us to extend two sparse coding schemes to Grassmann manifolds. Furthermore, we propose closed-form solutions for learning a Grassmann dictionary, atom by atom. Lastly, to handle non-linearity in data, we extend the proposed Grassmann sparse coding and dictionary learning algorithms through embedding into Hilbert spaces. Experiments on several classification tasks (gender recognition, gesture classification, scene analysis, face recognition, action recognition and dynamic texture classification) show that the proposed approaches achieve considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelized Affine Hull Method and graph-embedding Grassmann discriminant analysis.Comment: Appearing in International Journal of Computer Visio

Extrinsic methods for coding and dictionary learning on grassmann manifolds

Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in Euclidean spaces. With the aim of building a bridge between the two realms, we address the problem of sparse coding and dictionary learning in Grassmann manifolds, i.e., the space of linear subspaces. To this end, we propose to embed Grassmann manifolds into the space of symmetric matrices by an isometric mapping. This in turn enables us to extend two sparse coding schemes to Grassmann manifolds. Furthermore, we propose an algorithm for learning a Grassmann dictionary, atom by atom. Lastly, to handle non-linearity in data, we extend the proposed Grassmann sparse coding and dictionary learning algorithms through embedding into higher dimensional Hilbert spaces. Experiments on several classification tasks (gender recognition, gesture classification, scene analysis, face recognition, action recognition and dynamic texture classification) show that the proposed approaches achieve considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelized Affine Hull Method and graph-embedding Grassmann discriminant analysis