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

Survey of image-based representations and compression techniques

In this paper, we survey the techniques for image-based rendering (IBR) and for compressing image-based representations. Unlike traditional three-dimensional (3-D) computer graphics, in which 3-D geometry of the scene is known, IBR techniques render novel views directly from input images. IBR techniques can be classified into three categories according to how much geometric information is used: rendering without geometry, rendering with implicit geometry (i.e., correspondence), and rendering with explicit geometry (either with approximate or accurate geometry). We discuss the characteristics of these categories and their representative techniques. IBR techniques demonstrate a surprising diverse range in their extent of use of images and geometry in representing 3-D scenes. We explore the issues in trading off the use of images and geometry by revisiting plenoptic-sampling analysis and the notions of view dependency and geometric proxies. Finally, we highlight compression techniques specifically designed for image-based representations. Such compression techniques are important in making IBR techniques practical.published_or_final_versio