GEOMETRY DRIVEN PROBABILISTIC MODELS FOR SHAPE MATCHING, CLASSIFICATION AND RETRIEVAL
Emulating human vision in a computational framework—known as computer vision—is one of the next major research areas being pursued; this emulation of vision can be viewed from a Systems Engineering perspective. The goal would be to design and develop an Intelligent Vision System built on a framework that could be tailored for specific vision applications. One of the fundamental components of vision is shape, so to design effective vision systems one needs to incorporate shape based algorithms as a core component. This dissertation progresses three facets of shape analysis algorithms: classification, retrieval and registration. Through the use of probabilistic models we are able to leverage the manifold geometry of various shape representations to improve these facets. For classification and retrieval we utilize a wavelet density based approach where shapes are represented as the coefficients of a square-root wavelet density estimated on the shape representation or an equivalent embedding space. The ensuing manifold geometry is leveraged—prototype representations of shape classes are formed—to increase the speed and accuracy of classification and retrieval by reducing the size of the search index. Affine shape registration is progressed through the GrassGraphs algorithm which is a simple yet effective technique for obtaining an affine invariant coordinate representation. Under the Grassmannian representation, two affine related shapes span the same subspace, which makes them only differ by an arbitrary orthogonal transformation. This orthogonal transformation is rendered moot by obtaining a Laplacian embedding of graphs constructed on the Grassmannian coordinates. This yields true affine invariant coordinates where a simple mutual nearest neighbor search is used to find correspondences. The state-of-the-art performance of these algorithms is showcased on a multitude of classification, retrieval and registration datasets.