Image Classification and Retrieval Using Elastic Shape Metrics

This paper presents a shape-based approach for automatic classification and retrieval of imaged objects. The shape-distance used in clustering is an intrinsic elastic metric on a nonlinear, infinite-dimensional shape space, obtained using geodesic lengths defined on the manifold. This analysis is landmark free, does not require embedding shapes in R, and uses ODEs for flows (as opposed to PDEs). Clustering is performed in a hierarchical fashion. At any level of the hierarchy, clusters are generated using a minimum dispersion criterion and a MCMC-type search algorithm is employed to ensure near-optimal configurations. The Hierarchical clustering potentially forms an efficient (O(log(n)) searches) tool for retrieval from large shape databases. Examples are presented for demonstrating these tools using shapes from the ETH-80 shape database.