Symmetry constrained shape evolution in shape manifolds for shape based retrieval

Shape manifolds provide mathematically consistent and rigorous characterization of shapes and their variability. Continuous boundary based representations offer advantages of unambiguous reproduction of shape compared to landmark based methods and obviates the need for manual selection of landmark points. An important drawback of continuous shape representations is their inability to constrain shape to meaningful deformation modes, thus making template based shape retrievals impossible. We build a class of symmetric generators that yield a systematic methodology to constrain shape deformations within a submanifold of the infinite dimensional shape manifold. Geodesic distances on this submanifold estimate dissimilarities in physically meaningful deformation modes. Induced Riemannian metrics on the submanifold can be used to calculate directional derivatives, which can in turn be used to perform analysis of energy functions in the shape space. We finally describe a real valued match metric on the Riemannian shape manifold which is minimized to obtain projections of arbitrary shapes into the constrained submanifold and can be applied to shape based object retrieval.