Shape recognition on a Riemannian manifold

In this paper, we propose to perform shape recognition on a Riemannian manifold. Shape representation on a manifold have the advantage to be intrinsically invariant to shape preserving transformation, such as scaling and translation. Also, shape distance can be naturally computed because Riemannian manifolds are metric spaces. We propose to use the square-root velocity manifold (SRV), which model the shape external contour as a unit-length curve. We detail a dynamic programming algorithm for curve alignment w.r.t. parameterization, which respects the unit-length constraint. Then, we increase the robustness of the SRV representation to shape deformations with additional features. In order to be resilient to occlusion, the distance between two curves is performed in two steps. First the curves are aligned and the less matching parts are removed; then the resulting curves are aligned and the distance is evaluated. Finally, a support vector machine classifier is trained based on the pairwise shape distance for a robust recognition. Promising results are obtained using state-of-the-art benchmarks.