A New Joint Clustering and Diffeomorphism Estimation Algorithm for Non-Rigid Shape Matching

Matching shapes parameterized as unlabeled point-sets is a challenging problem since we have to solve for point correspondences in a non-rigid setting. Previous work on this problem such as modal matching, linear assignment, shape contexts etc. has focused more on the correspondence aspect and not on the non-rigid deformations. The principal motivation for the present work is to establish a distance measure between shapes on a shape manifold. A pre-requisite for achieving this goal is the diffeomorphic matching of point-sets. We show that a joint clustering and diffeomorphism estimation strategy is capable of simultaneously estimating correspondences and a diffeomorphism between unlabeled point-sets. Cluster centers for the two point-sets having the same label are always in correspondence. Essentially, as the cluster centers evolve during the iterations of an incremental EM algorithm, we estimate a diffeomorphism between the two sets of cluster centers. We apply our algorithm to 2D corpus callosum shapes.