Topology-preserving nonlinear shape registration on the shape manifold

Shape registration is a vital task in computer vision and image processing, but the topology changes always occur in registration process of two shapes with large deformation. In this paper, we address the shape registration with large deformation by an atlas based method. Concretely, we first represent the shape by the square root velocity functions (SRVFs) which makes registration of two shapes with small deformation well. Then, we hierarchically cluster all shapes and form a clustering tree under this representation. Further, by searching the shortest path connecting two shapes we realize the registration with topology preserving. Finally, the numerical results on the Kimia shape dataset show that our proposed method achieves a better performance of registration than the conventional method. That is, the atlas-based strategy is valid for shape registration with large deformation.