Surface Registration via Foliation

Abstract

This work introduces a novel surface registration method based on foliation. A foliation decomposes the surface into a family of closed loops, such that the decomposition has local tensor product structure. By projecting each loop to a point, the surface is collapsed into a graph. Two homeomorphic surfaces with consistent foliations can be registered by first matching their foliation graphs, then matching the corresponding leaves.,,This foliation based method is capable of handling surfaces with complicated topologies and large non-isometric deformations, rigorous with solid theoretic foundation, easy to implement, robust to compute. The result mapping is diffeomorphic. Our experimental results show the efficiency and efficacy of the proposed method.