Isometric shape correspondence based on the geodesic structure

Abstract

Non-rigid 3D shape correspondence is a fundamental and challenging problem. Isometric correspondence is an important topic because of its wide applications. But it is a NP hard problem if detecting the mapping directly. In this paper, we propose a novel approach to find the correspondence between two (nearly) isometric shapes. Our method is based on the geodesic structure of the shape and minimum cost flow. Firstly, several pre-computed base vertices are initialized for embedding the shapes into Euclidian space, which is constructed by the geodesic distances. Then we select a serials of sample point sets with FPS. After that, we construct some network flows separately with the level point sets of the two shapes and another two virtual points, source point and sink point. The arcs of the network flow are the edges between each point on two shapes. And the L2 distances in the k dimensional Euclidian embedding space are taken as the arc costs and a capacity value is added on each point in the above network flow. At last we solve the correspondence problem as some minimum cost max flow problems (MCFP) with shortest path faster algorithm (SPFA), and combine the results of these MCFP as the last correspondence result. Experiments show that our method is accurate and efficient for isometric, nearly isometric and partially shapes.