Isometric Shape Matching Based on the Geodesic Structure and Minimum Cost Flow

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 you detect 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 construct a network flow with the points 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 a minimum cost max flow problem (MCFP) with shortest path faster algorithm (SPFA). Experiments show that our method is accurate and efficient.