Abstract: Isometric mapping will cause wrong correspondence without the constraint local features. This paper proposed isometric bipartite graph to resolve the problem. Firstly, the algorithm builds reliable anchors by multi-scale features. Secondly, the corresponding cost matrix is constructed by combining anchor and geodesic distance. Finally, the best correspondence is obtained using maximum weight matching. In experiment, the algorithm can achieve correct correspondence under different poses and missing parts. In addition, it can get better performance than existing algorithms.