By decomposing polyhedron each into a set of several individual convex sub sets. A general optimization matching method was proposed. The matching process was divided into two steps for optimal mapping: topoligic relationship matching and structure relationship matching. And the relax iteration was used to reduce the matching error. This method can solve the morbid problem of two non homotopic objects matching. The experiments show that the method is a topologic relationship matching and it can be widely used in objects recognition, 3D object construction and medical image analysis.