Multiple Order Graph Matching

Abstract

This paper addresses the problem of finding correspondences between two sets of features by using multiple order constraints all together. First, we build a high-order supersymmetric tensor, called multiple order tensor, to incorporate the constraints of different orders (e.g., unary, pairwise, third order, etc.). The multiple order tensor naturally merges multi-granularity geometric affinities, thus it presents stronger descriptive power of consistent constraints than the individual order based methods. Second, to achieve the optimal matching, we present an efficient computational approach for the power iteration of the multiple order tensor. It only needs sparse tensor elements and reduces the sampling size of feature tuples, due to the supersymmetry of the multiple order tensor. The experiments on both synthetic and real image data show that our approach improves the matching performance compared to state-of-the-art algorithms.