Factorized Graph Matching

Graph matching plays a central role to solve correspondence problems in computer vision. Graph matching problems that incorporate pair-wise constraints can be casted as a quadratic assignment problem (QAP). Unfortunately, QAP is NP-hard and many algorithms have been proposed to solve different relaxations. This paper presents factorized graph matching (FGM), a novel framework for interpreting and optimizing graph matching problems. In this work we show that the affinity matrix of graph matching, that is quadratic in the number of nodes can be factorized as a Kronecker product of smaller components. This factorization allows for a compact representation and better relaxations. In particular, three benefits follow for using this factorization in graph matching: (1) There is no need to compute the pair-wise affinity matrix and it potentially allows for more efficient implementation; (2) The factorization provides a taxonomy for graph matching and reveals the connection among several methods; (3) Using the factorization we derive a new optimization framework that improves state-of-the-art algorithms in graph matching. Experimental results in synthetic and real databases illustrate the benefits of the factorized graph matching. The code will be available on-line in the final version.