Graph Matching with Low-rank Regularization

Graph matching is a widely researched topic which has been utilized in various applications of computer vision. Due to the combinatorial nature of graph matching, it is NP-hard to find an exact solution. So exact graph matching is always relaxed to inexact graph matching which seeks to find an approximate solution for the original problem. For a matching problem in quadratic form, semidefinite programming (SDP) relaxation is proven to be effective. However, previous SDP relaxation methods discard the constraint that the solution matrix is rank one, because the rank of a matrix is non-convex. In this paper, we explore some good properties of the solution matrix. By relaxing the rank into convex form using the properties, we propose to reformulate the graph matching with low rank constraint into a standard SDP, which can be easily solved. We test our method on both synthetic and real world data. The experimental results demonstrate that our method effectively handles low rank constraint and achieves competitive performance on robustness test against state-of-the-art counterparts.