Robust Point Matching Revisited: A Concave Optimization Approach

The well-known robust point matching (RPM) method uses deterministic annealing for optimization, and it has two problems. First, it cannot guarantee the global optimality of the solution and tends to align the centers of two point sets. Second, deformation needs to be regularized to avoid the generation of undesirable results. To address these problems, in this paper we first show that the energy function of RPM can be reduced to a concave function with very few non-rigid terms after eliminating the transformation variables and applying linear transformation; we then propose to use concave optimization technique to minimize the resulting energy function. The proposed method scales well with problem size, achieves the globally optimal solution, and does not need regularization for simple transformations such as similarity transform. Experiments on synthetic and real data validate the advantages of our method in comparison with state-of-the-art methods.