A Path-following Algorithm for Robust Point Matching

We propose a new point matching algorithm in this letter by minimizing a concave geometric matching cost function coming from the objective function of the robust point matching algorithm. Due to concavity of this function, naive optimization strategies such as gradient descent will fail. To address this problem, we use a path following strategy for optimization which works by adding a convex quadratic term to the objective function and then gradually transitioning from the state that there is only weight of the convex term to the state that there is only weight of the concave geometric matching cost term. Extensive experimental results demonstrate strong robustness of the method over several state-of-the-art methods and it also has good computational efficiency.