A concave optimization algorithm for matching partially overlapping point sets

Abstract

Matching partially overlapping point sets is a challenging problem in computer vision. To achieve this goal, we model point matching as a mixed linear assignment - least square problem. By eliminating the transformation variable, we reduce the minimization problem to a concave optimization problem with the property that the objective function can be converted into a form with few nonlinear terms. We then use a heuristic variant of the branch-and-bound algorithm for optimization where convergence of the upper bound is used as the stopping criterion. We also propose a new lower bounding scheme which involves solving a k-cardinality linear assignment problem. Two cases of transformations, transformation output being linear with respect to parameters and 2D/3D similarity transformations, are discussed, resulting in ability to handle unknown arbitrary translation and similarity, respectively. Experimental results demonstrate better robustness of the algorithm over state-of-the-art methods.