A Continuation Method for Graph Matching Based Feature Correspondence

Feature correspondence lays the foundation for many computer vision and image processing tasks, which can be well formulated and solved by graph matching. Because of the high complexity, approximate methods are necessary for graph matching, and the continuous relaxation provides an efficient approximate scheme. But there are still many problems to be settled, such as the highly nonconvex objective function, the ignorance of the combinatorial nature of graph matching in the optimization process, and few attention to the outlier problem. Focusing on these problems, this paper introduces a continuation method directly targeting at the combinatorial optimization problem associated with graph matching. Specifically, first a regularization function incorporating the original objective function and the discrete constraints is proposed. Then a continuation method based on Gaussian smoothing is applied to it, in which the closed forms of relevant functions with respect to the outlier distribution are deduced. Experiments on both synthetic data and real world images validate the effectiveness of the proposed method.