Geodesic-like features for point matching

Point matching problem seeks the optimal correspondences between two sets of points via minimizing the dissimilarities of the corresponded features. The features are widely represented by a graph model consisting of nodes and edges, where each node represents one key point and each edge describes the pair-wise relations between its end nodes. The edges are typically measured depending on the Euclidian distances between their end nodes, which is, however, not suitable for objects with non-rigid deformations. In this paper, we notice that all the key points are spanning on a manifold which is the surface of the target object. The distance measurement on a manifold, geodesic distance, is robust under non-rigid deformations. Hence, we first estimate the manifold depending on the key points and concisely represent the estimation by a graph model called the Geodesic Graph Model (GGM). Then, we calculate the distance measurement on GGM, which is called the geodesic-like distance, to approximate the geodesic distance. The geodesic-like distance can better tackle non-rigid deformations. To further improve the robustness of the geodesic-like distance, a weight setting process and a discretization process are proposed. The discretization process produces the geodesic-like features for the point matching problem. We conduct multiple experiments over widely used datasets and demonstrate the effectiveness of our method.