A new algorithm for non-rigid point matching using geodesic graph model

Point matching is a problem of finding the optimum matching between two sets of key points which are extracted from the surfaces of objects. A popular approach represents the features of a set of points with a graph model. Traditionally, the measurement applied in the graph model is the Euclidian distance, which is not suitable for objects with non-rigid deformations. In this paper, we propose a novel graph model called the geodesic graph model (GGM) which uses a geodesic-like distance as its measurement. GGM can better tackle non-rigid deformations because the geodesic-like distance is a kind of invariant structural feature during non-rigid deformations. The building process of the GGM is justified under the assumption that all the key points are spanning on a manifold. To further handle the deviations of key point locations, we come up with a feature weighting process to increase our algorithm's robustness. We conduct several experiments on different kinds of deformations over several widely used datasets. Experimental results demonstrate the effectiveness of our algorithm.