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This paper proposes a novel graph matching algorithm and applies it to shape recognition based on object silhouettes. The main idea is to match skeleton graphs by comparing the geodesic paths between skeleton endpoints. In contrast to typical tree or graph matching methods, we do not consider the topological graph structure. Our approach is motivated by the fact that visually similar skeleton graphs may have completely different topological structures. The proposed comparison of geodesic paths between endpoints of skeleton graphs yields correct matching results in such cases. The skeletons are pruned by contour partitioning with discrete. Curve evolution, which implies that the endpoints of skeleton branches correspond to visual parts of the objects. The experimental results demonstrate that our method is able to produce correct results in the presence of articulations, stretching, and contour deformations.