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This paper presents a new shape registration algorithm that establishes "meaningful correspondence " between objects, in that it preserves the local shape correspondence between the source and target objects. By observing that an object's skeleton corresponds to its local shape peaks, we use skeleton to characterize the local shape of the source and target objects. Unlike traditional graph-based skeleton matching algorithms that focus on matching skeletons alone and ignore the overall alignment of the boundaries, our algorithm is formulated in a variational framework which aligns local shape by registering two potential fields that are associated with skeletons. Also, we add a boundary constraint term to the energy functional, such that our algorithm can be applied to match bulky objects where skeleton and boundary are far away to each other. To increase the robustness of our algorithm, we incorporate M-estimator and dynamic pruning algorithm to form a feedback system that eliminates local shape outliers caused by nonrigid deformation, occlusion, and missing parts. Experiments on 2D binary shapes and 3D cardiac sequences validate the accuracy and robustness of this algorithm.