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This paper introduces a new method for shape registration by matching vector distance functions. The vector distance function representation is more flexible than the conventional signed distance map since it enables us to better control the shapes registration process by using more general transformations. Based on this model, a variational frame work is proposed for the global and local registration of shapes which does not need any point correspondences. The optimization criterion can handle efficiently the estimation of the global registration parameters. A closed form solution is provided to handle an incremental free form deformation model for covering the local deformations. This is an advantage over the gradient descent optimization which is biased towards the initialization and is more time consuming. Results of real shapes registration will be demonstrated to show the efficiency of the proposed approach with small and large global/local deformations.