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We present a method for nonrigid registration of 2-D geometric shapes. Our contribution is twofold. First, we extend the classic chamfer-matching energy to a variational functional. Secondly, we introduce a meshless deformation model that can adapt computation to the shape boundary. In our method, 2-D shapes are implicitly represented by a distance transform, and the registration error is defined based on the shape contours' mutual distances. Additionally, we model global shape deformation as an approximation blended from local fields using partition-of-unity. The deformation field is regularized by penalizing inconsistencies between local fields. This representation can be adaptive to the shape's contour, leading to registration that is both flexible and efficient. Finally, shape registration is achieved by minimizing a variational chamfer-energy functional combined with the consistency regularizer using an efficient quasi-Newton algorithm. We demonstrate the effectiveness of our registration method on a number of experiments.

A Meshless Method for Variational Nonrigid 2-D Shape Registration