A Meshless Method for Variational Nonrigid 2-D Shape Registration

Abstract: 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 handle significant high-curvature deformations. We represent 2-D shapes implicitly using distance transforms, and registration error is defined based on the shape contours' mutual distances. In addition, we model global shape deformation as an approximation blended from local deformation fields using partition-of-unity. The global deformation field is regularized by penalizing inconsistencies between local fields. The representation can be made adaptive to shape's contour, leading to registration that is both flexible and efficient. Finally, registration is achieved by minimizing a variational chamfer-energy functional combined with the consistency regularizer. We demonstrate the effectiveness of our method on a number of experiments.