Nonlinear registration of binary shapes

A novel approach is proposed to estimate the parameters of a diffeomorphism that aligns two binary images. Classical approaches usually define a cost function based on a similarity metric and then find the solution via optimization. Herein, we trace back the problem to the solution of a system of nonlinear equations which directly provides the parameters of the aligning transformation. The proposed method works without any time consuming optimization step or established correspondences. The advantage of our algorithm is that it is easy to implement, less sensitive to the strength of the deformation, and robust against segmentation errors. The efficiency of the proposed approach has been demonstrated on a large synthetic dataset as well as in the context of an industrial application.