Robust and efficient point registration based on clusters and Generalized Radial Basis Functions (C-GRBF)

Radial Basis Functions (RBF) are effective in modeling regularization stabilizers, and have been successfully utilized in several point-based registration algorithms. Unfortunately the solutions usually require the inversion of a matrix or solving a linear system, whose computational cost grows rapidly with the increase of the input data size. In this paper, we present a fast and robust approximation remedy for this issue. Our model formulates the registration objective function under the Generalized Radial Basis Function (GRBF) framework w.r.t the cluster centers of one point set. With fewer variables, an computationally efficient registration is achieved, which updates the non-rigid transformation and the correspondence matrix simultaneously. Since the cluster centers often capture the global structure of the point sets very well, enhanced registration robustness is also resulted due to the less likelihood of trapping into local minima. This is especially beneficial in the context of large or/and unevenly distributed data sets. By means of experiments on real and synthetic data, we demonstrate the improvements made over several state-of-the-art solutions.