Robust Nonrigid Point Set Registration Using Graph-Laplacian Regularization

We present a robust algorithm that registers one point set to another for nonrigid case. We formulate the problem as a Gaussian mixture model (GMM) density estimation by considering one of the point sets as the GMM centroids and the other as the data points generated by GMM. We displace the centroids and make them register to the data by maximizing the likelihood. To facilitate the process, we introduce a set of weights which provide the proximity information among pairs of points of both point sets and iteratively update the displacement and weights in alternating steps. We propose a priority based combination to update the proximity weights, which leverages the richness of Shape Context (SC). In the displacement updation step, we propose a graph-Laplacian regularization which helps in preserving the intrinsic geometry of the point set to be displaced. We also introduce a fast algorithm that reduces the computation complexity significantly. We apply our method on publicly available datasets. Our results validate the robustness of our approach by outperforming current state-of-the-art methods.