Abstract: We present a robust and efficient algorithm for the pairwise non-rigid registration of partially overlapping 3D surfaces. Our approach treats non-rigid registration as an optimization problem and solves it by alternating between correspondence and deformation optimization. Assuming approximately isometric deformations, robust correspondences are generated using a pruning mechanism based on geodesic consistency. We iteratively learn an appropriate deformation discretization from the current set of correspondences and use it to update the correspondences in the next iteration. Our algorithm is able to register partially similar point clouds that undergo large deformations, in just a few seconds. We demonstrate the potential of our algorithm in various applications such as example based articulated segmentation, and shape interpolation.