In Defence of RANSAC for Outlier Rejection in Deformable Registration

This paper concerns the robust estimation of non-rigid deformations from feature correspondences. We advance the surprising view that for many realistic physical deformations, the error of the mismatches (outliers) usually dwarfs the effects of the curvature of the manifold on which the correct matches (inliers) lie, to the extent that one can tightly enclose the manifold within the error bounds of a low-dimensional hyperplane for accurate outlier rejection. This justifies a simple RANSAC-driven deformable registration technique that is at least as accurate as other methods based on the optimisation of fully deformable models. We support our ideas with comprehensive experiments on synthetic and real data typical of the deformations examined in the literature.