Feature-based methods for non-rigid registration frequently encounter the correspondence problem. Regardless of whether points, lines, curves or surface parameterizations are used, feature-based non-rigid matching requires us to automatically solve for correspondences between two sets of features. In addition, there could be many features in either set that have no counterparts in the other. This outlier rejection problem further complicates an already di#cult correspondence problem. We formulate feature-based non-rigid registration as a non-rigid point matching problem. After a careful review of the problem and an in-depth examination of two types of methods previously designed for rigid robust point matching (RPM), we propose a new general framework for non-rigid point matching. We consider it a general framework because it does not depend on any particular form of spatial mapping. We have also developed an algorithm---the TPS-RPM algorithm---with the thin-plate spline (TPS) as the parameterization of the non-rigid spatial mapping and the softassign for the correspondence. The performance of the TPS-RPM algorithm is demonstrated and validated in a series of carefully designed synthetic experiments. In each of these experiments, an empirical comparison with the popular iterated closest point (ICP) algorithm is also provided. Finally, we apply the algorithm to the problem of non-rigid registration of cortical anatomical structures which is required in brain mapping. While these results are somewhat preliminary, they clearly demonstrate the applicability of our approach to real world tasks involving feature-based non-rigid registration.

. We construct probabilistic generative models for the nonrigid matching of point-sets. Our formulation is explicitly Platonist. Beginning with a Platonist super point-set, we derive real-world point-sets through the application of four operations: i) spline-based warping, ii) addition of noise, iii) point removal and iii) amnesia regarding the pointto -point correspondences between the real-world point-sets and the Platonist source. Given this generative model, we are able to derive new non-quadratic distance measures w.r.t. the "forgotten" correspondences by a) eliminating the spline parameters from the generative model and by b) integrating out the Platonist super point-set. The result is a new non-quadratic distance measure which has the interpretation of weighted graph matching. The graphs are related in a straightfoward manner to the spline kernel used for non-rigid warping. Experimentally, we show that the new distance measure outperforms the conventional quadratic assignment di...