A new distance measure for non - rigid

We construct probabilistic generative models for the non-rigid 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 point-to-point correspondences between the real-world point-sets and the Pla-tonist 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 distance measure when both distances use the same weighted graphs derived from the spline kernel.