Non-rigid registration of shapes via diffeomorphic point matching

Diffeomorphic non-rigid registration of shapes is a very difficult problem. We use the point-set representation for shapes since statistical shape analysis in this space is relatively straightforward. Diffeomorphic matching of point-sets requires an automated solution to the very difficult correspondence problem. We describe a joint clustering and diffeomorphism estimation strategy which allows us to simultaneously estimate the correspondence and fit a diffeomorphism between two unlabeled point-sets. Essentially, the cluster centers in each point-set are always in correspondence by virtue of having the same index. During clustering, the cluster center counterparts in each point-set are linked by a diffeomorphism and hence are forced to move in lock-step with one another. Experimental results are shown for 2D corpus callosum point-sets.