Diffeomorphic Point Matching with Applications in Biomedical Image Registration

The need for 3D diffeomorphic matching of unlabeled point sets arises in numerous registration and shape analysis oriented biomedical imaging applications. The correspondence problem coupled with the need for estimating a diffeomorphism in 3D space makes it a very difficult problem. In the present work, we show that a joint clustering and diffeomorphism estimation strategy is capable of simultaneously estimating correspondences and a diffeomorphism in 3D space to interpolate the two unlabeled point sets. Correspondence is established between the cluster centers. Cluster centers for the two point sets having the same labels are always in correspondence. Essentially, as the cluster centers evolve during the iterations of an incremental EM algorithm, we estimate a diffeomorphism in 3D space. The approach is completely symmetric w.r.t. inversion of the two point sets being matched. We demonstrate our approach on 3D hippocampal data.