Transitive Inverse-Consistent Manifold Registration

This paper presents a new registration method called Transitive Inverse-Consistent Manifold Registration (TICMR). The TICMR method jointly estimates correspondence maps between groups of three manifolds embedded in a higher dimensional image space while minimizing inverse consistency and transitivity errors. Registering three manifolds at once provides a means for minimizing the transitivity error which is not possible when registering only two manifolds. TICMR is an iterative method that uses the closest point projection operator to define correspondences between manifolds as they are non-rigidly registered. Examples of the TICMR method are presented for matching groups of three contours and groups of three surfaces. The contour registration is regularized by minimizing the change in bending energy of the curves while the surface registration is regularized by minimizing the change in elastic energy of the surfaces. The notions of inverse consistency error (ICE) and transitivity error (TE) are extended from volume registration to manifold registration by using a closest point projection operator. For the experiments in this paper, the TICMR method reduces the average ICE by 200 times (contour)/ 6 times (surface) and the average TE by 40 times (contour)/ 2-4 times (surface) compared to registering with a curvature constraint alone. Furthermore, the TICMR is shown to avoid some local minimum that are not avoided when registering with a curvature constraint alone.