Non-rigid registration by geometry-constrained diffusion

Abstract

Assume that only partial knowledge about a non-rigid registration is given so that certain points, curves, or surfaces in one 3D image map to certain certain points, curves, or surfaces in another 3D image. We are facing the aperture problem because along the curves and surfaces, point correspondences are not given. We will advocate the viewpoint that the aperture and the 3D interpolation problem may be solved simultaneously by finding the simplest displacement field. This is obtained by a geometry-constrained diffusion which yields the simplest displacement field in a precise sense. The point registration obtained may be used for growth modelling, shape statistics, or kinematic interpolation. The algorithm applies to geometrical objects of any dimensionality. We may thus keep any number of fiducial points, curves, and/or surfaces fixed while finding the simplest registration. Examples of inferred point correspondences in a longitudinal growth study of the mandible are given.