Non-rigid registration by geometry-constrained diffusion

Assume that only partial knowledge about a non-rigid registration is given: certain points, curves or surfaces in one 3D image are known to map to cer tain points, curves or surfaces in another 3D image. In trying to identify the non-rigid displacement field, we face a generalized aperture problem si nce along the curves and surfaces, point correspondences are not given. We will advocate the viewpoint that the aperture and the 3D interpolation prob lem may be solved simultaneously by finding the simplest displacement field . This is obtained by a geometry-constrained diffusion, which in a precise sense yields the simplest displacement field. The point registration obtain ed may be used for segmentation, growth modeling, shape analysis or kinemat ic interpolation. The algorithm applies to geometrical objects of any dimen sionality. We may thus keep any number of fiducial points, curves and/or su rfaces fixed while finding the simplest registration. Examples of inferred point correspondences in a synthetic example and a longitudinal growth stud y of the human mandible are given. (C) 2001 Elsevier Science B.V. All right s reserved.