| Abstract | 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 certain points, curves, or surfaces in another 3D image.
In trying to identify the non-rigid
registration field, we face a
generalized aperture problem since along
the curves and surfaces, {\em point} correspondences are not given.
We will advocate the viewpoint that the aperture and the 3D
interpolation problem may be solved {\em simultaneously} by finding
the {\em simplest} displacement field. This is obtained by a
geometry-constrained diffusion, which in a precise sense yields the
simplest displacement field. The point registration obtained may be
used for segmentation, growth modeling, shape analysis, 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
synthetic example and a longitudinal growth study of the
human mandible are given. |