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 certain points, curves or surfaces in another 3D image. In trying to identify the non-rigid displacement field, we face a generalized aperture problem since 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 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.

[1]  Sven Kreiborg,et al.  Surface-bounded growth modeling applied to human mandibles , 2000, IEEE Transactions on Medical Imaging.

[2]  Niklas Nordström,et al.  Biased anisotropic diffusion: a unified regularization and diffusion approach to edge detection , 1990, Image Vis. Comput..

[3]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[4]  Gregory M. Nielson,et al.  On Marching Cubes , 2003, IEEE Trans. Vis. Comput. Graph..

[5]  Alexis Gourdon,et al.  Computing the Differential Characteristics of Isointensity Surfaces , 1995, Comput. Vis. Image Underst..

[6]  Nicholas Ayache,et al.  A General Scheme for Automatically Building 3D Morphometric Anatomical Atlases: application to a Sku , 1995 .

[7]  Fred L. Bookstein,et al.  Landmark methods for forms without landmarks: morphometrics of group differences in outline shape , 1997, Medical Image Anal..

[8]  F. Bookstein.  Landmark methods for forms without landmarks: localizing group differences in outline shape , 1996, Proceedings of the Workshop on Mathematical Methods in Biomedical Image Analysis.

[9]  Alexis Gourdon,et al.  The 3D Marching Lines Algorithm , 1996, CVGIP Graph. Model. Image Process..

[10]  K. Mardia,et al.  A review of image-warping methods , 1998 .

[11]  F. Bookstein,et al.  Morphometric Tools for Landmark Data: Geometry and Biology , 1999 .

[12]  Mads Nielsen,et al.  Feature displacement interpolation , 1998, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269).

[13]  Karl Rohr,et al.  Performance of 3D differential operators for the detection of anatomical point landmarks in MR and CT images , 1999, Medical Imaging.

[14]  K. Mardia,et al.  Statistical Shape Analysis , 1998 .

[15]  Ruzena Bajcsy,et al.  Multiresolution elastic matching , 1989, Comput. Vis. Graph. Image Process..

[16]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Sven Kreiborg,et al.  4d Shape-preserving Modelling of Bone , 1998 .

[18]  Bart M. ter Haar Romeny,et al.  Geometry-Driven Diffusion in Computer Vision , 1994, Computational Imaging and Vision.

[19]  William E. Lorensen,et al.  Marching cubes: a high resolution 3D surface construction algorithm , 1996 .

[20]  F. Bookstein,et al.  Morphometric Tools for Landmark Data: Geometry and Biology , 1999 .

[21]  Guillermo Sapiro,et al.  Invariant Geometric Evolutions of Surfaces and Volumetric Smoothing , 1997, SIAM J. Appl. Math..

[22]  Max A. Viergever,et al.  A survey of medical image registration , 1998, Medical Image Anal..

[23]  Simon R. Arridge,et al.  A survey of hierarchical non-linear medical image registration , 1999, Pattern Recognit..

[24]  Lisa M. Brown,et al.  A survey of image registration techniques , 1992, CSUR.

[25]  Nicholas Ayache,et al.  A scheme for automatically building three-dimensional morphometric anatomical atlases: application to a skull atlas , 1998, Medical Image Anal..