Non-rigid registration by geometry-constrained diffusion

Per Rønsholt Andresen, Mads Nielsen

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    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, {\$\backslash\$em point} correspondences are not given. We will advocate the viewpoint that the aperture and the 3D interpolation problem may be solved {\$\backslash\$em simultaneously} by finding the {\$\backslash\$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.
    Original languageEnglish
    JournalMedical Image Analysis
    Issue number2
    Pages (from-to)81-88
    Publication statusPublished - 2001


    • Aperture-problem
    • Automatic landmark detection
    • Simplest displacement field
    • Homology

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