Correspondence Generation and Matching of 3D Shape Subparts

Universität Bonn, Technical Report number CG-2005-2, June 2005
 

Abstract

The task of setting up correspondences between 3D shapes is a prerequisite for numerous computer graphics applications, which has been performed manually up to now. We present an automatic method for characterizing 3D shape subparts and establishing correspondences between them. The corner stones of our algorithm are: (i) finding stable salient points that are representative for certain parts of shapes along with generating the associated local shape descriptors; and (ii) finding matching subsets of salient points so that the local shape dissimilarity and the deformation magnitude due to the resulting mapping is minimal. The salient points are found as minima of the scale space Laplacian-of-Gaussian applied to the characteristic object function, the rotation invariant local shape descriptors are a variant of Spherical Harmonic Descriptors. The matching is performed by finding sets of corresponding salient point pairs minimizing the 3D bending energy computed from the thin-plate spline interpolation of these discrete point mappings. Unlike the graph based methods, the resulting correspondences are completely independent of object topology but nevertheless stable. Possible applications include (sub-)shape similarity estimation, finding object subparts in a larger scene, generation of dense matching e.g. for morphing or statistical shape analysis.

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Bibtex

@TECHREPORT{cg-2005-2,
       author = {Novotni, Marcin and Degener, Patrick and Klein, Reinhard},
        title = {Correspondence Generation and Matching of 3D Shape Subparts},
       number = {CG-2005-2},
         year = {2005},
        month = jun,
  institution = {Universit{\"a}t Bonn},
     abstract = {The task of setting up correspondences between 3D shapes is a prerequisite for
                 numerous computer graphics applications, which has been performed manually up
                 to now. We present an automatic method for characterizing 3D shape subparts and
                 establishing correspondences between them. The corner stones of our algorithm
                 are: (i) finding stable salient points that are representative for certain parts of shapes
                 along with generating the associated local shape descriptors; and (ii) finding matching
                 subsets of salient points so that the local shape dissimilarity and the deformation
                 magnitude due to the resulting mapping is minimal. The salient points are found as
                 minima of the scale space Laplacian-of-Gaussian applied to the characteristic object
                 function, the rotation invariant local shape descriptors are a variant of Spherical
                 Harmonic Descriptors. The matching is performed by finding sets of corresponding
                 salient point pairs minimizing the 3D bending energy computed from the thin-plate
                 spline interpolation of these discrete point mappings.
                 Unlike the graph based methods, the resulting correspondences are completely
                 independent of object topology but nevertheless stable. Possible applications include
                 (sub-)shape similarity estimation, finding object subparts in a larger scene,
                 generation of dense matching e.g. for morphing or statistical shape analysis.},
         issn = {1610-8892}
}