Correspondence Generation and Matching of 3D Shape Subparts

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.