Indexation de maillages 3D par descripteur de forme Shape-based retrieval of 3D mesh models

This paper deals with 3D mesh indexation by using shape descriptors (SD) under constraints of geometrical invariance and topological robustness. The 3D Shape Spectrum Descriptor (3D SSD), recently adopted within the future MPEG-7 standard, is first introduced. The 3D SSD aims at providing an intrinsic shape description of a 3D mesh and is defined as the distribution of the shape index over the entire mesh. The shape index is a local geometric attribute of a 3D surface, expressed as the angular coordinate of a polar representation of the principal curvature vector. Intrinsically invariant to geometrical transformations, the 3D SSD is not robust with respect to multiple topological representations. A new shape descriptor (DH3D), topologically stable is thus proposed. Derived from the 3D Hough transform, the DH3D is not invariant to geometrical transformations. Nevertheless, we show mathematically how the DH3D can be optimally (in terms of representation compactness and computational complexity) associated with a spatial alignment procedure which leads to a geometric invariant behavior. Experimental results have been carried out upon the MPEG7 3D model database consisting of about 1300 meshes in VRML 2.0 format. Objective retrieval results, based upon the definition of a ground truth subset, are reported in terms of Bull Eye Percentage (BEP) score.