Symmetry analysis with multiscale descriptor

3D shape matching and retrieval is a challenging task. In order to solve for that problem, one has to extract some relevant descriptors from the shapes. A relevant descriptor is a compact data set computed from a shape that can be quickly generated and matched while still capturing the differences between dissimilar shapes. The research work on shape matching has given rise to a variety of local and global descriptors (statistical descriptor, parametrical descriptor, transform based descriptor ...). In the last decade, symmetry analysis has received a considerable attention, since most of 3D objects exhibit that kind of feature. Symmetry analysis relies on global or local descriptor matching while introducing symmetry data into a global descriptor can greatly improve its discriminative power. Early works on symmetry analysis was limited to global symmetry. In the last years, several approaches deal with multi-scale symmetry. The symmetry scale refers to the relative volume or surface of a symmetrical region from a shape. In that case, a probability distribution is built in the space of rigid euclidean transformation by pairing some points together when their associated descriptors are similar enough. However there is no particular matching condition according to the symmetry scale and every pairs of points have the same weight when voting regardless of the symmetry scale to be considered. The symmetry scale refers to the relative volume or surface of a symmetrical region from a shape. Assuming that the larger the symmetry scale is, the larger the descriptor to be matched must be, we present and analyze in this paper a method for multi-scale mirror symmetry analysis. The method works for 3D polygonal meshes and does not need to build any 3D Image representation of the model. Moreover the method increases accuracy of the pairing stage, leading to a more reliable probability distribution, without adding more complexity.