01136nas a2200145   4500000000100000000000100001008004100002260000600043100001800049700001400067700002100081700001400102245006400116520081000180       2008                            d  c61 aA. Srivastava1 aM. Daoudi1 aLeszek Luchowski1 aCh. Samir00aOn Analyzing Symmetry of Objects Using Elastic Deformations3 aWe introduce a framework for analyzing symmetry of 2D and 3D objects using elastic deformations of their boundaries. The basic idea is to define spaces of elastic shapes and to compute shortest (geodesic) paths between the objects and their reflections using a Riemannian structure. Elastic matching, based on optimal (nonlinear) re-parameterizations of curves, provides a better registration of points across shapes, as compared to the previously-used linear registrations. A crucial step of orientation alignment, akin to finding planes of symmetry, is performed as a search for shortest geodesic paths. This framework is fully automatic and provides: a measure of asymmetry, the nearest symmetric shape, the optimal deformation to make an object symmetric, and the plane of symmetry for a given object.