Multiscale, curvature-based shape representation for surfaces

This paper presents a multiscale, curvature-based shape representation technique for general genus zero closed surfaces. The method is invariant under rotation, translation, scaling, or general isometric deformations; it is robust to noise and preserves intrinsic symmetry. The method is a direct generalization of the Curvature Scale Space (CSS) shape descriptor for planar curves. In our method, the Riemannian metric of the surface is deformed under Ricci flow, such that the Gaussian curvature evolves according to a heat diffusion process. Eventually the surface becomes a sphere with constant positive curvature everywhere. The evolution of zero curvature curves on the surface is utilized as the shape descriptor. Our experimental results on a 3D geometric database with about 80 shapes demonstrate the efficiency and efficacy of the method.