On 3D Shape Similarity

This paper addresses the problem of 3D shape similarity between closed surfaces. A curved or polyhedral 3D object of genus zero is represented by a mesh that has nearly uniform distribution with known connectivity among mesh nodes. A shape similarity metric is defined based on the L2 distance between the local curvature distributions over the mesh representations of the two objects. For both convex and concave objects, the shape metric can be computed in time O(n 2), where n is the number of tessellations of the sphere or the number of meshes which approximate the surface. Experiments show that our method produces good shape similarity measurements