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