On 3D Shape Similarity

We study the 3D shape similarity between closed surfaces. We represent a curved or polyhedral 3D object of genus zero using a mesh representation that has nearly uniform distribution with known connectivity among mesh nodes. We define a shape similarity metric 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(n2), where n is the number of tessellation of sphere or the number of meshes which approximate the surface. Experiments show that our method produces good shape similarity measurements.