An improved 3D shape visibility graph with application to mesh segmentation

Abstract

While most existing 3D shape representation features exploit either surface or volumetric information to describe the mesh, in this paper we propose a method that efficiently combines this dual information. Using both representations, convex as well as concave regions are captured, a property which is necessary for effective shape segmentation. The method extends the well-known volumetric visibility descriptor to a novel geodesic variant that can represent the surface and thus provides complementary information. Specifically, for a pair of mesh nodes, this novel surface representation is constructed by computing the joint visibility among all nodes of the geodesic path connecting them and are at a certain absolute distance each other. By considering different such distances, multiple joint visibility values are computed, organized in a sequence. Although the proposed mesh descriptor can be used in many different ways, in this work two elements of the produced visibility sequence are used. All the above information is appropriately organized in a graph that enhances the connectedness between mesh points and reflects the geometric properties of the mesh, a fact which is supported by the provided experimental results on 3D mesh segmentation.