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.

尽管大多数现有的3D形状表示功能都利用表面或体积信息来描述网格，但在本文中，我们提出了一种有效地组合此双重信息的方法。使用这两种表示，可以捕获凸形和凹形区域，这是有效的形状分割所必需的属性。该方法将众所周知的体积可见性描述符扩展到可以表示表面并因此提供补充信息的新型测地线变体。具体地，对于一对网格节点，通过计算连接它们的测地路径的所有节点之间的联合可见性来构造这种新颖的表面表示，并且彼此之间具有一定的绝对距离。通过考虑不同的这种距离，可以按顺序组织多个关节可见性值。尽管提出的网格描述符可以以许多不同的方式使用，但是在这项工作中，使用了产生的可见性序列的两个元素。以上所有信息均以图表形式适当组织，该图表可增强网格点之间的连接性并反映网格的几何特性，这一事实得到了3D网格分割提供的实验结果的支持。