Hierarchical Matching Of 3D Shape Based On Heat Kernel Signature

With the development of 3D scanning technology,3D shape analysis is becoming more and more important. Shape matching is one of the fundamental problems in Computer Graphics, Computer Vision and so on, which is to find corresponding points on two pieces of geometry. It includes rigid and non-rigid matching, isometric matching, conformal matching, or general mappings between two surfaces. In this paper, we consider the problem of approximate isometric matching which conserves geodesic distances between corresponding points.In this paper, in order to solve two fundamental problems, i.e. robustness and efficiency, a hierarchical matching method of 3D shape based on heat kernel signature(HKS) and a new strategy on choosing points are proposed, i.e. we choose the fewest and stablest feature points which mostly describe the topological characteristic of 3D shape for original matching so as to improve dense matching hierarchically. Firstly, we detect feature points based on HKS function, at the same time, remove some redundant points and add a few "helpful points" by the fusion method and FPS method. After that we construct HKS descriptor and give these feature points an order based on entropy for first matching. Then according to partial matching in the neighborhood of feature points, we build a vertex-to-vertex matching from coarse to fine. Moreover, our approach is open to any isometric measures, such as geodesic distance, diffusion distance and biharmonic distances because of our optimized point set.Finally, by comparing to several state-of-art methods on the standard TOSCA data set, our method is more suitable for practical application because of its efficient and robust results.