非刚性三维形状匹配中基于谱分析的形状描述符综述

Survey on Shape Descriptors Based on Spectral Analysis for Non-rigid 3D Shape Matching

基于谱分析的形状描述符在非刚性三维形状匹配中取得了较好的匹配效果,引起了研究者的广泛关注.谱分析是基于流形上拉普拉斯贝尔特拉米算子谱分解的一种内蕴形状分析方法.谱形状描述符和谱距离分布函数是最主要的两类谱分析形状描述符,它们具有不同的数学性质和物理意义.基于两类不同的形状描述符,给出了详细的方法分析及其在形状匹配中的应用.首先,给出了应用基于谱分析的形状描述符的非刚性三维形状匹配框架,介绍了几种常用的谱形状描述符及谱距离分布函数的基本思想和计算方法;然后,分析比较了这些形状描述符的优缺点及应用场景,为研究者选择基于谱分析的形状描述符提供参考;最后,通过实验对比了不同基于谱分析的形状描述符的算法鲁棒性、时间耗费及非刚性匹配性能,以此推动谱分析形状描述符的应用进程.

The shape descriptors based on spectral analysis have achieved good matching results in 3D non-rigid shape matching, which have attracted wide attention of researchers. Spectral analysis is an intrinsic shape analysis method based on spectral decomposition of Laplace-Beltrami operator on manifold, including spectral shape descriptors and spectral distance distribution functions, which have different mathematical properties and physical meanings. Based on two different types of shape descriptors, this paper gives a detailed method analysis and its application in shape matching. Firstly, this paper provides a 3D non-rigid shape matching framework by applying the shape descriptors based on spectral analysis, and the basic ideas and calculation methods of several commonly used spectral shape descriptors and spectral distance distribution functions are introduced. Secondly, this paper analyzes and compares the advantages and disadvantages of these methods and their application scenarios and provides reference for researchers to choose shape descriptors based on spectral analysis. Finally, the robustness, time consumption, and non-rigid matching performances of different shape descriptors based on spectral analysis are compared through experiments to promote the application process of shape descriptors based on spectral analysis.