谱流形小波及其在三维几何处理中的应用  

Spectral Manifold Wavelets with Applications in 3D Geometric Processing

作　　者：胡玲 汪政 郭啸[4] HU Ling;WANG Zheng;GUO Xiao(School of Mathematics and Statistics,Central South University,Changsha 410083,China;a.School of Mathematics and Computing,b.School of Information Science and Engineering,Hunan First Normal College,Changsha 410205,China;Department of Junior Education,Changsha Normal University,Changsha 410000,China)

机构地区：[1]中南大学数学与统计学院,中国长沙410083 [2]湖南第一师范学院数学与计算科学学院,中国长沙410205 [3]湖南第一师范学院信息科学与工程学院,中国长沙410205 [4]长沙师范学院初等教育系,中国长沙410000

出　　处：《湖南师范大学自然科学学报》2018年第4期77-84,共8页Journal of Natural Science of Hunan Normal University

基　　金：湖南省教育厅科学研究一般项目(16C0333)

摘　　要：当处理三角网格(可微的二维流形)时,谱图小波采用的图拉普拉斯矩阵不能充分利用模型内蕴的几何信息.为此,将图拉普拉斯矩阵替换为包含模型几何描述的拉普拉斯贝尔特米算子矩阵,在此基础上建立三角网格上的谱流形小波.并将谱流行小波应用于多种几何处理,包括模型的多分辨表示、去噪等.To triangular meshes （differentiable 2-dimension manifolds）, graph Laplacian cannot sufficiently capture the geometric information of the underlying models. For this reason, graph Laplacian is adapted to the matrix of discrete Laplace-Beltrami operator which includes geometric descriptions of the model. Based on it, spectral manifold wavelets （SMWs） are constructed on meshes. Compared to SGWs, SMWs reflect more geometric features and are insusceptible to the quality of the meshes, and can be efficiently computed. SMWs can be conveniently and widely applied to many geometric processing such as multi-level representation and denoising of models.

关 键 词：拉普拉斯-贝尔特米算子 谱流形小波 几何处理 二维流形 三角网格 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]