A Spectral Segmentation Method for Large Meshes  

作　　者：Xiaohan Bao Weihua Tong Falai Chen 

机构地区：[1]School of Mathematical Sciences,University of Science and Technology of China,Hefei,230026,Anhui,People’s Republic of China

出　　处：《Communications in Mathematics and Statistics》2023年第3期583-607,共25页数学与统计通讯（英文）

基　　金：supported by the National Natural Science Foundation of China(Nos.61877056,61972368);the Anhui Provincial Natural Science Foundation,PR China(No.1908085QA11).

摘　　要：Mesh segmentation is a fundamental and critical task in mesh processing,and it has been studied extensively in computer graphics and geometric modeling communities.However,current methods are not well suited for segmenting large meshes which are now common in many applications.This paper proposes a new spectral segmentation method specifically designed for large meshes inspired by multi-resolution representations.Building on edge collapse operators and progressive mesh representations,we first devise a feature-aware simplification algorithm that can generate a coarse mesh which keeps the same topology as the input mesh and preserves as many features of the input mesh as possible.Then,using the spectral segmentation method proposed in Tong et al.(IEEE Trans Vis Comput Graph 26(4):1807–1820,2020),we perform partition on the coarse mesh to obtain a coarse segmentation which mimics closely the desired segmentation of the input mesh.By reversing the simplification process through vertex split operators,we present a fast algorithm which maps the coarse segmentation to the input mesh and therefore obtain an initial segmentation of the input mesh.Finally,to smooth some jaggy boundaries between adjacent parts of the initial segmentation or align with the desired boundaries,we propose an efficient method to evolve those boundaries driven by geodesic curvature flows.As demonstrated by experimental results on a variety of large meshes,our method outperforms the state-of-the-art segmentation method in terms of not only speed but also usability.

关 键 词：Mesh segmentation Spectral method Progressive mesh Feature-aware simplification Geodesic curvature flow 

分 类 号：O17[理学—数学]