Point cloud surface segmentation based on volumetric eigenfunctions of the Laplace-Beltrami operator

doi:10.1016/j.cagd.2019.03.004

CSpace

	Point cloud surface segmentation based on volumetric eigenfunctions of the Laplace-Beltrami operator
	Li, Xinge 1; Zhang, Yongjie Jessica 2; Yang, Xuyang 3; Xu, Haibo 1; Xu, Guoliang 4
	2019-05-01
发表期刊	COMPUTER AIDED GEOMETRIC DESIGN
ISSN	0167-8396
卷号	71 页码:157-175
摘要	In the process of surface modeling from scanned point data, a segmentation that partitions a point cloud into meaningful regions or extracts important features from the 3D point data plays an important role in compressing the scanned data and fitting surface patches. In this paper, a new spectral point cloud surface segmentation method is proposed based on volumetric eigenfunctions of the Laplace-Beltrami operator. The proposed algorithm consists of two main steps. Firstly, the point cloud surface is modeled as the union of a bunch of level set surfaces, on which the eigenfunctions are computed from the level set form of the Laplace-Beltrami operator using the finite element method. Secondly, a new vectorial volumetric eigenfunction segmentation model is developed based on the classical Mumford-Shah model, in which we approximate volumetric eigenfunctions by piecewise-constant functions, and the point cloud surface is segmented via segmenting the volumetric eigenfunctions. Instead of solving the Euler-Lagrange equation by evolution implementation, the split Bregman iteration, which is shown to be a fast algorithm, is utilized. Experimental results demonstrate that our volumetric eigenfunction based technique yields superior segmentation results in terms of accuracy and robustness, compared with the surface eigenfunction based method. (C) 2019 Elsevier B.V. All rights reserved.
关键词	Point cloud surface Segmentation Level set form of Laplace-Beltrami operator Volumetric eigenfunction Split Bregman iteration
DOI	10.1016/j.cagd.2019.03.004
语种	英语
资助项目	National Postdoctoral Program for Innovative Talents[BX201700038] ; NSF CAREER Award[OCI-1149591] ; NSF CAREER Award[CBET-1804929] ; CMU-PITA grant ; NSFC[11675021] ; NSFC Funds for Creative Research Groups of China[11321061]
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Software Engineering ; Mathematics, Applied
WOS记录号	WOS:000471088500012
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34929
专题	中国科学院数学与系统科学研究院
通讯作者	Xu, Guoliang
作者单位	1.Inst Appl Phys & Computat Math, Beijing, Peoples R China 2.Carnegie Mellon Univ, Dept Mech Engn, Pittsburgh, PA 15213 USA 3.Kunming Shipborne Equipment Res & Test Ctr, 750 Proving Ground, Kunming, Yunnan, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Li, Xinge,Zhang, Yongjie Jessica,Yang, Xuyang,et al. Point cloud surface segmentation based on volumetric eigenfunctions of the Laplace-Beltrami operator[J]. COMPUTER AIDED GEOMETRIC DESIGN,2019,71:157-175.
APA	Li, Xinge,Zhang, Yongjie Jessica,Yang, Xuyang,Xu, Haibo,&Xu, Guoliang.(2019).Point cloud surface segmentation based on volumetric eigenfunctions of the Laplace-Beltrami operator.COMPUTER AIDED GEOMETRIC DESIGN,71,157-175.
MLA	Li, Xinge,et al."Point cloud surface segmentation based on volumetric eigenfunctions of the Laplace-Beltrami operator".COMPUTER AIDED GEOMETRIC DESIGN 71(2019):157-175.