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Point cloud surface segmentation based on volumetric eigenfunctions of the Laplace-Beltrami operator
Li, Xinge1; Zhang, Yongjie Jessica2; Yang, Xuyang3; Xu, Haibo1; Xu, Guoliang4
2019-05-01
Source PublicationCOMPUTER AIDED GEOMETRIC DESIGN
ISSN0167-8396
Volume71Pages:157-175
AbstractIn 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.
KeywordPoint cloud surface Segmentation Level set form of Laplace-Beltrami operator Volumetric eigenfunction Split Bregman iteration
DOI10.1016/j.cagd.2019.03.004
Language英语
Funding ProjectNational 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 Research AreaComputer Science ; Mathematics
WOS SubjectComputer Science, Software Engineering ; Mathematics, Applied
WOS IDWOS:000471088500012
PublisherELSEVIER SCIENCE BV
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/34929
Collection中国科学院数学与系统科学研究院
Corresponding AuthorXu, Guoliang
Affiliation1.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
Recommended Citation
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.
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