The optimal centroidal Voronoi tessellations and the Gersho's conjecture in the three-dimensional space

doi:10.1016/j.camwa.2004.12.008

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	The optimal centroidal Voronoi tessellations and the Gersho's conjecture in the three-dimensional space
	Du, Q ; Wang, DS
	2005-05-01
发表期刊	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
卷号	49 期号:9-10 页码:1355-1373
摘要	Optimal centroidal Voronoi tessellations have important applications in many different areas such as vector quantization, data and image processing, clustering analysis, and resource management. In the three-dimensional Euclidean space, they are also useful to the mesh generation and optimization. In this paper, we conduct extensive numerical simulations to investigate the asymptotic structures of optimal centroidal Voronoi tessellations for a given domain. Such a problem is intimately related to the famous Gersho's conjecture, for which a full proof is still not available. We provide abundant evidence to substantiate the claim of the conjecture: the body-centered-cubic lattice (or Par6) based centroidal Voronoi tessellation has the lowest cost (or energy) per unit volume and is the most likely congruent cell predicted by the three-dimensional Gersho conjecture. More importantly, we probe the various properties of this optimal configuration including its dual triangulations which bear significant consequences in applications to three-dimensional high quality meshing. (c) 2005 Elsevier Ltd. All rights reserved.
关键词	optimal triangulation centroidal Voronoi tessellation Gersho's conjecture optimal vector quantizer mesh generation and optimization
DOI	10.1016/j.camwa.2004.12.008
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000229954700006
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/1951
专题	中国科学院数学与系统科学研究院
通讯作者	Du, Q
作者单位	1.Penn State Univ, Dept Math, University Pk, PA 16802 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China 3.Xiangtan Univ, Dept Math, Xiangtan 411105, Peoples R China 4.Univ Coll Swansea, Sch Engn, Civil & Computat Engn Ctr, Swansea SA2 8PP, W Glam, Wales
推荐引用方式 GB/T 7714	Du, Q,Wang, DS. The optimal centroidal Voronoi tessellations and the Gersho's conjecture in the three-dimensional space[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2005,49(9-10):1355-1373.
APA	Du, Q,&Wang, DS.(2005).The optimal centroidal Voronoi tessellations and the Gersho's conjecture in the three-dimensional space.COMPUTERS & MATHEMATICS WITH APPLICATIONS,49(9-10),1355-1373.
MLA	Du, Q,et al."The optimal centroidal Voronoi tessellations and the Gersho's conjecture in the three-dimensional space".COMPUTERS & MATHEMATICS WITH APPLICATIONS 49.9-10(2005):1355-1373.