The optimal centroidal Voronoi tessellations and the Gersho's conjecture in the three-dimensional space
文献类型：期刊论文
| 作者 | Du, Q; Wang, DS |
| 刊名 | COMPUTERS & MATHEMATICS WITH APPLICATIONS
 |
| 出版日期 | 2005-05-01 |
| 卷号 | 49期号:9-10页码:1355-1373 |
| 关键词 | optimal triangulation centroidal Voronoi tessellation Gersho's conjecture optimal vector quantizer mesh generation and optimization |
| ISSN号 | 0898-1221 |
| DOI | 10.1016/j.camwa.2004.12.008 |
| 英文摘要 | 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. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000229954700006 |
| 出版者 | PERGAMON-ELSEVIER SCIENCE LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/1950]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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