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Volume 3, Issue 2
Edge-Weighted Centroidal Voronoi Tessellations

Jie Wang & Xiaoqiang Wang

DOI: 10.4208/nmtma.2010.32s.7

Numer. Math. Theor. Meth. Appl., 3 (2010), pp. 223-244.

Published online: 2010-03

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  • Abstract

Most existing applications of centroidal Voronoi tessellations (CVTs) lack consideration of the length of the cluster boundaries. In this paper we propose a new model and algorithms to produce segmentations which would minimize the total energy — a sum of the classic CVT energy and the weighted length of cluster boundaries. To distinguish it with the classic CVTs, we call it an Edge-Weighted CVT (EWCVT). The concept of EWCVT is expected to build a mathematical base for all CVT related data classifications with requirement of smoothness of the cluster boundaries. The EWCVT method is easy in implementation, fast in computation, and natural for any number of clusters.

  • Keywords

Centroidal Voronoi tessellations, cluster boundary, edge detection, clustering, image processing.

  • AMS Subject Headings

52B55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-3-223, author = {Jie Wang and Xiaoqiang Wang}, title = {Edge-Weighted Centroidal Voronoi Tessellations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2010}, volume = {3}, number = {2}, pages = {223--244}, abstract = {

Most existing applications of centroidal Voronoi tessellations (CVTs) lack consideration of the length of the cluster boundaries. In this paper we propose a new model and algorithms to produce segmentations which would minimize the total energy — a sum of the classic CVT energy and the weighted length of cluster boundaries. To distinguish it with the classic CVTs, we call it an Edge-Weighted CVT (EWCVT). The concept of EWCVT is expected to build a mathematical base for all CVT related data classifications with requirement of smoothness of the cluster boundaries. The EWCVT method is easy in implementation, fast in computation, and natural for any number of clusters.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2010.32s.7}, url = {http://global-sci.org/intro/article_detail/nmtma/5998.html} }
TY - JOUR T1 - Edge-Weighted Centroidal Voronoi Tessellations AU - Jie Wang & Xiaoqiang Wang JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 223 EP - 244 PY - 2010 DA - 2010/03 SN - 3 DO - http://doi.org/10.4208/nmtma.2010.32s.7 UR - https://global-sci.org/intro/article_detail/nmtma/5998.html KW - Centroidal Voronoi tessellations, cluster boundary, edge detection, clustering, image processing. AB -

Most existing applications of centroidal Voronoi tessellations (CVTs) lack consideration of the length of the cluster boundaries. In this paper we propose a new model and algorithms to produce segmentations which would minimize the total energy — a sum of the classic CVT energy and the weighted length of cluster boundaries. To distinguish it with the classic CVTs, we call it an Edge-Weighted CVT (EWCVT). The concept of EWCVT is expected to build a mathematical base for all CVT related data classifications with requirement of smoothness of the cluster boundaries. The EWCVT method is easy in implementation, fast in computation, and natural for any number of clusters.

Jie Wang and Xiaoqiang Wang. (2010). Edge-Weighted Centroidal Voronoi Tessellations. Numerical Mathematics: Theory, Methods and Applications. 3 (2). 223-244. doi:10.4208/nmtma.2010.32s.7
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