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 - <p style="text-align: justify;">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.</p>