Edge-weighted centroidal Voronoi tessellations

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. © 2010 Global-Science Press.