Abstract
Most existing applications of centroidal Voronoi tessellations (CVTs) lack con- sideration 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 distin- guish 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 classifica- tions 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. AMS subject classifications: 52B55
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