Centroidal Voronoi tessellations: Applications and algorithms. (English) Zbl 0983.65021

A centroidal Voronoi tessellation is a Voronoi tessellation whose generating points are the centroids (centers of mass) of the corresponding Voronoi regions. This paper gives some applications of centroidal tessellation to problems in image compression, quadrature, finite difference methods and statistics, etc. The authors discuss methods for computing such tessellations, provide some analyses concerning both the tessellations and the methods for the determination. Numerical examples are provided.


65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
62H30 Classification and discrimination; cluster analysis (statistical aspects)
65D32 Numerical quadrature and cubature formulas
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
68U10 Computing methodologies for image processing
52B55 Computational aspects related to convexity


AS 136
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