Centroidal Voronoi Tessellation Algorithms for Image Processing

Centroidal Voronoi tessellations (CVT’s) are special Voronoi tessellations for which the generators of the tessellation are also the centers of mass (or means) of the Voronoi cells or clusters. CVT’s have been found to be useful in many disparate and diverse settings. In this paper, CVT-based algorithms are developed for image compression, image segmenation, and multichannel image restoration applications. In the image processing context and in its simplest form, the CVT-based methodology reduces to the wellknown k-means clustering technique. However, by viewing the latter within the CVT context, very useful generalizations and improvements can be easily made. Several such generalizations are exploited in this paper including the incorporation of cluster dependent weights, the incorporation of averaging techniques to treat noisy images, extensions to treat multichannel data, and combinations of the aforementioned. In each case, examples are provided to illustrate the efficiency, flexibility, and effectiveness of CVT-based image processing methodologies.

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