A Connected Area Weighted Centroidal Voronoi Tessellation Model For Image Segmentation

Centroidal Voronoi tessellation (CVT) is a special Voronoi tessellation whose generators are also the centers of masses of the Voronoi regions with respect to a given density function. CVT can be applied in many fields and CVT based image processing methods can be developed in image compression, image segmentation, and multichannel image restoration. The essential fact of image segmentation is dividing the image's physical space into non-overlapped sub-regions, and each sub-region is called a segment. In the image processing context, CVT is a nature technique for image segmentation. Generally speaking, if we get a Centroidal Voronoi Tessellation of an image's feature space (for example color space), we map each Voronoi region in feature space into image's physical space, and then we get segments of the image with respect to Voronoi regions. The simplest form of CVT-based methodology reduced to k-means clustering method which is widely used in image segmentation.In this paper, we developed a Connected Area Weighted CVT (CAWCVT) model for image segmentation. This model improved the basic CVT model's over-segmented problem. This model is based on the basic CVT model, considered both color space and physical space as factors, defined a Connected Area Weighted Voronoi Tessellation Energy. By way of minimizing this energy, we can get the image's Connected Area Weighted Centroidal Voronoi Tessellation (CAWCVT). From cluster analysis point of view, CAWCVT model is an optimum energy function based clustering methodology. We presented an effective algorithm to minimize this energy function. We demonstrated this model can be effectively applied in many segment instances.