Voronoi Random Fields

We propose a random field regarded as a generalization of Voronoi diagrams for the case where the positions of generators are distributed probabilistically. Our approach is a kind of stochastic approaches to Voronoi diagrams; however our definition is different from usual random Voronoi diagrams such as Poisson Voronoi diagrams. As numerical examples, first we discuss the case where the positions of generators are mutually independent and their marginal distributions are uniform distributions on disks. Second, we discuss the case where the distributions are given in the form of digital pictures.