A Stochastic Tessellation of Digital Space

Abstract

. A tessellation which is capable of producing rough boundaries is proposed. Some properties of the proposed tessellation are also described. Key words: tessellation, stochastic growth, roughness 1. Introduction The work described below is motivated by complex images such as that in Fig. 1, which displays grains in rolled aluminium, viewed through polarized light. Statistical analysis of grain characteristics (eg. size, shape) first requires segmentation of the grains. In order to compare quantitatively the performance of different segmentation techniques, it is useful to develop and analyse models which mimic the important characteristics of real images, such as that in Fig. 1. In this paper, we describe a tessellation which attempts to mimic those shape characteristics. One observation about the grains is that they have rough boundaries. Therefore common tessellations such as the Voronoi, Delaunay and Poisson line tessellations (see [9]) are inappropriate for our purpose, as they h..