Random Pattern Generation Processes *

This paper deals with a new class of image models called mosaic models that view an image as a random pattern and model it by an appropriate planar process. There are several different kinds of image models in use. Mandelbrot, [l] models irregular and fragmentary natural patterns by Brownian surfaces (Fig. 1). Wong [2], H assner [3], and others model images by two-dimensional random fields. Matheron [4] and a number of other French mathematicians describe random spatial patterns in terms of regionalized random variables. McCormick and Jayaramamurthy [5] and others use time series analysis to model the row-scan of the image. In this paper we provide an overview of a variety of mosaic models. Subsequent’ papers will discuss their specific properties and their applications to images. We describe a number of models for spatial point patterns in Section 2. The ‘<most random” of these, the Poisson point process, will be used in the construction of most of the succeeding patterns. In Section 3, we will model piecewise contiguous patterns by random mosaics. The use of mosaics to depict patterns is ancient. The Chaldeans were skilled mosaicists by 2500 BCE. The Greeks further developed the art and were thought to have used pattern books for standard motifs. The pieces of a mosaic were