ASPECTS OF RANDOM SET THEORY

This paper is mainly expository in nature, and rather than delving into the theoretical background of random set theory it is concerned with the use of concepts from this theory in the analysis of spatial pattern. The possible aims of such an analysis are varied. One aim is simply the description and summarisation of an image which contains a surfeit of information. The methods of description may be used to differentiate between some types of structure, and to establish similarities between others. Sometimes one is interested in identifying an underlying mechanism responsible for the structure under study, which involves fitting models and assessing goodness of fit. Another possible aim of spatial analysis is to detect correlations between geometrical properties of a structure and its physical characteristics. An example of the latter is the work done by Weibel (1970), who found relationships between the diffusion capacity of lungs (a physical property) and geometrical properties of microscopic sections of the lungs.