Random closed sets I — The Boolean model

The Boolean model is an important and relatively simple example of a random closed set. This chapter begins with introduction, basic properties and applications of Boolean model. It then talks about stationarity and isotropy, simulation, capacity functional and basic characteristics of Boolean models. The chapter explains Boolean model with convex grains in detail. Under the section of coverage and connectivity, the chapter presents coverage probabilities, clumps, connectivity and percolation in the Boolean model. A section discusses in detail statistical analysis for the Boolean model, both because of its intrinsic interest and as an example of parametric statistics for random closed sets. The chapter finally deals with generalisations and variations of the Boolean model. Controlled Vocabulary Terms random function; statistical measures