Discrete Random Sets: An Inverse Problem, Plus Tools for the Statistical Inference of the Discrete Boolean Model

We consider digital binary images as a realization of a bounded discrete random set, a mathematical object which can be defined directly on a finite lattice. In this setting, we show that it is possible to move between two equivalent probabilistic model specifications. We formulate a restricted version of the discrete-case analog of a Boolean random set model, obtain it' probability mass function. and employ some methods of Morphological image analysis to derive tools for its statistical inference.