Algebraic analysis of the generating functional for discrete random sets and statistical inference for intensity in the discrete Boolean random-set model

We consider binary digital images as realizations of a uniformly bounded discrete random set, a mathematical object that 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 its probability mass function, and use some methods of morphological image analysis to derive tools for its statistical inference.