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 fo 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 obtained its probability mass function, and use some methods of morphological image analysis to derive tools for its statistical stability