Discrete random sets: an inverse problem, plus tools for the statistical inference of the discrete Boolean model
Nicholas D. Sidiropoulos, John S. Baras, Carlos A. Berenstein · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1992
We consider digital binary images as realizations 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 its probability mass function, and employ some methods of Morphological image analysis to derive tools for its statistical inference.