Algebraic Analysis of the Generating Functional for Discrete Random Sets, and Statistical Inference for Intensity in the Discrete Boolean Random Set Model

N. D. Sidiropoulos, J.S. Baras and C.A. Berenstein

Journal of Mathematical Imaging and Vision, Vol. 4, Issue 3, pp. 273-290, June 1994.

Abstract

We consider binary digital images as realizations fo a uniformily 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 verson 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 statistica stability