30 June 1994 Brief survey of the relationships between finite random sets and morphology
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In order to be able to optimally design morphological shape extraction algorithms operating on binary digital images, there needs to be a probability theory for finite random sets and probability relations that show how the probability changes as a finite random set is propagated through a morphological operation. In this paper, we develop such a theory for finite random sets. We then demonstrate how to apply this theory for calculating the probability that a set S perturbed by min or max noise N and dilated or eroded by a structuring element K is a subset, superset, or hits a given set R. In some cases we obtain exact results and in some cases we obtain bounds for the desired probability.
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Robert M. Haralick, Su S. Chen, and Xinhua Zhuang "Brief survey of the relationships between finite random sets and morphology", Proc. SPIE 2300, Image Algebra and Morphological Image Processing V, (30 June 1994); doi: 10.1117/12.179200; https://doi.org/10.1117/12.179200

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