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Finite random sets and morphology

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3 Author(s)
Haralick, R.M. ; Dept. of Electr. Eng., Washington Univ., Seattle, WA, USA ; Chen, S. ; Zhuang, S.

In order to be able to optimally design morphological shape extraction algorithms operating on binary digital images, a probability theory is needed 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

Published in:

Pattern Recognition, 1994. Vol. 2 - Conference B: Computer Vision & Image Processing., Proceedings of the 12th IAPR International. Conference on  (Volume:2 )

Date of Conference:

9-13 Oct 1994