Computing the Output Distribution and Selection Probabilities of a Stack Filter from the DNF of Its Positive Boolean Function

Authors:
Marcel Wild
Affiliations:
Department of Mathematical Sciences, University of Stellenbosch, Matieland, South Africa 7602
Venue:
Journal of Mathematical Imaging and Vision
Year:
2013

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Abstract

Many nonlinear filters used in practise are stack filters. An algorithm is presented which calculates the output distribution of an arbitrary stack filter S from the disjunctive normal form (DNF) of its underlying positive Boolean function (PBF). Our algorithm avoids to enumerate the models of the PBF one by one, and thus is considerably more efficient than previous methods. The so called rank selection probabilities can be computed along the way.