Computing the output distribution and selection probabilities of a stack filter from the DNF of its positive Boolean function

TL;DR

This paper introduces an algorithm to compute the output distribution and selection probabilities of stack filters directly from the DNF of their positive Boolean functions, enhancing analysis capabilities for nonlinear filters.

Contribution

It provides a novel method to derive output distributions and selection probabilities of stack filters from their DNF representations, improving analytical tools for nonlinear filter design.

Findings

Efficient computation of output distribution from DNF

Calculation of selection probabilities during distribution computation

Applicable to arbitrary stack filters with positive Boolean functions

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. The so called selection probabilities can be computed along the way.