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

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...

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Bibliographic Details
Published inJournal of mathematical imaging and vision Vol. 46; no. 1; pp. 66 - 73
Main Author Wild, Marcel
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.05.2013
Springer
Subjects
Applications of Mathematics
Applied sciences
Computer Science
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
Image Processing and Computer Vision
Information, signal and communications theory
Mathematical Methods in Physics
Signal and communications theory
Signal, noise
Signal,Image and Speech Processing
Telecommunications and information theory
Rank selection probabilities
Binary decision diagram
Output distribution
Stack filter
Positive Boolean function
Probabilistic approach
Non linear filter
Disjunctive form
Normal form
Boolean function
Modeling
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Summary: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.
ISSN:0924-9907
1573-7683
DOI:10.1007/s10851-012-0370-y