Analysis of the properties of median and weighted median filters using threshold logic and stack filter representation

Olli Yli-Harja, Yrjö Neuvo, Jaakko Astola

Research output: Contribution to journalArticleScientificpeer-review

229 Citations (Scopus)

Abstract

The deterministic properties of weighted median (WM) filters are analyzed. Threshold decomposition and the stacking property together establish a unique relationship between integer and binary domain filtering. The authors present a method to find the weighted median filter which is equivalent to a stack filter defined by a positive Boolean function. Because the cascade of WM filters can always be expressed as a single stack filter this allows expression of the cascade of WM filters as a single WM filter. A direct application is the computation of the output distribution of a cascade of WM filters. The same method is used to find a nonrecursive expansion of a recursive WM filter. As applications of theoretical results, several interesting deterministic and statistical properties of WM filters are derived.
Original languageEnglish
Pages (from-to)395 - 410
Number of pages16
JournalIEEE Transactions on Signal Processing
Volume39
Issue number2
DOIs
Publication statusPublished - 1991
MoE publication typeA1 Journal article-refereed

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Threshold logic
Median filters
Boolean functions
Decomposition

Cite this

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title = "Analysis of the properties of median and weighted median filters using threshold logic and stack filter representation",
abstract = "The deterministic properties of weighted median (WM) filters are analyzed. Threshold decomposition and the stacking property together establish a unique relationship between integer and binary domain filtering. The authors present a method to find the weighted median filter which is equivalent to a stack filter defined by a positive Boolean function. Because the cascade of WM filters can always be expressed as a single stack filter this allows expression of the cascade of WM filters as a single WM filter. A direct application is the computation of the output distribution of a cascade of WM filters. The same method is used to find a nonrecursive expansion of a recursive WM filter. As applications of theoretical results, several interesting deterministic and statistical properties of WM filters are derived.",
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Analysis of the properties of median and weighted median filters using threshold logic and stack filter representation. / Yli-Harja, Olli; Neuvo, Yrjö; Astola, Jaakko.

In: IEEE Transactions on Signal Processing, Vol. 39, No. 2, 1991, p. 395 - 410.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Analysis of the properties of median and weighted median filters using threshold logic and stack filter representation

AU - Yli-Harja, Olli

AU - Neuvo, Yrjö

AU - Astola, Jaakko

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N2 - The deterministic properties of weighted median (WM) filters are analyzed. Threshold decomposition and the stacking property together establish a unique relationship between integer and binary domain filtering. The authors present a method to find the weighted median filter which is equivalent to a stack filter defined by a positive Boolean function. Because the cascade of WM filters can always be expressed as a single stack filter this allows expression of the cascade of WM filters as a single WM filter. A direct application is the computation of the output distribution of a cascade of WM filters. The same method is used to find a nonrecursive expansion of a recursive WM filter. As applications of theoretical results, several interesting deterministic and statistical properties of WM filters are derived.

AB - The deterministic properties of weighted median (WM) filters are analyzed. Threshold decomposition and the stacking property together establish a unique relationship between integer and binary domain filtering. The authors present a method to find the weighted median filter which is equivalent to a stack filter defined by a positive Boolean function. Because the cascade of WM filters can always be expressed as a single stack filter this allows expression of the cascade of WM filters as a single WM filter. A direct application is the computation of the output distribution of a cascade of WM filters. The same method is used to find a nonrecursive expansion of a recursive WM filter. As applications of theoretical results, several interesting deterministic and statistical properties of WM filters are derived.

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