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 journalArticle

238 Citations (Scopus)


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
Issue number2
Publication statusPublished - 1991
MoE publication typeA1 Journal article-refereed


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