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

• Published in: IEEE transactions on signal processing Vol. 39; no. 2; pp. 395 - 410
• Main Authors: Yli-Harja, O., Astola, J., Neuvo, Y.
• Format: Journal Article
• Language: English
• Published: IEEE 01-02-1991
• Subjects: Boolean functions; Computer applications; Distributed computing; Image processing; Logic; Morphology; Nonlinear filters; Samarium; Signal analysis; Stacking
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/78.80823

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.< >