A theoretical analysis of the properties of median filters

Gallagher, Neal C.; Wise, Gary L.

doi:10.1109/tassp.1981.1163708

Cited by 684 publications

(217 citation statements)

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“…In [130] several examples are given which demonstrate that successive passes of the median filter of window width 3 will eventually drive a signal of finite length to a signal which is invariant to further passes of the filter. The locally monotone nature of these finite-length fixed points was observed in [17], [130], [134] and then proven for all median filters of odd window width by Tyan [131], [132] and Gallagher and Wise [54]. If the signals being considered are infinite in length, then not all root signals are locally monotone; those that are not must be bivalued [131], [132].…”

Section: Theoretical Analysis Of Median Filtersmentioning

confidence: 99%

“…Gallagher and Wise [54] also showed that any finite-length signal is filtered to a root signal after a finite number of passes of a median filter of a fixed window width. This is an important result--it ties median-type filters to neural nets since such convergence behavior is the primary characteristic of associative memories.…”

Section: Theoretical Analysis Of Median Filtersmentioning

confidence: 99%

“…The structure of its root signals, and the convergence behavior of the median filter proved to be powerful analytical tools in analyzing the behavior of the filter [54]. This theory has since been extended to stack filters [49], where a graph-theoretic approach was used to prove necessary and sufficient conditions for a stack filter to have roots and an algorithm was devised to determine the roots of convergent stack filters.…”

Section: Theoretical Advancesmentioning

confidence: 99%

See 2 more Smart Citations

An overview of median and stack filtering

Coyle

Gallagher

Gabbouj

1992

Circuits Systems and Signal Process

108

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Abstract. Within the last two decades a small group of researchers has built a useful, nontrivial theory of nonlinear signal processing around the median-related filters known as rank-order filters, order-statistic filters, weighted median filters, and stack filters. This required significant effort to overcome the bias, both in education and research, toward linear theory, which has been dominant since the days of Fourier, Laplace, and "Convolute."We trace the development of this theory of nonlinear filtering from its beginnings in the study of noise-removal properties and structural behavior of the median filter to the recently developed theory of optimal stack filtering.The theory of stack filtering provides a point of view which unifies many different filter classes, including morphological filters, so it is discussed in detail. Of particular importance is the way this theory has brought together, in a single analytical framework, both the estimation-based and the structural-based approaches to the design of these filters.Some recent applications of median and stack filters are provided to demonstrate the effectiveness of this approach to nonlinear filtering. They include: the design of an optimal stack filter for image restoration; the use of vector median filters to attenuate impulsive noise in color images and to eliminate cross luminance and cross color in TV images; and the use of median-based filters for image sequence coding, reconstruction, and scan rate conversion in normal TV and HDTV systems.

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Section: Theoretical Analysis Of Median Filtersmentioning

confidence: 99%

Section: Theoretical Analysis Of Median Filtersmentioning

confidence: 99%

Section: Theoretical Advancesmentioning

confidence: 99%

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An overview of median and stack filtering

Coyle

Gallagher

Gabbouj

1992

Circuits Systems and Signal Process

108

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“…One filter without gray-level bias is the median filter, which simply outputs the median value of a windowed set of samples [34]. Median filters have noise removal and edge localization properties that are similar to those of morphological filters [35,36].…”

Section: The Lomo Scale-spacementioning

confidence: 99%

Morphological scale-space in image processing

Bosworth

Acton

2003

Digital Signal Processing

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“…In [26] described desirable signal properties for signals used in it which if the real signal has added noise, then it may or may not be possible to remove the noise by filtering. It show how some types of noise can be removed the noised by median filtering and how other types cannot be removed.…”

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confidence: 99%