Threshold decomposition of multidimensional ranked order operations

Fitch, J. Patrick; Coyle, Eugene; Gallagher, Neal C.

doi:10.1109/tcs.1985.1085740

Cited by 104 publications

(30 citation statements)

References 6 publications

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“…This idea is also at the basis of the so-called -"lters introduced by Preston [60] in 1983. More precisely, -"lters use the threshold decomposition and stacking (i.e., increasing) properties [18,40] of rank "lters for processing grey scale images with a "nite number of grey scale levels: the output image is obtained by summing up the thresholds of the convolution of each level set of the image. -"lters may use an additional &level parameter' which indicates whether a low rank/high rank or high rank/low rank sequence must be applied below or above the speci"ed level.…”

Section: Linksmentioning

confidence: 99%

On morphological operators based on rank filters

Soille

2002

Pattern Recognition

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Note that the term order xlters [15] concerns a generalization of rank order "lters whereby the sorted array of signal values is mapped by a real-valued not-necessarily linear function. When the function is linear, order "lters correspond to thȩ -"lters proposed earlier [16]. AbstractRank order morphological operators have been designed to better cope with shape variations and noise than the corresponding operators with plain structuring elements. In this paper, starting from a brief historical overview of rank order "lters and erosions/dilations in digital image processing, rank order based morphological operators are surveyed. We also highlight the relations between these operators and show that many are similar if not equivalent. An extensive bibliography is provided.

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Section: Linksmentioning

confidence: 99%

On morphological operators based on rank filters

Soille

2002

Pattern Recognition

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“…They showed that all rank-order-based filters possess a limited superposition property called the threshold decomposition [43], [44], which says that median filtering any sequence whose elements take on values in the set Q = {0, 1,..., M -1} is equivalent to decomposing the signal into binary sequences by thresholding at each level from 1 through M -1, filtering each resulting binary sequence by a (binary) median filter, and then adding up the results.…”

Section: Generalization Of Median-type Filters : Theoretical Analysismentioning

confidence: 99%

“…Getting back to the threshold decomposition of the median filter, Fitch et al [44] showed that this property was a powerful tool that can be used to analyze the whole class of rank-order filters, not just median filters as in [43]. Arce and McLoughlin [10] also used this tool to analyze the behavior of their max/median filters.…”

Section: Generalization Of Median-type Filters : Theoretical Analysismentioning

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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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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“…Several VLSI designs for median filters are studied in [3], where it is stated that for a relatively small pixel value resolution the threshold decomposition technique [4] is probably the best choice. However, implementation of filters capable of handling high-resolution numbers is not practical, since the complexity increases exponentially with both the data resolution and data window size.…”

Section: Introductionmentioning

confidence: 99%

A new algorithm for weighted order statistics operations

Γαστεράτος

Andreadis

1999

IEEE Signal Process. Lett.

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Abstract.A new algorithm suitable for the computation of weighted order statistics operations is presented in this letter. The algorithm is based on local histogram and a successive approximation technique. The successive approximation technique ensures that the result of the weighted order statistics operation is computed in a fixed number of steps, equal to the pixel value resolution. Comparative experimental results are also included. It is shown that the proposed algorithm is faster than the quick sort algorithm for weighted order statistics operations.

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Threshold decomposition of multidimensional ranked order operations

Cited by 104 publications

References 6 publications

On morphological operators based on rank filters

On morphological operators based on rank filters

An overview of median and stack filtering

A new algorithm for weighted order statistics operations

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