Morphological representation of order-statistics filters

Charif-Chefchaouni, M.; Schonfeld, Dan

doi:10.1109/83.388087

Cited by 8 publications

(6 citation statements)

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“…Finally, criteria for the morphological characterization of roots of nonlinear operators were proposed. For an application of the results presented in this paper to the morphological representation of order-statistics (median) filters refer to [12].…”

Section: Discussionmentioning

confidence: 98%

“…Maragos and Schafer [8]- [11] approximated median filters by deriving morphological bounds on median filters for one-dimensional signals. Charif-Chefchaouni and Schonfeld [12] proposed on extension of this approach to the approximation of order-statistics (median) filters by constructing morphological bounds on order-statistics (median) filters for multidimensional signals.…”

Section: Introductionmentioning

confidence: 99%

“…An important example of our approach has been investigated in the approximation of orderstatistics (median) filters by morphological operators [8]- [12]. Order-statistics (median) filters (and their repeated iterations) have been shown to yield an outstanding performance in the restoration of noisy images [13]- [20].…”

Section: Introductionmentioning

confidence: 99%

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Morphological representation of nonlinear filters

Charif-Chefchaouni

Schonfeld

1994

J Math Imaging Vis

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Abstract. Morphological operators provide very efficient algorithms for signal (image) processing. The efficiency of morphological operators has been captured by using them as approximations of nonlinear operators in numerous applications (e.g., image restoration). Our approach to the approximation of nonlinear operators is the construction of morphological bounds on them. We present a general theory on the morphological bounds on nonlinear operators, propose conditions for the existence of these bounds, and derive several fundamental morphological bounds. We also derive morphological bounds on iterations of nonlinear operators, which are superior to the original nonlinear operator in some applications. Because obtaining the results of the convergence of iterations of a nonlinear operator is often particularly desirable, we provide morphological bounds on the convergence of such iterations, and propose conditions for their convergence based on morphological properties. Finally, we propose several criteria for the morphological characterization of roots of nonlinear operators.

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Section: Discussionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Morphological representation of nonlinear filters

Charif-Chefchaouni

Schonfeld

1994

J Math Imaging Vis

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“…One approach to such an approximation is obtained by the generation of morphological filters as bounds on median filters (and their repeated iterations) [9]. The morphological filters generated, however, possess a. fundamental limitation: morphological filters are biased estimators; i.e., morphological filters are not self-dual operators [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

<title>Generalized morphological center: self-duality</title>

Charif-Chefchaouni

Schonfeld

1994

SPIE Proceedings

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“…From Fig. 3(a) (4) where., +, and ® stand for logical AND, OR, NOT and XNOR, respectively. Also, from Fig.…”

Section: A Systolic Array Implementation For Rank Order Filteringmentioning

confidence: 99%

Realization of rank order filters based on majority gate

Γαστεράτος

Andreadis

Tsalides

1997

Pattern Recognition

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Abstract--A new technique for the implementation of a single hardware structure capable of computing any rank order filter is presented in this paper. The proposed technique, which is based on the majority gate, achieves faster extraction of setting flag signals and, therefore, shorter processing times are attained. A pipelined systolic array, suitable for performing rank order filtering, is also presented. Applications of rank order filters include digital image processing, speech processing and coding and digital TV applications. ~ 1997 Pattern Recognition Society. Published by Elsevier Science Ltd. Nonlinear filtersComputer visionRank order filters are a class of nonlinear filters. The input of such filters is a window of data with an odd number of elements. These elements are sorted in ascending order and the output of the rank order filter with rank r is the rth element (rth order statistic)J 1) Special cases of rank order filters are median, minimum and maximum filters, where the outputs are the median, the minimum and the maximum values of the input data window, respectively. Rank order filters exhibit excellent robustness properties and provide solutions in many cases where linear filters are inappropriate. They can suppress high-frequency and impulse noise in an image, avoiding at the same time extensive blurting of the image, since they have good edge preservation properties. They have found numerous applications, such as in digital image analysis, in speech processing and coding, in digital TV applications, etc. (~'2) Median and rank order filters are strongly related with morphological filters, another class of nonlinear illters. (3'4) It has been shown that erosions and dilations are special cases of rank order filters and that any rank order filter can be expressed either as a maximum of erosions or as a minimum of dilations. °) Therefore, algorithms which originally have been devised for rank order and median filters can be used for realization of morphological operators. (5'6) Several algorithms have been proposed for the realization of rank order filters, such as tree sorts, shell sorts and quick sorts. (1) Although these algorithms are suitable for software implementation, they result in inefficient hardware structures, since they handle the numbers in wordlevel. Rank order filters can be implemented in VLSI

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Morphological representation of order-statistics filters

Cited by 8 publications

References 9 publications

Morphological representation of nonlinear filters

Morphological representation of nonlinear filters

<title>Generalized morphological center: self-duality</title>

Realization of rank order filters based on majority gate

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