Median filters: Some modifications and their properties

Nodes, T.; Gallagher, Neal C.

doi:10.1109/tassp.1982.1163951

Cited by 461 publications

(131 citation statements)

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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]. However, the median filter has two major disadvantages.…”

Section: The Lomo Scale-spacementioning

confidence: 99%

Morphological scale-space in image processing

Bosworth

Acton

2003

Digital Signal Processing

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Section: The Lomo Scale-spacementioning

confidence: 99%

Morphological scale-space in image processing

Bosworth

Acton

2003

Digital Signal Processing

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“…Two papers by Nodes and Gallagher [97], [99] extended the median filter to nth rank-order filters. These filters operate exactly like the median except that they put out x(,), the nth largest sample in the window, instead of the sample of middle rank.…”

Section: Generalization Of Median-type Filters : Theoretical Analysismentioning

confidence: 99%

“…The simplest examples of rank-order filters other than the median are the filters which put out x(1), the minimum, and X(2N+I) , the maximum, values in the window. Rank-order filters all possess the convergence property of the median filter, but as shown in [97] a nonmedian rank-order filter reduces any sequence to a constant value after repeated filtering.…”

Section: Generalization Of Median-type Filters : Theoretical Analysismentioning

confidence: 99%

“…The recursive median filter was introduced by Nodes and Gallagher in [97]. Letting the input sequence be denoted by {Xk} and the output sequence by {Yk}, the recursive median of window width 2N + 1 is defined by replacing some of the input samples in (1.1) by previously derived output samples as follows:…”

Section: Generalization Of Median-type Filters : Theoretical Analysismentioning

confidence: 99%

“…One very interesting result concerning this filter [97] is that just one pass of the filter produces a sequence which is invariant to any subsequent passes; in other words, a root signal is reached after only one pass of the recursive median filter. A recursive median filter has exactly the same set of root signals as the (nonrecursive) median filter of the same window width, but a given input signal might be filtered to different roots by the two 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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The plasma structure of coronal hole solar wind: Origins and evolution

Borovsky

2016

JGR Space Physics

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Whereas slow solar wind is known to be highly structured, the fast (coronal hole origin) wind is usually considered to be homogeneous. Using measurements from Helios 1 + 2, ACE, Wind, and Ulysses, structure in the coronal hole origin solar wind is examined from 0.3 AU to 2.3 AU. Care is taken to collect and analyze intervals of “unperturbed coronal hole plasma.” In these intervals, solar wind structure is seen in the proton number density, proton temperature, proton specific entropy, magnetic field strength, magnetic field to density ratio, electron heat flux, helium abundance, heavy‐ion charge‐state ratios, and Alfvenicity. Typical structure amplitudes are factors of 2, far from homogeneous. Variations are also seen in the solar wind radial velocity. Using estimates of the motion of the solar wind origin footpoint on the Sun for the various spacecraft, the satellite time series measurements are converted to distance along the photosphere. Typical variation scale lengths for the solar wind structure are several variations per supergranule. The structure amplitude and structure scale sizes do not evolve with distance from the Sun from 0.3 to 2.3 AU. An argument is quantified that these variations are the scale expected for solar wind production in open magnetic flux funnels in coronal holes. Additionally, a population of magnetic field foldings (switchbacks, reversals) in the coronal hole plasma is examined: this population evolves with distance from the Sun such that the magnetic field is mostly Parker spiral aligned at 0.3 AU and becomes more misaligned with distance outward.

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Median filters: Some modifications and their properties

Cited by 461 publications

References 10 publications

Morphological scale-space in image processing

Morphological scale-space in image processing

An overview of median and stack filtering

The plasma structure of coronal hole solar wind: Origins and evolution

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