Some statistical properties of median filters

Ataman, E.; Aatre, V. K.; Wong, K.M.

doi:10.1109/tassp.1981.1163659

Cited by 89 publications

(27 citation statements)

References 2 publications

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“…The median filter is a nonlinear smoothing technique that preserves signal edges or monotonic changes in trend and particularly removes short-duration impulse noise, which is not possible using linear algorithms [46]. The median filter employs a window moving over the temporal curve and obtains the median value, a particular case of the order statistic (or rank statistic) of a finite set of real numbers, that is taken as the output.…”

Section: Image Denoisingmentioning

confidence: 99%

Comparative Analysis of MODIS Time-Series Classification Using Support Vector Machines and Methods Based upon Distance and Similarity Measures in the Brazilian Cerrado-Caatinga Boundary

et al. 2015

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Abstract:We have mapped the primary native and exotic vegetation that occurs in the Cerrado-Caatinga transition zone in Central Brazil using MODIS-NDVI time series (product MOD09Q1) data over a two-year period (2011)(2012)(2013). Our methodology consists of the following steps: (a) the development of a three-dimensional cube composed of the NDVI-MODIS time series; (b) the removal of noise; (c) the selection of reference temporal curves and classification using similarity and distance measures; and (d) classification using support vector machines (SVMs). We evaluated different temporal classifications using similarity and distance measures of land use and land cover considering several combinations of attributes. Among the classification using distance and similarity measures, the best result employed the Euclidean distance with the NDVI-MODIS data by considering more than one reference temporal curve per class and adopting six mapping classes. In the majority of tests, the SVM classifications yielded better results than other methods. The best OPEN ACCESSRemote Sens. 2015, 7 12161 result among all the tested methods was obtained using the SVM classifier with a fourth-degree polynomial kernel; an overall accuracy of 80.75% and a Kappa coefficient of 0.76 were obtained. Our results demonstrate the potential of vegetation studies in semiarid ecosystems using time-series data.

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Section: Image Denoisingmentioning

confidence: 99%

Comparative Analysis of MODIS Time-Series Classification Using Support Vector Machines and Methods Based upon Distance and Similarity Measures in the Brazilian Cerrado-Caatinga Boundary

et al. 2015

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“…To be specific, they derived the bivariate distribution function for median-filtered sequences of independent, second-order random variables. Ataman et al [16] showed that, under certain conditions, median filters can remove impulsive plus Gaussian white noise better than Harming filters. In [99] the output distribution of the one-dimensional median filter was derived for several cases including the kth-order output distribution with any input distribution.…”

Section: Theoretical Analysis Of Median Filtersmentioning

confidence: 99%

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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“…Fixed value (or salt and pepper) impulsive noise is one such noise that gets added with the digital images at random locations due to errors in transmission; pixel element's malfunctioning in the camera sensors, and faulty memory locations [1][2][3].Noise of this type possess an important and unique characteristic in that, it alters only a portion of the pixels' intensities at random positions into either relatively 'low' or 'high' intensity values enforcing those contaminated pixels with high intensity values to appear as white spots (or bright dots) on the image (that is 'salt'), while pixels noised with low grey values to appear as black spots (or dark dots) on the image (that is 'pepper'), while the rest are unaltered. Impulsive noise pixels of this nature, termed as salt-and-pepper noise (SPN) corrupted pixels [2][3] posses a relatively high contrast toward their neighborhood, even though the corruption percentage is low and can severely affect to degrade the appearance and the retrievation accuracy of the underlying image quite significantly [1][2] Further, it is to be noted that the human perception is heavily based on image edge information [1,[3][4].…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, the major essence and a prime goal in image restoration applications is to de-noise and reduce the salt and pepper impulsive noise effects [4][5][6] with vital features such as image edges preserved intact. This requirement can be met with some success using nonlinear basic median filter introduced by John Tukey [7] as an effective alternative to linear smoothers such as mean filters [1,2] for filtering signals having a wide spectrum.…”

Section: Introductionmentioning

confidence: 99%