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Proceedings Paper

Some Statistical Properties Of The Median Window
Author(s): B. Roy Frieden
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Paper Abstract

Abstract. The median window operation is being increasingly used to process images. Although the deterministic properties of the median are fairly well known, its statistical properties are not. Consider a median window of width N scanning a noisy background image with white power spectrum. We present here the probability law for the median outputs, its mean, variance, and signal-to-noise ratio, and the probability that two successive median outputs are equal. Specialization is made to speckle imagery. Key results are as follows: the probability law is of a Bernoulli multinomial form; the mean is asymptotic with N to the average background times In 2, and hence is about 30% less than the background value; the variance is asymptotic with N to a 1/N dependence; signal-to-noise ratio is asymptotic with N to Ni171 In 2. Finally, the probability that two successive median outputs are equal is 2-1(N-1)/N, or slightly less than 0.5 for N ⪆ 7. This is independent of the type of image data at hand, i.e., whether speckle, Poisson, or normal, provided that it has a white power spectrum.

Paper Details

Date Published: 27 February 1984
PDF: 6 pages
Proc. SPIE 0373, Transformations in Optical Signal Processing, (27 February 1984); doi: 10.1117/12.934553
Show Author Affiliations
B. Roy Frieden, University of Arizona (United States)


Published in SPIE Proceedings Vol. 0373:
Transformations in Optical Signal Processing
William T. Rhodes; James R. Fienup; Bahaa Saleh, Editor(s)

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