DocumentCode :
1194488
Title :
Some convergence properties of median filters
Author :
Wendt, Peter D. ; Coyle, Edward J. ; Gallagher, Neal C., Jr.
Volume :
33
Issue :
3
fYear :
1986
fDate :
3/1/1986 12:00:00 AM
Firstpage :
276
Lastpage :
286
Abstract :
A median filter is a nonlinear digital filter which consists of a window of length 2N + 1 that moves over a signal of finite length. For each input sample, the corresponding output point is the median of all samples in the window centered on that input sample. Any finite length, M -level, signal that ends with constant regions of length N + 1 will converge to an invariant signal in a finite number of passes of this median filter. Such an invariant signal is called a root. The concept of a root signal has proved to be crucial in understanding the properties of the median filter, root signals are to median filters what passband signals are to linear signals. In this paper, two results concerning the rate at which a signal is filtered to a root are developed. For a window of width 3, we derive a recursive formula to count the number of binary signals of length L that converge to a root in exactly m passes of a median filter. Also, we show that, given a window of width 2N + 1 , any signal of length L will converge to a root in at most 3\\lceil frac{(L-2)}{2(N + 2)}\\rceil passes of the filter.
Keywords :
DSP; Digital signal processing (DSP); Image processing; Multidimensional digital filters; Additive noise; Convergence; Copper; Digital filters; Gaussian noise; Laser noise; Layout; Nonlinear filters; Signal processing; Speckle;
fLanguage :
English
Journal_Title :
Circuits and Systems, IEEE Transactions on
Publisher :
ieee
ISSN :
0098-4094
Type :
jour
DOI :
10.1109/TCS.1986.1085911
Filename :
1085911
Link To Document :
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