Abstract
By considering all orderings of the input samples, which are discrete-time continuous-valued, it is shown here that a weighted median (WM) filter of spanN can be specified unambiguously by 2N−1 consistent linear inequalities relating the weights. This specification is identical to that of a self-dual threshold function with the same weights. It is also shown that WM filters with symmetric weights can be specified by ternary threshold functions. Based on these inequalities, properties of WM filters which can be used to check equivalence of some WM filters are derived.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
N. S. Jayant, Average and median-based smoothing techniques for improving quality in the presence of transmission errors,IEEE Trans. Comm., vol. 24, pp. 1043–1045, September 1976.
W. K. Pratt,Digital Image Processing, New York, Wiley, 1978.
A. Rosenfeld and A. C. Kak,Digital Picture Processing, vol. I, 2nd edn., New York, Academic Press, 1982.
B. I. Justusson, Median filtering: statistical properties, inTwo Dimensional Digital Signal Processing II, ed. T. S. Huang, Springer-Verlag, Berlin, 1981.
D. R. K. Brownrigg, The weighted median filter,Comm. ACM, vol. 27, no. 8, pp. 807–818, August 1984.
D. R. K. Brownrigg, Generation of representative members of an RrSst weighted median filter class,Proc. IEE P-F, vol. 133, no. 5, pp. 445–448, August 1986.
P. D. Wendt, E. J. Coyle, and N. C. Gallagher, Jr., Stack filters,IEEE Trans. Acoust. Speech Signal Process., vol. 34, no. 4, pp. 898–911, August 1986.
O. Yli-Harja, J. Astola, and Y. Neuvo, Analysis of the properties of weighted median filters using threshold logic and stack filter representation, Research Report 9/88, Department of Information Technology, Lappeenranta University of Technology, Lappeenranta, Finland.
O. Yli-Harja, J. Astola, and Y. Neuvo, A response based design method for weighted median filters, Research Report 9/88, Department of Information Technology, Lappeenranta University of Technology, Lappeenranta, Finland.
S.-J. Ko and Y. H. Lee, Center weighted median filters and their applications to image enhancement, to appear inIEEE Trans. Circuits and Systems in September 1991.
S. S. Perlman, S. Eisenhandler, P. W. Lyons, and M. J. Shumila, Adaptive median filtering for impulse noise elimination in real-time TV signals,IEEE Trans. Comm. vol. 35, no. 6, pp. 646–652, June 1987.
T. Loupas, W. N. McDicken, and P. L. Allan, An adaptive weighted median filter for speckel suppression in medical ultrasonic images,IEEE Trans. Circuits and Systems, vol. 36, no. 1, pp. 129–135, January 1989.
S. Muroga,Threshold Logic and Its Applications, Wiley Interscience, New York, 1971.
Y. Murakami, Formal structure of decision making,Econometrica, vol. 34, no. 3, pp. 709–718, July 1966.
F. Rosenblatt,Principles of Neurodynamics: Perceptrons and the Theory of Brain Mechanisms, Spartan Books, Washington, DC, 1962.
S. B. Akers and B. H. Rutter, The use of threshold logic in character recognition,Proc. IEEE, vol. 52, no. 8, pp. 931–938, August 1964.
W. H. Hanson, Ternary threshold logic,IEEE Trans. Electron. Comput., vol. 12, pp. 191–197, June 1963.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Prasad, M.K., Lee, Y.H. Analysis of weighted median filters based on inequalities relating the weights. Circuits Systems and Signal Process 11, 115–136 (1992). https://doi.org/10.1007/BF01189223
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01189223