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Gibbs Random Field Model Based Weight Selection for the 2-D Adaptive Weighted Median Filter
August 1994 (vol. 16 no. 8)
pp. 831-837

A generalized filtering method based on the minimization of the energy of the Gibbs model is described. The well-known linear and median filters are all special cases of this method. It is shown that, with that selection of appropriate energy functions, the method can be successfully used to adapt the weights of the adaptive weighted median filter to preserve different textures within the image white eliminating the noise. The newly developed adaptive weighted median filter is based on a 3/spl times/3 square neighborhood structure. The weights of the pixels are adapted according to the clique energies within this neighborhood structure. The assigned energies to 2- or 3-pixel cliques are based on the local statistics within a larger estimation window. It is shown that the proposed filter performance is better compared to some well-known similar filters like the standard, separable, weighted and some adaptive weighted median filters.

[1] O. Yli-Harja, J. Astola, and Y. Neuvo, "Analysis of the properties of median and weighted median filters using threshold logic and stack filter representation,"IEEE Trans. Signal Processing, vol. 39, no. 2, pp. 395-410, Feb. 1991.
[2] P. Heinonen, and Y. Neuvo, "FIR-median hybrid filters,"IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-35, pp. 832-838, June 1987.
[3] G. R. Arce and M. P. McLoughlin, "Theoretical analysis of the max/median filter,"IEEE Trans. Acoust. Speech Signal Processing, vol. ASSP-35, Jan. 1987.
[4] S.-J. Ko, Y. H. Lee, and A. T. Fam, "Selective median filters," inISCAS'88, 1988, pp. 1495-1498.
[5] N. Soundararajan, "Axiomatic semantics of CSP," inProc. ACM TOPLAS, 1984, pp. 647-662.
[6] P. Salembier, "Adaptive rank order based filters,"Signal Processing, vol. 27, pp. 1-25, 1992.
[7] L. Yin, J. T. Astola, and Y. A. Neuvo, "Adaptive stack filtering with application to image processing,"IEEE Trans. Signal Processing, vol. 4I, no. 1, pp. 162-184, Jan. 1993.
[8] R. Kutka, "A variable median filter for image restoration adaptable to different types of spike noise,"Signal Processing, vol. 18, no. 2, pp. 217-224, Oct. 1989.
[9] 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. Commun., vol. COM-35, no. 6, pp. 646-652, June 1987.
[10] T. Loupas, W. N. Mcdicken, and P. L. Allan, "An adaptive weighted median filter for speckle suppression in medical ultrasonic images,"IEEE Trans. Circuits Syst., vol. 36, no. 1, pp. 129-135, Jan. 1989.
[11] H. Derin and H. Elliott, "Modeling and segmentation of noisy and textured images using Gibbs random fields,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, pp. 39-55, Jan. 1987.
[12] S. Geman and D. Geman, "Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, no. 6, pp. 721-741, Nov. 1984.
[13] D. R. Brownrigg, "The weighted median filter,"Commun. Assoc. Comput. Mach., vol. 27, pp. 204-208, Aug. 1984.
[14] J. Astola, P. Haavisto, and Y. Neuvo, "Vector Median Filters," inProc. IEEE, vol. 78, no. 4, pp. 678-689, Apr. 1990.
[15] M. I. Gürelli and L. Onural, "The adaptive directional median filter," inProc. Sixth Int. Symp. Comput. Inform. Sci., Side, Turkey, vol. II, Oct. 1991, pp. 973-979.
[16] T. A. Nodes and N. C. Gallagher, "Two-dimensional root structures and convergence properties of the separable median filter,"IEEE Trans. Acoust., Speech, and Signal Processing, vol. ASSP-31, no. 6, pp. 1350-1365, Dec. 1983.

Index Terms:
adaptive filters; minimisation; filtering and prediction theory; two-dimensional digital filters; Gibbs random field model based weight selection; 2-D adaptive weighted median filter; generalized filtering method; energy minimisation; linear filters; 3/spl times/3 square neighborhood structure; clique energies; 3-pixel cliques; 2-pixel cliques; local statistics
Citation:
L. Onural, M. Bilge Alp, M.I. Gürelli, "Gibbs Random Field Model Based Weight Selection for the 2-D Adaptive Weighted Median Filter," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 8, pp. 831-837, Aug. 1994, doi:10.1109/34.308480
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