A New Fuzzy Additive Noise Reduction Method
A New Fuzzy Additive Noise Reduction Method Stefan Schulte , Val´erie De Witte, Mike Nachtegael, Tom M´elange, and Etienne E. Kerre Department of Applied Mathematics and Computer Science, The Fuzziness and Uncertainty Modelling Research Group, Ghent University, Krijgslaan 281 (Building S9), 9000 Gent, Belgium [email protected], [email protected] http://fuzzy.ugent.be/
Abstract. In this paper we present a new alternative noise reduction method for color images that were corrupted with additive Gaussian noise. We illustrate that color images have to be processed in a different way than most of the state-of-the-art methods. The proposed method consists of two sub-filters. The main concern of the first subfilter is to distinguish between local variations due to noise and local variations due to image structures such as edges. This is realized by using the color component distances instead of component differences as done by most current filters. The second subfilter is used as a complementary filter which especially preserves differences between the color components. This is realized by calculating the local differences in the red, green and blue environment separately. These differences are then combined to calculate the local estimation of the central pixel. Experimental results show the feasibility of the proposed approach.
1
Introduction
In the last years the area of vector filters (multichannel, multispectral, multicomponent) signal processing has dramatically increased [1,2,3,4,5]. Numerous filtering techniques are based on multivariate order statistics [6], which were developed to improve the componentwise filtering techniques, i.e., the pixel value rearranging and chromatic shifting. The fact that different types of noise contaminated color images in distinct ways poses a major challenge for the vector filtering techniques [7]. Most of the vector filters were specially designed to remove impulse noise. Some vector filters are designed to cope with additive and mixed noise corruption, but at the cost of possible image edges and details smearing. Some fuzzy vector filtering techniques [8,9] have tried to combine different types of standard vector filters using a large number of fuzzy rules. All these vector based approaches do not receive the same noise suppression as the more complex wavelet based methods for the additive Gaussian noise case. Most
The authors acknowledge the support of Ghent University under the GOA-project 12.0515.03.
M. Kamel and A. Campilho (Eds.): ICIAR 2007, LNCS 4633, pp. 12–23, 2007. c Springer-Verlag Berlin Heidelberg 2007
A New Fuzzy Additive Noise Reduction Method
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Fig. 3. The restoration of a noisy “Baboon” image with (a) a noise-free part, (b) the same part contaminated with additive Gaussian noise with σ = 30, (c) FCG, (d) BLSGSM, (e) BiShrink, (f) TLS, (g) FuzzyShrink, (h) HMT, (i) FBF, (j) GOA, (k) EIFCF, (l) GMAV
based methods. We also illustrated that we get a better performance (numerically as well as visually) when a wavelet based method (e.g. the FuzzyShrink method) is combined with our proposed method. Future research can be focused on this issue and on the construction of other fuzzy wavelet filtering methods for color images to suppress other noise types as well (rician noise, speckle noise, stripping noise, etc.).
References 1. Guo, S.M., Lee, C.S., Hsu, C.Y.: An intelligent image agent based on softcomputing techniques for color image processing. Expert Systems with Applications 28, 483–494 (2005) 2. Lucchese, L., Mitra, S.K.: A New Class of Chromatic Filters for Color Image Processing: Theory and Applications. IEEE Transactions on Image Processing 13(4), 534–543 (2004)
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3. Plataniotis, K.N., Androutsos, D., Venetsanopoulos, A.N.: Colour image processing using fuzzy vector directional filters. In: Proceedings of the IEEE International Workshop on Nonlinear Signal and Image Processing, pp. 535–538. IEEE Computer Society Press, Los Alamitos (1995) 4. Plataniotis, K.N., Venetsanopoulos, A.N.: Color Image Processing and Applications. Springer, Berlin, Germany (2000) 5. Vertan, C., Buzuloiu, V.: Fuzzy nonlinear filtering of color images. In: Kerre, E.E., Nachtegael, M. (eds.) Fuzzy Techniques in Image Processing, vol. 52, pp. 248–264. Springer Physica Verlag, Heidelberg (2000) 6. Arce, G.R., Foster, R.E.: Detail-preserving ranked-order based filters for image processing. IEEE Transactions on Acoustics, Speech, and Signal Processing 37(1), 83–93 (1989) 7. Lukac, R., Smolka, B., Martin, K., Plataniotis, K.N., Venetsanopoulos, A.N.: Vector filtering for color imaging. IEEE Signal Processing Magazine 22(1), 74–86 (2005) 8. Hore, S., Qiu, B., Wu, H.R.: Improved vector filtering for color images using fuzzy noise detection. Optical Engineering 42(6), 1656–1664 (2003) 9. Tsai, H.H., Yu, P.T.: Genetic-based fuzzy hybrid multichannel filters for color image restoration. Fuzzy Sets and Systems 114(2), 203–224 (2000) 10. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems Man and Cybernetic 15, 116–132 (1985) 11. Kerre, E.E.: Fuzzy Sets and Approximate Reasoning. Xian Jiaotong University Press, Xian Jiaotong (1998) 12. Zadeh, L.A.: Fuzzy Sets. Information and Control 8(3), 338–353 (1965) 13. Cornelis, C., Deschrijver, G., Kerre, E.E.: Classification of intuitionistic fuzzy implicators: an algebraic approach. In: Proceedings of the 6th Joint Conference on Information Sciences, pp. 105–108 (2002) 14. Kwan, H.K.: Fuzzy filters for noise reduction in images. In: Nachtegael, M., Van der Weken, D., Van De Ville, D., Kerre, E.E. (eds.) Fuzzy Filters for Image Processing, vol. 122, pp. 25–53. Springer Physica Verlag, Heidelberg (2003) 15. Arakawa, K.: Median filter based on fuzzy rules and its application to image restoration. Fuzzy Sets and Systems 77, 3–13 (1996) 16. Morillas, S., Gregori, V., Sapena, A.: Fuzzy Bilateral Filtering for Color Images. In: Campilho, A., Kamel, M. (eds.) ICIAR 2006. LNCS, vol. 4141, pp. 138–145. Springer, Heidelberg (2006) 17. Van De Ville, D., Nachtegael, M., Van der Weken, D., Kerre, E.E., Philips, W.: Noise reduction by fuzzy image filtering. IEEE Transactions on Fuzzy Systems 11, 429–436 (2003) 18. Farbiz, F., Menhaj, M.B.: A fuzzy logic control based approach for image filtering. In: Kerre, E.E., Nachtegael, M. (eds.) Fuzzy Techniques in Image Processing, vol. 52, pp. 194–221. Springer Physica Verlag, Heidelberg (2000) 19. Romberg, J.K., Choi, H., Baraniuk, R.G., Kingbury, N.: Multiscale classification using complex wavelets and hidden Markov tree models. In: ICIP. Proceedings of the IEEE International Conference on Image Processing, pp. 371–374. IEEE Computer Society Press, Los Alamitos (2000) 20. Romberg, J.K., Choi, H., Baraniuk, R.G.: Bayesian tree-structured image modeling using wavelet-domain hidden Markov models. IEEE Transactions on Image Processing 10(7), 1056–1068 (2001)
A New Fuzzy Additive Noise Reduction Method
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21. Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Image Denoising with BlockMatching and 3D Filtering. In: Proceedings of SPIE Electronic Imaging: Algorithms and Systems, Neural Networks, and Machine Learning, pp. 354–365 (2006) 22. Portilla, J., Strela, V., Wainwright, M., Simoncelli, E.: Image denoising using gaussian scale mixtures in the wavelet domain. IEEE Transactions on Image Processing 12, 1338–1351 (2003) 23. S ¸ endur, L., Selesnick, I.W.: Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency. IEEE Transactions on Signal Processing 50, 2744–2756 (2002) 24. Hirakawa, K., Parks, T.W.: Image Denoising for Signal-Dependent Noise. In: Proceedings of the IEEE Acoustics, Speech, and Signal Processing, pp. 18–23. IEEE Computer Society Press, Los Alamitos (2005) 25. Schulte, S., Huysmans, A., Piˇzurica, A., Kerre, E.E., Philips, W.: A new fuzzybased wavelet shrinkage image denoising technique. In: Blanc-Talon, J., Philips, W., Popescu, D., Scheunders, P. (eds.) ACIVS 2006. LNCS, vol. 4179, pp. 12–23. Springer, Heidelberg (2006) 26. Gilboa, G., Zeevi, Y.Y., Sochen, N.A.: Complex diffusion processes for image filtering. In: Kerckhove, M. (ed.) Scale-Space 2001. LNCS, vol. 2106, pp. 299–307. Springer, Heidelberg (2001)
Abstract. In this paper we present a new alternative noise reduction method for color images that were corrupted with additive Gaussian noise. We illustrate that color images have to be processed in a different way than most of the state-of-the-art methods. The proposed method consists of two sub-filters. The main concern of the first subfilter is to distinguish between local variations due to noise and local variations due to image structures such as edges. This is realized by using the color component distances instead of component differences as done by most current filters. The second subfilter is used as a complementary filter which especially preserves differences between the color components. This is realized by calculating the local differences in the red, green and blue environment separately. These differences are then combined to calculate the local estimation of the central pixel. Experimental results show the feasibility of the proposed approach.
1
Introduction
In the last years the area of vector filters (multichannel, multispectral, multicomponent) signal processing has dramatically increased [1,2,3,4,5]. Numerous filtering techniques are based on multivariate order statistics [6], which were developed to improve the componentwise filtering techniques, i.e., the pixel value rearranging and chromatic shifting. The fact that different types of noise contaminated color images in distinct ways poses a major challenge for the vector filtering techniques [7]. Most of the vector filters were specially designed to remove impulse noise. Some vector filters are designed to cope with additive and mixed noise corruption, but at the cost of possible image edges and details smearing. Some fuzzy vector filtering techniques [8,9] have tried to combine different types of standard vector filters using a large number of fuzzy rules. All these vector based approaches do not receive the same noise suppression as the more complex wavelet based methods for the additive Gaussian noise case. Most
The authors acknowledge the support of Ghent University under the GOA-project 12.0515.03.
M. Kamel and A. Campilho (Eds.): ICIAR 2007, LNCS 4633, pp. 12–23, 2007. c Springer-Verlag Berlin Heidelberg 2007
A New Fuzzy Additive Noise Reduction Method
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
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Fig. 3. The restoration of a noisy “Baboon” image with (a) a noise-free part, (b) the same part contaminated with additive Gaussian noise with σ = 30, (c) FCG, (d) BLSGSM, (e) BiShrink, (f) TLS, (g) FuzzyShrink, (h) HMT, (i) FBF, (j) GOA, (k) EIFCF, (l) GMAV
based methods. We also illustrated that we get a better performance (numerically as well as visually) when a wavelet based method (e.g. the FuzzyShrink method) is combined with our proposed method. Future research can be focused on this issue and on the construction of other fuzzy wavelet filtering methods for color images to suppress other noise types as well (rician noise, speckle noise, stripping noise, etc.).
References 1. Guo, S.M., Lee, C.S., Hsu, C.Y.: An intelligent image agent based on softcomputing techniques for color image processing. Expert Systems with Applications 28, 483–494 (2005) 2. Lucchese, L., Mitra, S.K.: A New Class of Chromatic Filters for Color Image Processing: Theory and Applications. IEEE Transactions on Image Processing 13(4), 534–543 (2004)
22
S. Schulte et al.
3. Plataniotis, K.N., Androutsos, D., Venetsanopoulos, A.N.: Colour image processing using fuzzy vector directional filters. In: Proceedings of the IEEE International Workshop on Nonlinear Signal and Image Processing, pp. 535–538. IEEE Computer Society Press, Los Alamitos (1995) 4. Plataniotis, K.N., Venetsanopoulos, A.N.: Color Image Processing and Applications. Springer, Berlin, Germany (2000) 5. Vertan, C., Buzuloiu, V.: Fuzzy nonlinear filtering of color images. In: Kerre, E.E., Nachtegael, M. (eds.) Fuzzy Techniques in Image Processing, vol. 52, pp. 248–264. Springer Physica Verlag, Heidelberg (2000) 6. Arce, G.R., Foster, R.E.: Detail-preserving ranked-order based filters for image processing. IEEE Transactions on Acoustics, Speech, and Signal Processing 37(1), 83–93 (1989) 7. Lukac, R., Smolka, B., Martin, K., Plataniotis, K.N., Venetsanopoulos, A.N.: Vector filtering for color imaging. IEEE Signal Processing Magazine 22(1), 74–86 (2005) 8. Hore, S., Qiu, B., Wu, H.R.: Improved vector filtering for color images using fuzzy noise detection. Optical Engineering 42(6), 1656–1664 (2003) 9. Tsai, H.H., Yu, P.T.: Genetic-based fuzzy hybrid multichannel filters for color image restoration. Fuzzy Sets and Systems 114(2), 203–224 (2000) 10. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems Man and Cybernetic 15, 116–132 (1985) 11. Kerre, E.E.: Fuzzy Sets and Approximate Reasoning. Xian Jiaotong University Press, Xian Jiaotong (1998) 12. Zadeh, L.A.: Fuzzy Sets. Information and Control 8(3), 338–353 (1965) 13. Cornelis, C., Deschrijver, G., Kerre, E.E.: Classification of intuitionistic fuzzy implicators: an algebraic approach. In: Proceedings of the 6th Joint Conference on Information Sciences, pp. 105–108 (2002) 14. Kwan, H.K.: Fuzzy filters for noise reduction in images. In: Nachtegael, M., Van der Weken, D., Van De Ville, D., Kerre, E.E. (eds.) Fuzzy Filters for Image Processing, vol. 122, pp. 25–53. Springer Physica Verlag, Heidelberg (2003) 15. Arakawa, K.: Median filter based on fuzzy rules and its application to image restoration. Fuzzy Sets and Systems 77, 3–13 (1996) 16. Morillas, S., Gregori, V., Sapena, A.: Fuzzy Bilateral Filtering for Color Images. In: Campilho, A., Kamel, M. (eds.) ICIAR 2006. LNCS, vol. 4141, pp. 138–145. Springer, Heidelberg (2006) 17. Van De Ville, D., Nachtegael, M., Van der Weken, D., Kerre, E.E., Philips, W.: Noise reduction by fuzzy image filtering. IEEE Transactions on Fuzzy Systems 11, 429–436 (2003) 18. Farbiz, F., Menhaj, M.B.: A fuzzy logic control based approach for image filtering. In: Kerre, E.E., Nachtegael, M. (eds.) Fuzzy Techniques in Image Processing, vol. 52, pp. 194–221. Springer Physica Verlag, Heidelberg (2000) 19. Romberg, J.K., Choi, H., Baraniuk, R.G., Kingbury, N.: Multiscale classification using complex wavelets and hidden Markov tree models. In: ICIP. Proceedings of the IEEE International Conference on Image Processing, pp. 371–374. IEEE Computer Society Press, Los Alamitos (2000) 20. Romberg, J.K., Choi, H., Baraniuk, R.G.: Bayesian tree-structured image modeling using wavelet-domain hidden Markov models. IEEE Transactions on Image Processing 10(7), 1056–1068 (2001)
A New Fuzzy Additive Noise Reduction Method
23
21. Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Image Denoising with BlockMatching and 3D Filtering. In: Proceedings of SPIE Electronic Imaging: Algorithms and Systems, Neural Networks, and Machine Learning, pp. 354–365 (2006) 22. Portilla, J., Strela, V., Wainwright, M., Simoncelli, E.: Image denoising using gaussian scale mixtures in the wavelet domain. IEEE Transactions on Image Processing 12, 1338–1351 (2003) 23. S ¸ endur, L., Selesnick, I.W.: Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency. IEEE Transactions on Signal Processing 50, 2744–2756 (2002) 24. Hirakawa, K., Parks, T.W.: Image Denoising for Signal-Dependent Noise. In: Proceedings of the IEEE Acoustics, Speech, and Signal Processing, pp. 18–23. IEEE Computer Society Press, Los Alamitos (2005) 25. Schulte, S., Huysmans, A., Piˇzurica, A., Kerre, E.E., Philips, W.: A new fuzzybased wavelet shrinkage image denoising technique. In: Blanc-Talon, J., Philips, W., Popescu, D., Scheunders, P. (eds.) ACIVS 2006. LNCS, vol. 4179, pp. 12–23. Springer, Heidelberg (2006) 26. Gilboa, G., Zeevi, Y.Y., Sochen, N.A.: Complex diffusion processes for image filtering. In: Kerckhove, M. (ed.) Scale-Space 2001. LNCS, vol. 2106, pp. 299–307. Springer, Heidelberg (2001)
