本論文提出一個基於軟式計算技術之智慧型影像濾波器包括基因型模糊影像濾波器(Genetic-based Fuzzy Image Filter, GFIF)及多維基因型模糊影像濾波器(Multilayer Genetic-based Fuzzy Image Filter, MGFF)，用來去除突波雜訊及復原高污染影像。GFIF包括模糊數建構程序、模糊濾波程序、基因學習程序及一個影像知識庫。第一步，模糊數建構程序會讀取一張樣品影像或是無雜訊影像，然後建構初始影像知識庫。第二步，模糊濾波程序包括平行模糊推論機制、模糊均值程序及模糊決策程序。模糊濾波程序會參考影像知識庫以去除突波雜訊。最後，利用基因學習程序調整影像知識庫內含的參數以達到更佳的濾波能力。本論文將GFIF處理灰階影像能力保留並修改其模糊濾波程序及調整基因學習的編碼，使其更適合應用於彩色影像濾波上，稱之為MGFF。由MSE及MAE統計曲線圖及相關實驗結果得知，GFIF及MGFF皆比現今所提出之濾波方法更有效率。透過濾波後影像的客觀觀察，GFIF及MGFF對於影像本身的色度及影像邊緣，與影像細節和紋理都有比較好的保留，而且其具有較好的去除雜訊能力。

　　In this paper, we propose an intelligent image filter based on soft-computing techniques including a genetic based fuzzy image filter (GFIF) and a multilayer genetic based fuzzy image filter (MGFF) to remove impulse noise from highly corrupted images. GFIF consists of a fuzzy number construction process, a fuzzy filtering process, a genetic learning process, and an image knowledge base. First, the fuzzy number construction process will receive a sample image or the noise-free image, then construct an image knowledge base for the fuzzy filtering process. Second, the fuzzy filtering process contains a parallel fuzzy inference mechanism, a fuzzy mean process, and a fuzzy decision process to perform the task of noise removing. Finally, based on genetic algorithm, the genetic learning process will adjust the parameters of the image knowledge base. MGFF is extended from GFIF to apply color image. By the experimental results, GFIF and MGFF achieve better performance than the state-of-the-art filters based on the criteria of Mean-Square-Error (MSE) and Mean-Absolute-Error (MAE). On the subjective evaluation of those filtered images, GFIF and MGFF also result in a higher quality of global restoration.

[1] R. C. Gonzalez and R. E. Woods, Dogital Image Processing. Pearson Education, Upper Saddle River, New Jersey.
[2] K. Arakawa, “Median filter based on fuzzy rules and its application to image restoration,” Fuzzy Sets and Systems, vol. 77, pp. 3-13, 1996.
[3] E. Abreu and S.K. Mitra, “A signal-dependent rank ordered mean (SD-ROM) filter”, Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP-95, Detroit, pp. 2371-2374, 1995.
[4] C. S. Lee, Y. H. Kuo, and P. T. Yu, “Weighted fuzzy mean filters for image processing”, Fuzzy Sets and Systems, vol. 89, pp. 157-180, 1997.
[5] Y. H. Kuo, C. S. Lee, and C. L. Chen, “High-stability AWFM filter for signal restoration and its hardware design,” Fuzzy Sets and Systems, vol. 114, no. 2, pp. 185-202, 2000.
[6] F. Russo, “Hybrid neuro-fuzzy filter for impulse noise removal,” Pattern Recognition, vol. 32, pp. 1843-1855, 1999.
[7] F. Russo, “Noise removal from image data using recursive neurofuzzy filters,” IEEE Trans. on Instrumentation and Measurement, vol. 49, no. 2, pp. 307-314, 2000.
[8] J. H. Wang, W. J. Liu, and L. D. Lin, “Histogram-based fuzzy filter for image restoration,” IEEE Trans. On Systems, Man and Cybernetics, Part B, vol.32, no. 2, pp. 230-238, 2002.
[9] R. Lukac, “Adaptive vector median filtering,” Pattern Recognition Letters, vol. 24, pp. 1889-1899, 2003.
[10] G. Pok, J. C. Liu, and A. S. Nair, “Selective removal of impulse noise based on homogeneity level information,” IEEE Trans. on Image Processing, vol. 12, no. 1, pp. 85-92, 2003.
[11] J. Y. Chang and J. L. Chen, “Classified-augmented median filters for image restoration,” IEEE Trans. on Instrumentation and Measurement, vol. 53, no. 2, pp.351-356, 2004.
[12] P. Liu, “Representation of digital image by fuzzy neural network,” Fuzzy Sets and Systems, vol. 130, pp.109-123, 2002.
[13] H. H. Tsai and P. T. Yu, “Adaptive fuzzy hybrid multichannel filters for removal of impulsive noise from color images,” Signal Processing, vol. 74, pp. 127-151, 1999.
[14] R. S. Lin and Y. C. Hsueh, “Multichannel filtering by gradient information,” Signal Processing, vol. 80, no. 2, pp. 279-293, 2000.
[15] H. H. Tsai and P. T. Yu, “Genetic-based fuzzy hybrid multichannel filters for color image restoration,” Fuzzy Sets and Systems, vol. 114, no. 2, pp. 203-224, 2000.
[16] M. Barni, F. Buti, F. Bartolini, and V. Cappellini, “A quasi-Euclidean norm to speed up vector median filtering,” IEEE Trans. on Image Processing, Vol. 9, no. 10, pp. 1704-1709, 2000.
[17] M. I. Vardavoulia, I. Andreadis, and Ph. Tsalides, “A new vector median filter for colour image processing,” Pattern Recognition Letters, vol. 22, no. 6-7, pp. 675-689, 2001.
[18] R. Lukac, “Adaptive vector median filtering,” Pattern Recognition Letters, vol. 24, no. 12, pp. 1889-1899, 2003.
[19] O. Cord’on, F. Herrera, and P. Villar, “Generating the Knowledge Base of a Fuzzy Rule-Based System by the Genetic Learning of the Data Base,” IEEE Trans. on Fuzzy System, vol. 9, no. 4, pp. 667-674, 2001.
[20] V. Castelli and L. D. Bergman, Image Database Theory and Application. John Wiley & Sons, Inc., New York, 2002.
[21] C. S. Lee and C. Y. Pan, “An intelligent fuzzy agent for meeting scheduling decision support system”, Fuzzy Sets and Systems, vol. 142, pp. 467-488, 2004.
[22] G. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic Theory and Applications. Pearson Education Taiwan Ltd., Twiwan.
[23] 孫宗瀛、楊英魁，「Fuzzy控制：理論、時作與應用」，台北，全華科技圖書股份有限公司，2001。
[24] 李允中、王小璠、蘇木春，「模糊理論及其應用」，台北，全華科技圖書股份有限公司，2003。
[25] 王文俊，「認識Fuzzy」，台北，台北，全華科技圖書股份有限公司，2000。
[26] C. T. Lin and C. S. G. Lee, “Neural-network-based fuzzy logic control and decision system,” IEEE Transactions on Computers, vol. 40, no. 12, pp. 1320-1336, 1991.
[27] C. S. Lee, J. X. Liao, and Y. H. Kuo, “A semantic-based concept clustering mechanism for chinese news ontology construction,” International Computer Symposium, Taiwan, 2002.
[28] C. S. Lee, C. P. Chen, H. J Chen, and Y. H. Kuo, “A fuzzy classification agent for personal e-news service,” International Journal of Fuzzy Systems, vol. 4, no. 4, pp. 849-856, 2002.
[29] I. Pitas and P. Tsakalides, “Multivariate ordering in color image filtering,” IEEE Trans. on Circuits and Systems for Video Technology, vol. 1, no. 3, pp. 247-259, 1991.