Fuzzy Filters for Noise Reduction: The Case of Gaussian Noise

Noise reduction is a well-known problem in image processing. The reduction of noise in an image sometimes is as a goal itself, and sometimes is considered as a pre-processing step. Besides the classical filters for noise reduction, quite a lot of fuzzy inspired filters have been proposed during the past years. However, it is very difficult to judge the quality of this wide variety of filters. For which noise types are they designed? How do they perform for those noise types? How do they perform compared to each other? Can we select filters that clearly outperform the others? Is there a difference between numerical and visual results? In this paper, we answer these questions for images that are corrupted with Gaussian noise

[1]  Pao-Ta Yu,et al.  Weighted fuzzy mean filters for image processing , 1997, Fuzzy Sets Syst..

[2]  Raghu Krishnapuram,et al.  Image enhancement based on fuzzy logic , 1995, Proceedings., International Conference on Image Processing.

[3]  D. Van De Ville,et al.  An overview of classical and fuzzy-classical filters for noise reduction , 2001, 10th IEEE International Conference on Fuzzy Systems. (Cat. No.01CH37297).

[4]  D. Ville,et al.  Fuzzy Filters for Image Processing , 2003 .

[5]  Etienne Kerre,et al.  Fuzzy Filters for Noise Reduction: the Case of Impulse Noise , 2004 .

[6]  M. Mancuso,et al.  A fuzzy decision directed filter for impulsive noise reduction , 1996, Fuzzy Sets Syst..

[7]  Kaoru Arakawa,et al.  Median filter based on fuzzy rules and its application to image restoration , 1996, Fuzzy Sets Syst..

[8]  Dimitri Van De Ville,et al.  Noise reduction by fuzzy image filtering , 2003, IEEE Trans. Fuzzy Syst..

[9]  H. Kwan.  Fuzzy Filters for Noise Reduction in Images , 2003 .

[10]  Etienne E. Kerre,et al.  Using similarity measures and homogeneity for the comparison of images , 2004, Image Vis. Comput..

[11]  Etienne E. Kerre,et al.  Using Similarity Measures for Histogram Comparison , 2003, IFSA.

[12]  Kaoru Arakawa,et al.  Fuzzy Rule-Based Image Processing with Optimization , 2000 .

[13]  Fabrizio Russo,et al.  FIRE operators for image processing , 1999, Fuzzy Sets Syst..

[14]  Jung-Hua Wang,et al.  HAF: an Adaptive Fuzzy Filter for Restoring Highly Corrupted Images by Histogram Estimation , 1999 .

[15]  Ivan Kalaykov,et al.  Fuzzy-Similarity-Based Image Noise Cancellation , 2002, AFSS.

[16]  F. Russo,et al.  A fuzzy filter for images corrupted by impulse noise , 1996, IEEE Signal Processing Letters.

[17]  Dimitri Van De Ville,et al.  A comparative study of classical and fuzzy filters for noise reduction , 2001, 10th IEEE International Conference on Fuzzy Systems. (Cat. No.01CH37297).

[18]  Ivan Kalaykov,et al.  Real-time Image Noise Cancellation Based on Fuzzy Similarity , 2003 .

[19]  Ivan Kalaykov,et al.  Fuzzy-similarity-based noise cancellation for real-time image processing , 2001, 10th IEEE International Conference on Fuzzy Systems. (Cat. No.01CH37297).

[20]  Giovanni Ramponi,et al.  Corrupted A Fuzzy Filter for Images by Impulse Noise , 1996 .

[21]  Mohammad Bagher Menhaj,et al.  A Fuzzy Logic Control Based Approach for Image Filtering , 2000 .

[22]  Vladimir Zlokolica,et al.  A new two step color filter for impulse noise , 2004 .

[23]  Giovanni Ramponi,et al.  A noise smoother using cascaded FIRE filters , 1995, Proceedings of 1995 IEEE International Conference on Fuzzy Systems..

[24]  Yau-Hwang Kuo,et al.  Adaptive Fuzzy Filter and Its Application to Image Enhancement , 2000 .

[25]  Dimitri Van De Ville,et al.  An overview of fuzzy filters for noise reduction , 2001, 10th IEEE International Conference on Fuzzy Systems. (Cat. No.01CH37297).

[26]  Giovanni Ramponi,et al.  Removal of impulse noise using a FIRE filter , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.