Journal of Soft Computing and Information Technology

Journal of Soft Computing and Information Technology

An Efficient Fuzzy Filter for Impulse Noise Reduction in Color Images

Document Type : Persian Original Article

Authors
Reza Ghasemi 1
Mohsen Yoosefi Nejad 2
1 Department of Statistics, Payame Noor University (PNU), Tehran, Iran.
2 Department of Computer Engineering and Information Technology, Payame Noor University (PNU), Tehran, Iran.
10.22034/jscit.2025.218868
Abstract
Impulsive noise reduction from color images is a fundamental challenge in image processing, as this noise commonly occurs during the acquisition and transmission of digital images and negatively impacts image quality. In this paper, a novel method for reducing this noise from color images based on fuzzy filtering is proposed. This approach utilizes fuzzy metrics to evaluate the color similarity of pixels and their spatial proximity within a fuzzy framework. The color of each pixel is defined as a fuzzy number, and substitute values for noisy pixels are computed using fuzzy metrics. In this method, color similarity is assessed using three-component color vectors (RGB), while spatial proximity is evaluated using fuzzy metrics. The proposed algorithm utilizes a sliding window and is executed in three main steps: (1) converting the pixel values in the window into fuzzy numbers, (2) computing the color similarity and spatial distance of pixels using two fuzzy distance metrics, and (3) selecting the most suitable pixel based on the obtained criteria and replacing it with the central pixel of the window. The proposed algorithm has been tested on various images, including grayscale and color noisy images. The results indicate that this approach outperforms existing approaches in noise reduction and detail preservation. This superiority includes higher Peak Signal-to-Noise Ratio (PSNR), higher Structural Similarity Index Measure (SSIM), and more accurate edge and detail restoration.
Keywords
Fuzzy filter
image processing
impulsive noise reduction
salt-and-pepper noise
color similarity evaluation
[1] K. Menger, "Statistical metrics," Proc. Natl. Acad. Sci. U.S.A., vol. 28, no. 12, pp. 535–537, Dec. 1942, doi: 10.1073/pnas.28.12.535.
[2] I. Kramosil and J. Michálek, "Fuzzy metrics and statistical metric spaces," Kybernetika, vol. 11, no. 5, pp. 336–344, 1975.
[3] L. Nedović, N. M. Ralević, and I. Pavkov, "Aggregated distance functions and their application in image processing," Soft Comput., vol. 22, no. 14, pp. 4723–4739, Jul. 2018, doi: 10.1007/s00500-017-2657-9.
[4] S. Bandyopadhyay, S. Das, and A. Datta, "A hybrid fuzzy filtering-fuzzy thresholding technique for region of interest detection in noisy images," Appl. Intell., vol. 50, no. 4, pp. 1112–1132, Apr. 2020, doi: 10.1007/s10489-019-01551-z.
[5] S. Morillas, V. Gregori, G. Peris-Fajarnes, and A. Sapena, "New adaptive vector filter using fuzzy metrics," Journal of Electronic Imaging, vol. 16, no. 3, Art. no. 033007-033007-15, Jul.–Sep. 2007, doi: 10.1117/1.2754647.
[6] V. Gregori, S. Morillas, and A. Sapena, "Examples of fuzzy metrics and applications," Fuzzy sets and systems, vol. 170, no. 1, pp. 95-111, Jan. 2011, doi: 10.1016/j.fss.2010.10.019.
[7] V. Gregori, S. Morillas, B. Roig, and A. Sapena, "Fuzzy averaging filter for impulse noise reduction in colour images with a correction step," Journal of Visual Communication and Image Representation, vol. 55, pp. 518-528, Aug. 2018, doi: 10.1016/j.jvcir.2018.06.025.
[8] N. M. Ralević, D. Karaklić, and N. Pištinjat, "Fuzzy metric and its applications in removing the image noise," Soft Computing, vol. 23, no. 22, pp. 12049–12061, Nov. 2019, doi: 10.1007/s00500-019-03762-5.
[9] M. M. Piroozmandan, F. Farokhi, K. Kangarloo, and M. Jahanshahi, "Removing the impulse noise from images based on fuzzy cellular automata by using a two-phase innovative method," Optik, vol. 255, p. 168713, 2022, doi: 10.1016/j.ijleo.2022.168713.
[10] B. Smolka, D. Kusnik, and K. Radlak, "On the reduction of mixed Gaussian and impulsive noise in heavily corrupted color images," Scientific Reports, vol. 13, no. 1, Art. no. 21035, 2023, doi: 10.1038/s41598-023-48260-2.
[11] D. Kusnik and B. Smolka, "Robust mean shift filter for mixed Gaussian and impulsive noise reduction in color digital images," Scientific Reports, vol. 12, no. 1, Art. no. 14951, 2022, doi: 10.1038/s41598-022-18909-8.
[12] B. Charmouti, A. K. Junoh, A. Abdurrazzaq, and M. Y. Mashor, "A new denoising method for removing salt & pepper noise from image," Multimedia Tools and Applications, vol. 81, no. 3, pp. 3981–3993, 2022, doi: 10.1007/s11042-021-11596-2.
[13] A. Abdurrazzaq, I. Mohd, A. K. Junoh, and Z. Yahya, "A hybrid of tropical-singular value decomposition method for salt and pepper noise removal," Turkish Journal of Electrical Engineering and Computer Sciences, vol. 27, no. 3, pp. 1667-1679, 2019, doi: 10.3906/elk-1808-85.
[14] R. Ghasemi, M. R. Rabiei, and A. Nezakati, "Strong law of large numbers for fuzzy random variables in fuzzy metric space," International Journal of Fuzzy Logic and Intelligent Systems, vol. 20, no. 4, pp. 278-289, 2020, doi: 10.5391/IJFIS.2020.20.4.278.
[15] A. George and P. Veeramani, "On some results in fuzzy metric spaces," Fuzzy sets and systems, vol. 64, no. 3, pp. 395-399, 1994.
[16] B. Schweizer and A. Sklar, "Statistical metric spaces," Pacific J. Math, vol. 10, no. 1, pp. 313-334, 1960.
[17] E. Klement, R. Mesiar, and E. Pap, "Triangular norms," Tatra Mountains Mathematical Publications, vol. 13, pp. 169-193, 1997.
[18] L. A. Zadeh, "Fuzzy sets," Information and Control, vol. 8, no. 3, pp. 338–353, 1965, doi: 10.1016/S0019-9958(65)90241-X.
[19] Z. Deng, "Fuzzy pseudo-metric spaces," Journal of Mathematical Analysis and Applications, vol. 86, no. 1, pp. 74-95, 1982, doi: 10.1016/0022-247X(82)90255-4.
[20] O. Kaleva and S. Seikkala, "On fuzzy metric spaces," Fuzzy sets and systems, vol. 12, no. 3, pp. 215-229, 1984, doi: 10.1016/0165-0114(84)90069-1.
[21] M. A. Erceg, "Metric spaces in fuzzy set theory," Journal of Mathematical Analysis and Applications, vol. 69, no. 1, pp. 205-230, 1979, doi: 10.1016/0022-247X(79)90189-6.
[22] R. Saadati and S. Vaezpour, "Some results on fuzzy Banach spaces," Journal of Applied Mathematics and Computing, vol. 17, no. 1–2, pp. 475–484, 2005, doi: 10.1007/BF02936060.
Journal of Soft Computing and Information Technology
Volume 14, Issue 1
Spring - June
Spring 2025
Pages 27-36