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Fuzzy Metrics and Its Applications in Image Processing

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Artificial Intelligence: Theory and Applications

Part of the book series: Studies in Computational Intelligence ((SCI,volume 973))

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Abstract

This paper is a review of recent research, in which fuzzy metrics and their applications in image processing are studied. The notions of the fuzzy T-metric and the fuzzy S-metric are presented, after which, examples of known fuzzy metrics are provided, along with theorems that enable algorithms to develop new metrics. Two applications of fuzzy metrics in image processing are illustrated: Image filtering and Copy-move forgery detection. Image filtering reduces the amount of noise, while maintaining satisfactory image quality. The aim was to improve the sharpness and quality of the image, measured by the image quality indices UIQI and CPBD. It is illustrated that the image filtered with this modified algorithm has better quality and greater sharpness than images filtered with the median filter. The fuzzy metric parameters that produce images with the best quality and sharpness are determined experimentally. The digital image falsification obtained by copying and pasting part of the original image into another part of the same image is also considered. Copy-move forgery detection (CMFD) is one of the methods used to detect such forgeries in images. A cluster algorithm that successfully solves this problem is presented.

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References

  1. Alkawaz, M.H., Sulong, G., Saba, T., Rehman, A.: Detection of copymove image forgery based on discrete cosine transform. Neural Comput. Appl. 1–10 (2016). https://doi.org/10.1007/s00521-016-2663-3

  2. Astola, J., Haavisto, P., Neuvo, Y.: Vector median filters. Proc. IEEE 78(4), 678–689 (1990). https://doi.org/10.1109/554807

    Article  Google Scholar 

  3. Bloch, I.: On fuzzy distances and their use in image processing under imprecision. Pattern Recognit. Lett. 32, 1873–1895 (1999)

    Article  Google Scholar 

  4. Davidović, T., Teodorović, D., Šelmić, M.: Bee colony optimization part i: the algorithm overview. Yugoslav J. Oper. Res. 25(1), 33–56 (2015). https://doi.org/10.2298/YJOR131011017D

    Article  MathSciNet  MATH  Google Scholar 

  5. Davidović, T., Glišović, N., Rašković, M.: Bee colony optimization for clustering incomplete data. In: The 7th International Conference on Optimization Problems and Their Applications OPTA-2018, pp. 8–14 (2018)

    Google Scholar 

  6. Deza, M.M., Deza, E.: Encyclopedia of Distances. Springer, Berlin (2009)

    Book  Google Scholar 

  7. Glišović, N., Davidović, T., Rašković, M.: Clustering when data are missing using the environment variable method. In: XLIV Symposium on Operations Research SYMOPIS, pp. 158–165, Zlatibor, September 25–28, ISBN 978-86-7488- 135-4 (2017)

    Google Scholar 

  8. Grabisch, M., Marichal, J.L., Mesiar, R., Pap, E.: Aggregation functions. Cambridge University Press, Cambridge (2009)

    Google Scholar 

  9. Gregori, V., Morillas, S., Roig, B., Sapena, A.: Fuzzy averaging filter for impulse noise reduction in colour images with a correction step. J. Vis. Commun. Image Represent. 55, 518–528 (2018). https://doi.org/10.1016/j.jvcir.2018.06.025

    Article  Google Scholar 

  10. Gregori, V., Morillas, S., Sapena, A.: Examples of fuzzy metrics and applications. Fuzzy Sets Syst. 170(1), 95–111 (2011). https://doi.org/10.1018/f.fss.2010.10.019

    Article  MathSciNet  MATH  Google Scholar 

  11. Gregori, V., Romaguera, S.: Some properties of fuzzy metric spaces. Fuzzy Sets Syst. 115(3), 485–489 (2000). https://doi.org/10.1016/S0165-0114(98)00281-4

    Article  MathSciNet  MATH  Google Scholar 

  12. Jain, A.K.: Data clustering: 50 years beyond \(K-\)means. Pattern Recognit. Lett. 31(8), 651–666 (2010). https://doi.org/10.1016/j.patrec.2009.09.011

    Article  Google Scholar 

  13. Karaklić, D., Gajić, Lj., Ralević, N.M.: Some fixed point results in a strong probabilistic metric spaces. Filomat 33(8), 2201–2209 (2019). https://doi.org/10.2298/FIL1908201K

  14. Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht (2000)

    Book  Google Scholar 

  15. Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall, New Jersey (1995)

    MATH  Google Scholar 

  16. Lučić, P., Teodorović, D.: Bee system: modeling combinatorial optimization transportation engineering problems by swarm intelligence. In: Preprints 340 of the TRISTAN IV Triennial Symposium on Transportation Analysis, Sao Miguel, Azores Islands, Portugal, pp. 441–445 (2001)

    Google Scholar 

  17. Martin, D., Fowlkes, C., Tal, D., Malik, J.: A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: Proceedings eighth IEEE international conference on computer vision. ICCV 2001, pp. 416–423 (2001)

    Google Scholar 

  18. Milosavljević, N.S., Ralević, N. M.: Fuzzy Metaheuristics Algorithm for Copy-Move Forgery Detection in Images. 20th International Workshop on Combinatorial Image Analysis, Novi Sad, Serbia, 16–18 Jul, 2020, Springer Nature Switzerland AG 2020 T. Lukić et al. (Eds.): IWCIA 2020, LNCS 12148, pp. 273–281 (2020). https://doi.org/10.1007/978-3-030-51002-2_20

  19. Mladenović, N., Hansen, P.: Variable neighborhood searchs. Comput. Oper. Res. 24(11), 1097–1100 (1997)

    Article  MathSciNet  Google Scholar 

  20. Mladenović, N., Brimberg, J., Hansen, P., Moreno-Perez, J.: The \(p-\)median problem: a survey of metaheuristic approaches. Eur. J. Oper. Res. 179(3), 927–939 (2007). https://doi.org/10.1016/j.ejor.2005.05.034

    Article  MathSciNet  MATH  Google Scholar 

  21. Morillas, S., Gregori, V., Peris-Fajarnes, G., Latorre, P.: A fast impulsive noise color image filter using fuzzy metrics. Real-Time Imaging 11(5–6), 417–428 (2005). https://doi.org/10.1016/j.rti.2005.06.007

    Article  Google Scholar 

  22. Morillas, S., Gregori, V., Peris-Fajarnes, G., Latorre, P.: A new vector median filter based on fuzzy metrics. In: Kamel, M., Campilho, A. (Eds.). Image Analysis and Recognition - ICIAR2005, Lecture Notes in Computer Science, vol. 3656, pp. 81–90. Springer, Berlin (2005). https://doi.org/10.1117/1.2767335

  23. Morillas, S., Gregori, V., Peris-Fajarnes, G., Sapena, A.: New adaptive vector filter using fuzzy metrics. J. Electron. Imaging 16(3), 033,007:1–15 (2007). https://doi.org/10.1116/1.2767335

  24. Narvekar, N.D., Karam, L.J.: An improved no-reference sharpness metric based on the probability of blur detection. In: Conference Proceedings 2009 International Workshop on Video Processing and Quality Metrics or Consumer Electronics (VPQM) (2010)

    Google Scholar 

  25. Nedovic, L., Ralevic, N., Pavkov, I.: Aggregated distance functions and their application in image processing. Soft Comput. 22(14), 4723–4739 (2018). https://doi.org/10.1007/s00500-017-2657-9

    Article  MATH  Google Scholar 

  26. Ralević, N.M., Karaklić, D., Pištinjat, N.: Fuzzy metric and its applications in removing the image noise. Soft Comput. 23(22), 12049–12061 (2019). https://doi.org/10.1007/s00500-019-03762-5

    Article  MATH  Google Scholar 

  27. Ralević, N.M., Paunović, M., Iričanin, B.: Fuzzy metric spaces and applications in imahe processing. Math. Montisnigri 48, 103–117 (2020). https://doi.org/10.20948/mathmontis-2020-48-9

    Article  MathSciNet  Google Scholar 

  28. Ralević, N.M., Gajić, Lj.: Max-min combination fuzzy \(S-\)metrics. In: The Proceedings of the Fifth Conference on Mathematics in Engineering: Theory and Applications. META: Faculty of Technical Sciences, May 9–10th, 2020. Novi Sad, Serbia (2020)

    Google Scholar 

  29. Ralević, N., Paunović, M.: Applications of the Fuzzy Metrics in Image Denoising and Segmentation. Technical Gazette 28(3) (2021). https://doi.org/10.17559/TV-20200305075136

  30. Ralević, N. M., Milosavljević, N.S.: Fuzzy metric and its applications in Copy-move forgery detection in image. Iranian journal of fuzzy systems (submitted)

    Google Scholar 

  31. Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. Elsevier North-Holland, New York (1983)

    MATH  Google Scholar 

  32. Smolka, B., Szczepanski, M., Plataniotis, K.N., Venetsanopoulos, A.N.: On the fast modified vector median filter. Can. Conf. Electr. Comput. Eng. 2(2), 1315–1320 (2001). https://doi.org/10.1109/CCECE.2001.93.23636

    Article  MATH  Google Scholar 

  33. Wang, Z., Bovik, A.C.: A universal image quality index. IEEE Signal Proc. Lett. 9(3), 81–84 (2002). https://doi.org/10.1109/97.995823

    Article  Google Scholar 

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Acknowledgements

The author has been supported by the Ministry of Education, Science and Technological Development through the project no. 451-03-68/2020-14/200156: “Innovative scientific and artistic research from the FTS (activity) domain”.

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  1. Department of Fundamental Sciences, Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000, Novi Sad, Serbia

    Nebojša Ralević

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Correspondence to Nebojša Ralević .

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  1. Singidunum University, Belgrade, Serbia

    Endre Pap

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Ralević, N. (2021). Fuzzy Metrics and Its Applications in Image Processing. In: Pap, E. (eds) Artificial Intelligence: Theory and Applications. Studies in Computational Intelligence, vol 973. Springer, Cham. https://doi.org/10.1007/978-3-030-72711-6_6

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