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Low-Level Image Processing Based on Interval-Valued Fuzzy Sets and Scale-Space Smoothing

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Recent Contributions in Intelligent Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 657))

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Abstract

In this paper, a new technique based on interval-valued fuzzy sets and scale-space smoothing is proposed for image analysis and restoration. Interval-valued fuzzy sets (IVFS) are associated with type-2 semantic uncertainty that makes it possible to take into account usually ignored (or difficult to manage) stochastic errors during image acquisition. Indeed, the length of the interval (of IVFS) provides a new tool to define a particular resolution scale for scale-space smoothing. This resolution scale is constructed from two smoothed image histograms and is associated with interval-valued fuzzy entropy (IVF entropy). Then, IVF entropy is used for analyzing the image histogram to find the noisy pixels of images and to define an efficient image quality metric. To show the effectiveness of this new technique, we investigate two specific and significant image processing applications: no-reference quality evaluation of computer-generated images and speckle noise filtering.

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References

  1. Pratt, B.: Digital Image Processing. Wiley-Interscience (1978)

    Google Scholar 

  2. Kajiya, J.T.: The rendering equation. ACM Comput. Graph. 20(4), 143–150 (1986)

    Article  Google Scholar 

  3. Shirley, P., Wang, C.Y., Zimmerman, K.: Monte Carlo techniques for direct lighting calculations. ACM Trans. Graph. 15(1), 1–36 (1996)

    Article  Google Scholar 

  4. Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4) (2004)

    Google Scholar 

  5. Ferzli, R., Karam, L.: No-reference objective wavelet based noise immune image sharpness metric. Int. Conf. Image Process. (2005)

    Google Scholar 

  6. Lopes, A., Nezri, E., Touzi, R., Laur, H.: Maximum a posteriori speckle filtering and first order texture models in SAR images. IGARSS (1990)

    Google Scholar 

  7. Bigand, A., Bouwmans, T., Dubus, J.P.: Extraction of line segments from fuzzy images. Pattern Recogn. Lett. 22, 1405–1418 (2001)

    Article  MATH  Google Scholar 

  8. Cheng, H.D., Chen, C.H., Chiu, H.H., Xu, H.J.: Fuzzy homogeneity approach to multilevel thresholding. IEEE Trans. Image Process. 7(7), 1084–1088 (1998)

    Article  Google Scholar 

  9. Tizhoosh, H.R.: Image thresholding using type 2 fuzzy sets. Pattern Recogn. 38, 2363–2372 (2005)

    Article  MATH  Google Scholar 

  10. Bloch, I.: Lattices of fuzzy sets and bipolar fuzzy sets, and mathematical morphology. Inf. Sci. 181, 2002–2015 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  11. Nachtegael, M., Sussner, P., Melange, T., Kerre, E.E.: On the role of complete lattices in mathematical morphology: from tool to uncertainty model. Inf. Sci. 181, 1971–1988 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mendel, J.M., Bob John, R.I.: Type-2 fuzzy sets made simple. IEEE Trans. Fuzzy Syst. 10(2), 117–127 (2002)

    Google Scholar 

  13. Bloch, I.: Information combination operators for data fusion: a comparative review with classification. IEEE Trans. SMC—Part B 26, 52–67 (1996)

    Google Scholar 

  14. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Inf. Sci. 8, 199–249 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  15. Wu, H., Mendel, J.M.: Uncertainty bounds and their use in the design of interval type-2 fuzzy logic systems. IEEE Trans. Fuzzy Syst. 10(5), 622–639 (2002)

    Article  Google Scholar 

  16. Liang, Q., Karnish, N.N., Mendel, J.M. Connection admission control in ATM networks using survey-based type-2 fuzzy logic systems. IEEE Trans. Syst. Man Cyber—Part B 30(3), 329–339 (2000)

    Google Scholar 

  17. Sussner, P., Nachtegael, M., Esmi, E.: An approach towards edge detection and watershed segmentation based on an interval-valued morphological gradient. ICPV’11 (2011)

    Google Scholar 

  18. Bigand, A., Colot, O.: Fuzzy filter based on interval-valued fuzzy sets for image filtering. Fuzzy Sets Syst. 161, 96–117 (2010)

    Article  MathSciNet  Google Scholar 

  19. Bigand, A., Colot, O.: Speckle noise reduction using an interval type-2 fuzzy sets filter. In: Intelligent Systems IS’12 IEEE Congress (Sofia, Bulgaria) (2012)

    Google Scholar 

  20. Delepoulle, S., Bigand, A., Renaud, C.: an interval type-2 fuzzy sets no-reference computer-generated images quality metric and its application to denoising. In: Intelligent Systems IS’12 IEEE Congress (Sofia, Bulgaria) (2012)

    Google Scholar 

  21. Astrom, K., Heyden, A.: Stochastic analysis of scale-space smoothing. ICPR (1996a)

    Google Scholar 

  22. Babaud, J., Witkin, A.P., Baudin, M., Duda, R.O.: Uniqueness of the Gaussian kernel for scape-space filtering. IEEE Trans. PAMI-8 8, 26–33 (1986)

    Google Scholar 

  23. Strauss, O.: Quasi-continuous histograms. Fuzzy Sets Syst. 160, 2442–2465 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  24. Jacquey, F., Loquin, K., Comby, F., Strauss, O.: Non-additive approach for gradient-based edge detection. ICIP (2007)

    Google Scholar 

  25. Astrom, K., Heyden, A.: Stochastic analysis of sub-pixel edge detection. ICPR (1996b)

    Google Scholar 

  26. Bustince, H., Barrenechea, E., Pergola, M., Fernandez, J.: Interval-valued fuzzy sets constructed from matrices: application to edge detection. Fuzzy Sets Syst. 160(13), 1819–1840 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  27. Starck, J.L., Murtagh, F., Bijaoui, A.: Image processing and data analysis: the multiscale approach. Cambridge University Press (1998)

    Google Scholar 

  28. Kaufmann, A.: Introduction to the Theory of Fuzzy Set—Fundamental Theorical Elements, vol. 28. Academic Press, New York (1975)

    Google Scholar 

  29. Deluca, A., Termini, S.: A definition of a nonprobabilistic entropy in the setting of fuzzy set theory. Inf. Control 20(4), 301–312 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  30. Pal, N.R., Bezdek, J.C.: Measures of Fuzziness: A Review and Several Classes. Van Nostrand Reinhold, New York (1994)

    Google Scholar 

  31. Burillo, P., Bustince, H.: Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst. 78, 305–316 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  32. Bustince, H., Barrenechea, E., Pergola, M., Fernandez, J., Sanz, J.: Comments on: image thresholding using type 2 fuzzy sets. Importance of this method. Pattern Recogn. 43, 3188–3192 (2010)

    Article  MATH  Google Scholar 

  33. Cheng, H.D., Sun, Y.: A hierarchical approach to color image segmentation using homogeneity. IEEE Trans. Image Process. 9(12), 2071–2081 (2000)

    Article  Google Scholar 

  34. Cheng, H., Jiang, X., Wang, J.: Color image segmentation based on homogram thresholding and region merging. Pattern Recogn. 35(2), 373–393 (2002)

    Article  MATH  Google Scholar 

  35. Nachtegael, M., Schulte, S., Weken, D.V., Witte, V.D., Kerre, E.E.: Fuzzy filters for noise reduction: the case of Gaussian noise. Int. Conf. Fuzzy Syst. (2005)

    Google Scholar 

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Correspondence to Samuel Delepoulle .

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Delepoulle, S., Bigand, A., Renaud, C., Colot, O. (2017). Low-Level Image Processing Based on Interval-Valued Fuzzy Sets and Scale-Space Smoothing. In: Sgurev, V., Yager, R., Kacprzyk, J., Atanassov, K. (eds) Recent Contributions in Intelligent Systems. Studies in Computational Intelligence, vol 657. Springer, Cham. https://doi.org/10.1007/978-3-319-41438-6_1

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  • DOI: https://doi.org/10.1007/978-3-319-41438-6_1

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