Hybrid BBO-DE Algorithms for Fuzzy Entropy-Based Thresholding

  • Ilhem Boussaïd
  • Amitava Chatterjee
  • Patrick Siarry
  • Mohamed Ahmed-Nacer


This chapter shows how a recently proposed stochastic optimization algorithm, called biogeography-based optimization (BBO), can be efficiently employed for development of three-level thresholding-based image segmentation. This technique is utilized to determine suitable thresholds utilizing a fuzzy entropy-based fitness function, which the optimization procedure attempts to maximize. The chapter demonstrates how improved BBO-based strategies, employing hybridizations with differential evolution (DE) algorithms, can be employed to incorporate diversity in the basic BBO algorithm that can help the optimization algorithm avoid getting trapped at local optima and seek the global optimum in a more efficient manner. Several such hybrid BBO-DE algorithms have been utilized for this optimum thresholding-based image segmentation procedure. A detailed implementation analysis for a popular set of well-known benchmark images has been carried out to qualitatively and quantitatively demonstrate the utility of the proposed hybrid BBO-DE optimization algorithm.


Membership Function Gray Level Differential Evolution Differential Evolution Algorithm Mutation Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Acharya, T., Ray, A.K.: Image Processing—Principles and Applications. Wiley-Interscience, New Jersey (2005)CrossRefGoogle Scholar
  2. 2.
    Bhandari, D., Pal, N.R.: Some new information measures for fuzzy sets. Inf. Sci. 67, 209–228 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Boussaïd, I., Chatterjee, A., Siarry, P., Ahmed-Nacer, M.: Two-stage update biogeography-based optimization using differential evolution algorithm (dbbo). Comput. Oper. Res. 38, 1188–1198 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Chang, C.I., Du, Y., Wang, J., Guo, S.M., Thouin, P.D.: Survey and comparative analysis of entropy and relative entropy thresholding techniques. IEE Proc. Vis. Image Signal Process. 153(6), 837–850 (2006)CrossRefGoogle Scholar
  5. 5.
    Cheng, H., Chen, J., Li, J.: Threshold selection based on fuzzy c-partition entropy approach. Pattern Recogn. 31(7), 857–870 (1998)CrossRefGoogle Scholar
  6. 6.
    Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley-Interscience, New York (1991)zbMATHCrossRefGoogle Scholar
  7. 7.
    Darwin, C.: Origin of Species. Gramercy, New York (1995)Google Scholar
  8. 8.
    De Luca, A., Termini, S.: A definition of a non-probabilistic entropy in the setting of fuzzy sets theory. Inf. Control 20, 301–312 (1972)zbMATHCrossRefGoogle Scholar
  9. 9.
    Fan, J., Xie, W.: Distance measure and induced fuzzy entropy. Fuzzy Sets Syst. 104, 305–314 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Freixenet, J., Muñoz, X., Raba, D., Martí, J., Cufí, X.: Yet another survey on image segmentation: region and boundary information integration. In: Proceedings of the 7th European Conference on Computer Vision-Part III, ECCV ’02, pp. 408–422. Springer-Verlag, London, UK (2002)Google Scholar
  11. 11.
    Gong, W., Cai, Z., Ling, C.: DE/BBO: a hybrid differential evolution with biogeography-based optimization for global numerical optimization. Soft Comput. Fusion Found. Methodol. Appl. (2010)Google Scholar
  12. 12.
    Kapur, J., Sahoo, P., Wong, A.: A new method for gray-level picture thresholding using the entropy of the histogram. Comput. Vision Graph. Image Process. 29(3), 273–285 (1985)CrossRefGoogle Scholar
  13. 13.
    Kaufmann, A.: Introduction to the Theory of Fuzzy Subsets. Academic Press, New York (1975)zbMATHGoogle Scholar
  14. 14.
    Kaufmann, A.: Measures of Fuzzy Information. Mathematical Sciences Trust Society, New Delhi (1977)Google Scholar
  15. 15.
    Klir, G.J., St. Clair, U., Yuan, B.: Fuzzy Set Theory: Foundations and Applications. Prentice-Hall, Inc., Upper Saddle River (1997)Google Scholar
  16. 16.
    Levine, M., Nazif, A.: Dynamic measurement of computer generated image segmentations. IEEE Trans. Pattern Anal. Mach. Intell. 7, 155–164 (1985)CrossRefGoogle Scholar
  17. 17.
    MacArthur, R., Wilson, E.: The Theory of Biogeography. Princeton University Press, Princeton (1967)Google Scholar
  18. 18.
    Noman, N., Iba, I.: Accelerating differential evolution using an adaptive local search. IEEE Trans. Evol. Comput. 12(1), 107–125 (2008)CrossRefGoogle Scholar
  19. 19.
    Pal, N.R., Pal, S.K.: Higher order fuzzy entropy and hybrid entropy of a set. Inf. Sci. 61, 211–231 (1992)zbMATHCrossRefGoogle Scholar
  20. 20.
    Pal, N.R., Pal, S.K.: A review on image segmentation techniques. Pattern Recognit. 26(9), 1277–1294 (1993)CrossRefGoogle Scholar
  21. 21.
    Price, K.V., Storn, R.M., Lampinen, J.A.: Differential Evolution: A Practical Approach to Global Optimization. Natural Computing Series. Springer, Berlin (2005)Google Scholar
  22. 22.
    Pun, T.: A new method for gray-level picture thresholding using the entropy of histogram. Signal Process. 2(3), 223–237 (1980)CrossRefGoogle Scholar
  23. 23.
    Pun, T.: Entropic thresholding, a new approach. Comput. Graph. Image Process. 16(3), 210–239 (1981)CrossRefGoogle Scholar
  24. 24.
    Sahoo, P.K., Soltani, S., Wong, A.K., Chen, Y.C.: A survey of thresholding techniques. Comput. Vision Graph. Image Process. 41, 233–260 (1988)CrossRefGoogle Scholar
  25. 25.
    Sahoo, P.K., Wilkins, C., Yeager, J.: Threshold selection using Renyi’s entropy. Pattern Recognit. 30(i1), 71–84 (1997)zbMATHCrossRefGoogle Scholar
  26. 26.
    Sezgin, M., Sankur, B.: Survey over image thresholding techniques and quantitative performance evaluation. J. Electron. Imaging 13(1), 146–168 (2004)CrossRefGoogle Scholar
  27. 27.
    Shannon, C.E.: A Mathematical theory of communication. CSLI Publications (1948)Google Scholar
  28. 28.
    Simon, D.: Biogeography-based optimization. IEEE Trans. Evol. Comput. 12, 702–713 (2008)CrossRefGoogle Scholar
  29. 29.
    Storn, R.M., Price, K.V.: Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11, 341–359 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    Tao, W., Jin, H., Liu, L.: Object segmentation using ant colony optimization algorithm and fuzzy. entropy 28(7), 788–796 (2007)Google Scholar
  31. 31.
    Tao, W., Tian, J., Liu, J.: Image segmentation by three-level thresholding based on maximum fuzzy entropy and genetic algorithm. Pattern Recogn. Lett. 24(16), 3069–3078 (2003)CrossRefGoogle Scholar
  32. 32.
    Tobias, O., Seara, R.: Image segmentation by histogram thresholding using fuzzy sets. IEEE Trans. Image Process. 11(12), 1457–1465 (2002)CrossRefGoogle Scholar
  33. 33.
    Tsallis, C.: Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 52, 479–487 (1988)MathSciNetzbMATHCrossRefGoogle Scholar
  34. 34.
    Wallace, A.R.: The Geographical Distribution of Animals (two volumes). Adamant Media Corporation, Boston (2005)Google Scholar
  35. 35.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)MathSciNetzbMATHCrossRefGoogle Scholar
  36. 36.
    Zhao, M., Fu, A., Yan, H.: A technique of three-level thresholding based on probability partition and fuzzy 3-partition. IEEE Trans. Fuzzy Syst. 9(3), 469–479 (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ilhem Boussaïd
    • 1
  • Amitava Chatterjee
    • 2
  • Patrick Siarry
    • 3
  • Mohamed Ahmed-Nacer
    • 1
  1. 1.University of Science and Technology Houari Boumediene (USTHB)Bab-EzzouarAlgeria
  2. 2.Electrical Engineering DepartmentJadavpur UniversityKolkataIndia
  3. 3.Université de Paris-Est Créteil Val de MarneCréteilFrance

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