Multimedia Tools and Applications

, Volume 78, Issue 10, pp 12663–12687 | Cite as

A modified intuitionistic fuzzy c-means clustering approach to segment human brain MRI image

  • Dhirendra KumarEmail author
  • Hanuman Verma
  • Aparna Mehra
  • R. K. Agrawal


Fuzzy c-means (FCM) is one of the prominent method utilized for medical image segmentation. In literature intuitionistic fuzzy c-means (IFCM) is suggested which is based on intuitionistic fuzzy sets (IFSs) theory to handle uncertainty and vagueness associated with real data. The objective function of which is defined using the hesitation degree along with membership degree. However, instead of solving the objective function analytically, the approximate solution is obtained using FCM. In this paper, we have proposed a modified intuitionistic fuzzy c-means algorithm (MIFCM) and solved analytically the objective function of the MIFCM method using Lagrange method of undetermined multiplier. To incorporate hesitation degree, two parametric intuitionistic fuzzy complements namely Sugeno’s negation function and Yager’s negation function are investigated. The performance of the MIFCM method is compared with three intuitionistic fuzzy clustering methods and the FCM on two publicly available MRI dataset and a synthetic dataset. The performance measures (average segmentation accuracy, dice score, jaccard score, false negative ratio and false positive ratio) are used to compare the performance of the MIFCM method with three variants of intuitionistic fuzzy clustering methods and the FCM. Experimental results demonstrate the superior performance of the MIFCM method over others.


Intuitionistic fuzzy sets Fuzzy c-means Intuitionistic fuzzy c-means Hesitation degree Image segmentation Magnetic resonance imaging 



The authors would like to thank CSIR (Grant no. 09/263(1016)/2014-EMR-I) and DST PURSE for the financial support. The authors are also thankful to the anonymous reviewers for their constructive suggestions.

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.


  1. 1.
    Alipour S, Shanbehzadeh J (2014) Fast automatic medical image segmentation based on spatial kernel fuzzy c-means on level set method. Mach Vis Appl 25 (6):1469–1488Google Scholar
  2. 2.
    Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96MathSciNetzbMATHGoogle Scholar
  3. 3.
    Atanassov KT (2003) Intuitionistic fuzzy sets: past, present and future. In: EUSFLAT conference, pp 12–19Google Scholar
  4. 4.
    Balafar MA, Ramli AR, Saripan MI, Mashohor S (2010) Review of brain mri image segmentation methods. Artif Intell Rev 33(3):261–274Google Scholar
  5. 5.
    Benaichouche A, Oulhadj H, Siarry P (2013) Improved spatial fuzzy c-means clustering for image segmentation using pso initialization, mahalanobis distance and post-segmentation correction. Digital Signal Process 23(5):1390–1400MathSciNetGoogle Scholar
  6. 6.
    Bezdek JC (1981) Objective Function Clustering. In: Pattern recognition with fuzzy objective function algorithms. Springer, pp 43–93Google Scholar
  7. 7.
    Bustince H, Kacprzyk J, Mohedano V (2000) Intuitionistic fuzzy generators application to intuitionistic fuzzy complementation. Fuzzy Sets Syst 114(3):485–504MathSciNetzbMATHGoogle Scholar
  8. 8.
    Chaira T (2011) A novel intuitionistic fuzzy c means clustering algorithm and its application to medical images. Appl Soft Comput 11(2):1711–1717Google Scholar
  9. 9.
    Chen X, Nguyen BP, Chui CK, Ong SH (2016) Automated brain tumor segmentation using kernel dictionary learning and superpixel-level features. In: 2016 IEEE international conference on systems, man, and cybernetics (SMC). IEEE, pp 002,547–002,552Google Scholar
  10. 10.
    Chuang KS, Tzeng HL, Chen S, Wu J, Chen TJ (2006) Fuzzy c-means clustering with spatial information for image segmentation. Comput Med Imaging Graph 30(1):9–15Google Scholar
  11. 11.
    Cocosco CA, Kollokian V, Kwan RKS, Pike GB, Evans AC (1997) Brainweb: online interface to a 3d mri simulated brain database. In: NeuroImage. CiteseerGoogle Scholar
  12. 12.
    Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18Google Scholar
  13. 13.
    Friedman M (1937) The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J Am Stat Assoc 32(200):675–701zbMATHGoogle Scholar
  14. 14.
    Huang CW, Lin KP, Wu MC, Hung KC, Liu GS, Jen CH (2015) Intuitionistic fuzzy c-means clustering algorithm with neighborhood attraction in segmenting medical image. Soft Comput 19(2):459–470Google Scholar
  15. 15.
    Iakovidis D, Pelekis N, Kotsifakos E, Kopanakis I (2008) Intuitionistic fuzzy clustering with applications in computer vision. In: Advanced concepts for intelligent vision systems. Springer, pp 764–774Google Scholar
  16. 16.
    Iman RL, Davenport JM (1980) Approximations of the critical region of the fbietkan statistic. Communications in Statistics-Theory and Methods 9(6):571–595zbMATHGoogle Scholar
  17. 17.
    Ji ZX, Sun QS, Xia DS (2014) A framework with modified fast fcm for brain mr images segmentation (retraction of vol 44, pg 999, 2011). Pattern Recogn 47 (12):3979–3979Google Scholar
  18. 18.
    Kannan S, Devi R, Ramathilagam S, Takezawa K (2013) Effective fcm noise clustering algorithms in medical images. Comput Biol Med 43(2):73–83Google Scholar
  19. 19.
    Krinidis S, Chatzis V (2010) A robust fuzzy local information c-means clustering algorithm. IEEE Trans Image Process 19(5):1328–1337MathSciNetzbMATHGoogle Scholar
  20. 20.
    Krishnapuram R, Keller JM (1993) A possibilistic approach to clustering. IEEE Trans Fuzzy Syst 1(2):98–110Google Scholar
  21. 21.
    Li C, Huang R, Ding Z, Gatenby JC, Metaxas DN, Gore JC (2011) A level set method for image segmentation in the presence of intensity inhomogeneities with application to mri. IEEE Trans Image Process 20(7):2007–2016MathSciNetzbMATHGoogle Scholar
  22. 22.
    Murofushi T, Sugeno M (2000) Fuzzy measures and fuzzy integrals. In: Fuzzy measures and integrals: theory and applications, pp 3–41Google Scholar
  23. 23.
    Olabarriaga SD, Smeulders AW (2001) Interaction in the segmentation of medical images: a survey. Med Image Anal 5(2):127–142Google Scholar
  24. 24.
    Pelekis N, Iakovidis DK, Kotsifakos EE, Kopanakis I (2008) Fuzzy clustering of intuitionistic fuzzy data. International Journal of Business Intelligence and Data Mining 3(1):45–65Google Scholar
  25. 25.
    Pham DL, Xu C, Prince JL (2000) Current methods in medical image segmentation 1. Annu Rev Biomed Eng 2(1):315–337Google Scholar
  26. 26.
    Qiu C, Xiao J, Yu L, Han L, Iqbal MN (2013) A modified interval type-2 fuzzy c-means algorithm with application in mr image segmentation. Pattern Recogn Lett 34(12):1329–1338Google Scholar
  27. 27.
    Sato M, Lakare S, Wan M, Kaufman A, Nakajima M (2000) A gradient magnitude based region growing algorithm for accurate segmentation. In: 2000 international conference on image processing, 2000. Proceedings, vol 3. IEEE, pp 448–451Google Scholar
  28. 28.
    Szmidt E, Kacprzyk J (2000) Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst 114(3):505–518MathSciNetzbMATHGoogle Scholar
  29. 29.
    Verma H, Agrawal R (2015) Possibilistic intuitionistic fuzzy c-means clustering algorithm for mri brain image segmentation. Int J Artif Intell Tools 24(05):1550,016Google Scholar
  30. 30.
    Verma H, Agrawal R, Sharan A (2016) An improved intuitionistic fuzzy c-means clustering algorithm incorporating local information for brain image segmentation. Appl Soft Comput 46:543–557Google Scholar
  31. 31.
    Vlachos IK, Sergiadis GD (2007) The role of entropy in intuitionistic fuzzy contrast enhancement. In: International fuzzy systems association world congress. Springer, pp 104–113Google Scholar
  32. 32.
    Vovk U, Pernus F, Likar B (2007) A review of methods for correction of intensity inhomogeneity in mri. IEEE Trans Med Imaging 26(3):405–421Google Scholar
  33. 33.
    Wang L, Chen Y, Pan X, Hong X, Xia D (2010) Level set segmentation of brain magnetic resonance images based on local gaussian distribution fitting energy. J Neurosci Methods 188(2):316–325Google Scholar
  34. 34.
    Wang Z, Song Q, Soh YC, Sim K (2013) An adaptive spatial information-theoretic fuzzy clustering algorithm for image segmentation. Comput Vis Image Underst 117(10):1412–1420Google Scholar
  35. 35.
    Xu Z, Wu J (2010) Intuitionistic fuzzy c-means clustering algorithms. J Syst Eng Electron 21(4):580–590Google Scholar
  36. 36.
    Yager RR (1979) On the measure of fuzziness and negation part i: membership in the unit interval. Int J Gen Syst 5(4):221–229zbMATHGoogle Scholar
  37. 37.
    Yager RR (1980) On the measure of fuzziness and negation. II. Lattices. Inf Control 44(3):236–260MathSciNetzbMATHGoogle Scholar
  38. 38.
    Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Computer & Systems SciencesJawaharlal Nehru UniversityNew DelhiIndia
  2. 2.Department of Computer ScienceBanasthali VidyapithBanasthaliIndia
  3. 3.Acharya Narendra Dev CollegeDelhi UniversityNew DelhiIndia
  4. 4.Department of MathematicsIndian Institute of TechnologyNew DelhiIndia

Personalised recommendations