Liver CT Image Segmentation with an Optimum Threshold Using Measure of Fuzziness

  • Abder-Rahman Ali
  • Micael Couceiro
  • Ahmed M. Anter
  • Aboul Ella Hassanien
  • Mohamed F. Tolba
  • Václav Snášel
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 303)


This paper presents a Fuzzy C-Means based image segmentation approach with an optimum threshold using measure of fuzziness. The optimized version, herein denoted as FCM-t, benefits from an optimum threshold, calculated using measure of fuzziness. This allows the revealing of ambiguous pixels, which are eventually assigned to the appropriate clusters by calculating the rounded average cluster values in the ambiguous pixels neighbourhood. The proposed approach showed significantly better results compared to the traditional Fuzzy C-Means, at the cost of some processing power. By benefiting from the optimum threshold approach, one is able to increase the segmentation performance by approximately three times more than with the traditional FCM.


Segmentation fuzzy C-means threshold clustering 


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  1. 1.
    Annadurai, S., Shanmugalakshmi, R.: Fundamentals of Digital Image Processing. Dorling Kindersley, Delhi (2006)Google Scholar
  2. 2.
    Läthén, G.: Segmentation Methods for Digital Image Analysis: Blood Vessels, Multi-scale Filtering, and Level Set Methods. Linköping studies in science and technology, thesis no. 1434 (2010)Google Scholar
  3. 3.
    Huang, X., Tsechpenakis, G.: Medical Image Segmentation. In: Hristidis, V. (ed.) Information Discovery on Electronic Health Records, ch. 10. Chapman & Hall (2009)Google Scholar
  4. 4.
    Leeuwen, M., Noorddzij, J., Feldberg, M., Hennipman, A., Doornewaaard, H.: Focal Liver Lesions: Characterization with Triphasic Spiral CT. Radiology 201, 327–336 (1996)Google Scholar
  5. 5.
    Digestive Disorders Health Center, (accessed on March 11, 2014) (retrieved)
  6. 6.
    Bronzino, J.: The Biomedical Engineering Handbook, 2nd edn. Springer, Heidelberg (2000)Google Scholar
  7. 7.
    Mharib, A., Ramli, A., Mashohor, S., Mahmood, R.: Survey on Liver CT Image Segmentation Methods. Artificial Intelligence Review 37(2), 83–95 (2012)CrossRefGoogle Scholar
  8. 8.
    Maji, P., Pal, S.: Maximum Class Separability for Rough-Fuzzy C-Means Based Brain MR Image Segmentation. T. Rough Sets 9, 114–134 (2008)Google Scholar
  9. 9.
    Tizhoosh, H.: Image thresholding using type II fuzzy sets. Pattern Recognition 38(12), 2363–2372 (2005)CrossRefzbMATHGoogle Scholar
  10. 10.
    Zadeh, L.: Calculus of Fuzzy Restrictions. In: Zadeh, L.A., Fu, K.S., Tanaka, K., Shimura, M. (eds.) Fuzzy Sets and their Applications to Cognitive and Decision Processes, pp. 1–39. Academic Press, New York (1975)Google Scholar
  11. 11.
    Bush, B.: Fuzzy Clustering Techniques: Fuzzy C-Means and Fuzzy Min-Max Clustering Neural Networks, (accessed on March 12, 2014) (retrieved)
  12. 12.
    Anter, A., Azar, A., Hassanien, A., El-Bendary, N., ElSoud, M.: Automatic Computer Aided Segmentation for Liver and Hepatic Lesions Using Hybrid Segmentations Techniques. In: IEEE Proceedings of Federated Conference on Computer Science and Information Systems 2013, pp. 193–198 (2013)Google Scholar
  13. 13.
    Jaccard, P.: Etude Comparative de la Distribution Orale Dansune Portion des Alpes et des Jura. Bulletin del la Socit Vaudoise des Sciences Naturelles 37, 547–579 (1901)Google Scholar
  14. 14.
    Peacock, J.: Two-dimensional Goodness-of-fit Testing in Astronomy. Monthly Notices Royal Astronomy Society 202, 615–627 (1983)Google Scholar
  15. 15.
    Pallant, J.: SPSS Survival Manual, Kindle Edition Ed, 4th edn. Open University Press (2011)Google Scholar
  16. 16.
    Narayana, C., Sreenivasa Reddy, E., Seetharama Prasad, M.: Automatic Image Segmentation using Ultrafuzziness. International Journal of Computer Applications 49(12), 6–13 (2012)CrossRefGoogle Scholar
  17. 17.
    Chaira, T., Ray, A.: Segmentation Using Fuzzy Divergence. Pattern Recognition Lett. 24(12), 18371–18844 (2003)Google Scholar
  18. 18.
    Huang, L., Wang, M.: Image Thresholding by Minimizing the Measure of Fuzziness. Pattern Recognition 28, 41–51 (1995)CrossRefGoogle Scholar
  19. 19.
    Pal, N., Bhandari, D., Majumder, D.: Fuzzy Divergence, Probability Measure of Fuzzy Events and Image Thresholding. Pattern Recognition Lett. 13, 857–867 (1992)CrossRefGoogle Scholar
  20. 20.
    Wang, Q., Chi, Z., Zhao, R.: Image Thresholding by Maximizing the Index of Nonfuzziness of the 2-D Grayscale Histogram. Comput. Vision Image Understanding 85(2), 100–116 (2002)CrossRefzbMATHGoogle Scholar
  21. 21.
    Zenzo, S., Cinque, L., Levialdi, S.: Image Thresholding Using Fuzzy Entropies. SMC 28(1), 15–23 (1998)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Abder-Rahman Ali
    • 1
  • Micael Couceiro
    • 2
    • 3
  • Ahmed M. Anter
    • 4
    • 1
  • Aboul Ella Hassanien
    • 1
    • 5
  • Mohamed F. Tolba
    • 6
  • Václav Snášel
    • 7
  1. 1.Scientific Research Group in Egypt (SRGE)CairoEgypt
  2. 2.Artificial Perception for Intelligent Systems and Robotics (AP4ISR), Institute of Systems and Robotics (ISR)University of CoimbraCoimbraPortugal
  3. 3.Ingeniarius, Lda.MealhadaPortugal
  4. 4.Faculty of Computers and InformationMansoura UniversityMansouraEgypt
  5. 5.Faculty of Computers and InformationCairo UniversityCairoEgypt
  6. 6.Faculty of Computers and InformationAin Shams UniversityCairoEgypt
  7. 7.Electrical Engineering & Computer ScienceVSB-TUOstravaCzech Republic

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