Skip to main content
SpringerLink
Log in

Effective algorithm for determining the number of clusters and its application in image segmentation

  • Published:
Cluster Computing Aims and scope Submit manuscript

Abstract

The k-means algorithm is a popular clustering method for image segmentation. However, the main disadvantage of this algorithm is its dependence on the number of initial clusters. In this paper, we present an optimal criterion which can select the best segmentation result with less number of clusters. The optimal criterion overcomes the shortcoming of initialization based on the intra-class and inter-class difference. Eight digital images were employed to verify the segmentation results of the optimal criterion. Simultaneously, we have improved the traditional k-means algorithm to find the initial clustering centers efficiently. Experimental results show that the segmented images selected by the optimal criterion have sufficient stability and robustness. In addition, we verify the consistency of results by two kinds of objective assessment measures. The proposed optimal criterion can successfully display the best segmentation results precisely and efficiently so as to instead of artificial selection.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Wang, T.N., et al.: An improved K-means clustering method for cDNA microarray image segmentation. Genet. Mol. Res. 14(3), 7771–7781 (2015)

    Article  Google Scholar 

  2. Jain, A.: Data clustering: 50 years beyond K-means. Pattern Recogn. Lett. 31(8), 651–666 (2010)

    Article  Google Scholar 

  3. Han, C.: Improved SLIC imagine segmentation algorithm based on K-means. Clust. Comput. 20(2), 1017–1023 (2017)

    Article  Google Scholar 

  4. Dunn, J.: A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters. J. Cybern. 3, 32–57 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  5. Hu, C., Xu, Z., Liu, Y., Mei, L.: Video structural description technology for the new generation video surveillance systems. Front. Comput. Sci. 9(6), 980–989 (2015)

    Article  Google Scholar 

  6. Xu, Z., Hu, C., Mei, L.: Video structured description technology based intelligence analysis of surveillance videos for public security applications. Multimed. Tools Appl. 75(19), 12155–12172 (2016)

    Article  Google Scholar 

  7. Jiang, X., Li, C., Sun, J.: A modified K-means clustering for mining of multimedia databases based on dimensionality reduction and similarity measures. Clust. Comput. 6(2), 1–8 (2017)

    Google Scholar 

  8. Kanungo, T., Mount, D.M., Netanyahu, N.S.: An efficient k-means clustering algorithm: analysis and implementation. IEEE Trans. Pattern Anal. Mach. Intell. 24(7), 881–892 (2002)

    Article  Google Scholar 

  9. Gibou, F., Fedkiw, R.: A fast hybrid k-means level set algorithm for segmentation. In: 4th Annual Hawaii International Conference on Statistics and Mathematics, pp. 281–291 (2005)

  10. Ng, H.P., et al.: Masseter segmentation using an improved watershed algorithm with unsupervised classification. Comput. Biol. Med. 38(2), 171–184 (2008)

    Article  Google Scholar 

  11. Dhanachandra, N., Manglem, K., Chanu, Y.J.: Image segmentation using K-means clustering algorithm and subtractive clustering algorithm. Procedia Comput. Sci. 54, 764–771 (2015)

    Article  Google Scholar 

  12. Zhang, Y.: A survey on evaluation methods for image segmentation. Pattern Recogn. Lett. 29(8), 1335–1346 (1996)

    Article  Google Scholar 

  13. Liu, J., Yang, Y.H.: Multiresolution color image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 16(7), 689–700 (1994)

    Article  Google Scholar 

  14. Clausi, D.: K-means Iterative Fisher (KIF) unsupervised clustering algorithm applied to image texture segmentation. Pattern Recogn. Lett. 35(9), 1959–1972 (2002)

    Article  MATH  Google Scholar 

  15. Ray, S., Turi, R.: Determination of number of clusters in k-means clustering and application in colour image segmentation. In: Proceedings of the 4th International Conference on Advances in Pattern Recognition and Digital Techniques, pp. 137–143 (1999)

  16. Cao, F., Liang, J., Jiang, G.: An initialization method for the K-Means algorithm using neighborhood model. Comput. Math. Appl. 58(3), 474–483 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  17. Luo, M., Ma, Y.F., Zhang, H.J.: A spatial constrained k-means approach to image segmentation. In: Proceedings of the 2003 Joint Conference of the Fourth International Conference on Information Communications and Signal Processing and the Fourth Pacific Rim Conference on Multimedia, vol. 2, pp. 738–742. IEEE (2003)

  18. Bezdek, J.C., Pal, N.R.: Some new indexes of cluster validity. IEEE Trans. Syst. Man Cybern. B Cybern. 28(3), 301–315 (1998)

    Article  Google Scholar 

  19. Milligan, G.W., Cooper, M.C.: An examination of procedures for determining the number of clusters in a data set. Psychometrika 50(2), 159–179 (1985)

    Article  Google Scholar 

  20. MC Cooper, G.M., The effect of measurement error on determining the number of clusters in cluster analysis. Data, expert knowledge and decisions. Springer Berlin Heidelberg, 1988: p. 319-328

  21. Pham, D.T., Dimov, S.S., Nguyen, C.D.: Selection of K in K-means clustering. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 219(1), 103–119 (2005)

    Article  Google Scholar 

  22. Weber, A.: The USC-SIPI Image Database: Version 5. Signal and Image Processing Institute (1997)

  23. Lee, M.C., et al.: Fuzzy C-means clustering of magnetic resonance imaging on apparent diffusion coefficient maps for predicting nodal metastasis in head and neck cancer. Br. J. Radiol. 2016(89), 20150059 (1063)

    Google Scholar 

  24. Vala, M.H.J., Baxi, A.: A review on Otsu image segmentation algorithm. Int. J. Adv. Res. Comput. Eng. Technol. 2(2), 387–389 (2013)

    Google Scholar 

  25. Levine, M.D., Nazif, A.M.: Dynamic measurement of computer generated image segmentations. IEEE Trans. Pattern Anal. Mach. Intell. 7(2), 155–164 (1985)

    Article  Google Scholar 

  26. Sulaiman, S.N., Isa, N.A.M.: Adaptive fuzzy-K-means clustering algorithm for image segmentation. IEEE Trans. Consum. Electron. 56(4), 2661–2668 (2010)

    Article  Google Scholar 

  27. Borsotti, M., Campadelli, P., Schettini, R.: Quantitative evaluation of color image segmentation results. Pattern Recogn. Lett. 19(8), 741–747 (1998)

    Article  MATH  Google Scholar 

Download references

Acknowledgements

This work was partly supported by National Natural Science Foundation of China (71271125, 61502260). We thank the National Natural Science Foundation of China and Natural Science Foundation of Shandong Province for funding. The authors also thank the USC-SIPI image test library in University of Southern California for providing digital images. We are grateful to every researcher who made comments to our work.

Author information

Authors and Affiliations

  1. School of Information, Qilu University of Technology, Jinan, China

    Jialun Pei, Long Zhao & Xiangjun Dong

  2. School of Mathematical Sciences, University of Jinan, Jinan, China

    Xue Dong

Authors
  1. Jialun Pei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Long Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiangjun Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xue Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiangjun Dong.

Ethics declarations

Conflict of interest

The authors declare that they have no conflicts of interests.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pei, J., Zhao, L., Dong, X. et al. Effective algorithm for determining the number of clusters and its application in image segmentation. Cluster Comput 20, 2845–2854 (2017). https://doi.org/10.1007/s10586-017-1083-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10586-017-1083-1

Keywords

Search

Navigation