Skip to main content
SpringerLink
Log in

A hierarchical multilevel thresholding method for edge information extraction using fuzzy entropy

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

Image thresholding is the fundamental procedure in image processing. Meanwhile, edge information is a very useful and important image representation. A hierarchical multilevel thresholding method for edge information extraction using fuzzy entropy is presented in this paper. To realize multilevel thresholding fast and effectively, a tree structure is used to express the histogram hierarchy of an image. In each level of the tree structure, the image is segmented by three-level thresholding algorithm based on the maximum fuzzy entropy principle. In theory, the histogram hierarchy can be combined arbitrarily with multilevel thresholding. In order to evaluate the edge information extraction performance of multilevel thresholding methods, an edge similarity function is developed for according to the edge matching metric. Several images are employed to calculate their edge similarity coefficients. Experiments show that the proposed edge similarity coefficient is a valid one to measure the similarity between two image edge maps and it avoids the process effectively to obtain truth edge maps of images which can be realized only by labor statistics. To evaluate the performance of the proposed multilevel thresholding algorithm, the thresholded values of test images are calculated and compared using the proposed method, the Otsu and Kapur method, as well as edge similarity coefficients with the original images. The experimental results show that the proposed method spends less time to reach the better thresholds in edge similarity than existing multilevel thresholding methods.

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

Similar content being viewed by others

References

  1. Arora S, Acharya J et al (2008) Multilevel thresholding for image segmentation through a fast statistical recursive algorithm. Pattern Recogn Lett 29(2):119–125

    Article  Google Scholar 

  2. Bao P, Wang DH (2001) Edge-preserved neural network model for image restoration. J Electron Imag 10(3):735–743

    Article  Google Scholar 

  3. Chang Y, Fu AMN et al (2002) Efficient two-level image thresholding method based on Bayesian formulation and the maximum entropy principle. Optical Eng 41(10):2487–2498

    Article  Google Scholar 

  4. Cheng HD, Chen JR et al (1998) Threshold selection based on fuzzy c-partition entropy approach. Pattern Recogn 31(7):857–870

    Article  MathSciNet  Google Scholar 

  5. de Albuquerque MP, Esquef IA et al (2004) Image thresholding using Tsallis entropy. Pattern Recogn Lett 25(9):1059–1065

    Article  Google Scholar 

  6. Gao H, Xu WB et al (2010) Multilevel thresholding for image segmentation through an improved quantum-behaved particle swarm algorithm. IEEE Transact Instrum Meas 59(4):934–946

    Article  Google Scholar 

  7. Jun W, W Shitong et al (2011) Positive and negative fuzzy rule system, extreme learning machine and image classification. Int J Mach Learn Cybernet: 1–11

  8. Kapur JN, Sahoo PK et al (1985) A new method for gray-level picture thresholding using the entropy of the histogram. Comput Vision Graphics Image Process 29(3):273–285

    Article  Google Scholar 

  9. Kosko B (1986) Fuzzy entropy and conditioning. Inf Sci 40(2):165–174

    Article  MathSciNet  MATH  Google Scholar 

  10. Liang J, Song W (2011) Clustering based on Steiner points. Int J Mach Learn Cybernet: 1–8

  11. Martin D, Fowlkes C et al (2001) A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. Proceedings of eighth IEEE international conference on computer vision, vol 2, pp 416–423

  12. Otsu N (1979) Threshold selection method from Gray-Level histograms. IEEE Transact Syst Man Cybernet 9(1):62–66

    Article  MathSciNet  Google Scholar 

  13. Pun T (1980) A new method for grey-level picture thresholding using the entropy of the histogram. Signal Process 2(3):223–237

    Article  Google Scholar 

  14. Sathya P, Duraisamy RK (2010) A new multilevel thresholding method using swarm intelligence algorithm for image segmentation. Intell Learn Syst Appl (2)

  15. Sezgin M, Sankur B (2004) Survey over image thresholding techniques and quantitative performance evaluation. J Electron Imag 13(1):146–168

    Article  Google Scholar 

  16. Tao W (2003) Image segmentation by three-level thresholding based on maximum fuzzy entropy and genetic algorithm. Pattern Recogn Lett 24(16):3069–3078

    Article  Google Scholar 

  17. Tao W, Jin H et al (2007) Object segmentation using ant colony optimization algorithm and fuzzy entropy. Pattern Recogn Lett 28(7):788–796

    Article  Google Scholar 

  18. Tao WB, Jin H et al (2008) Image thresholding using graph cuts. IEEE Transact Syst Man Cybernet Part A-Syst Humans 38(5):1181–1195

    Article  Google Scholar 

  19. Tian W, Geng Y et al (2009) Maximum fuzzy entropy and immune clone selection algorithm for image segmentation. Asia-Pacific Conf Inf Process 1:38–41

    Article  Google Scholar 

  20. Wang, D. H. and T. S. Dillon (2002) Theoretical foundation for nonlinear edge-preserving regularized learning image restoration. Al 2002: Adv Artif Intell 2557:693–703

    Google Scholar 

  21. Wang X, Chen B et al (2000) On the optimization of fuzzy decision trees. Fuzzy Sets Syst 112(1):117–125

    Article  Google Scholar 

  22. Wang XZ, Dong CR (2009) Improving generalization of fuzzy if–then rules by maximizing fuzzy entropy. IEEE Trans Fuzzy Syst 17(3):556–567

    Article  Google Scholar 

  23. Wang XZ, Dong CR et al (2007) Training T-S norm neural networks to refine weights for fuzzy if-then rules. Neurocomputing 70(13–15):2581–2587

    Article  Google Scholar 

  24. Wong AKC, Sahoo PK (1989) A gray-level threshold selection method based on maximum-entropy principle. IEEE Transact Syst Man Cybernet 19(4):866–871

    Article  Google Scholar 

  25. Yan CX, Sang N et al (2003) Local entropy-based transition region extraction and thresholding. Pattern Recogn Lett 24(16):2935–2941

    Article  Google Scholar 

  26. Yan H (1996) Unified formulation of a class of image thresholding techniques. Pattern Recogn 29(12):2025–2032

    Article  Google Scholar 

  27. Yin PY (1999) A fast scheme for optimal thresholding using genetic algorithms. Signal Process 72(2):85–95

    Article  MATH  Google Scholar 

  28. Zhao MS, Fu AMN et al (2001) A technique of three-level thresholding based on probability partition and fuzzy 3-partition. IEEE Trans Fuzzy Syst 9(3):469–479

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong

    Pearl P. Guan & Hong Yan

  2. School of Electrical and Information Engineering, University of Sydney, Sydney, NSW, 2006, Australia

    Hong Yan

Authors
  1. Pearl P. Guan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hong Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pearl P. Guan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Guan, P.P., Yan, H. A hierarchical multilevel thresholding method for edge information extraction using fuzzy entropy. Int. J. Mach. Learn. & Cyber. 3, 297–305 (2012). https://doi.org/10.1007/s13042-011-0063-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-011-0063-7

Keywords

Search

Navigation