JACIII Vol.22 No.3 pp. 369-379
doi: 10.20965/jaciii.2018.p0369


2D Direction Histogram-Based Rényi Entropic Multilevel Thresholding

Adiljan Yimit and Yoshihiro Hagihara

Faculty of Science and Engineering, Iwate University
4-3-5 Ueda, Morioka-city, Iwate 020-8551, Japan

December 9, 2016
March 22, 2018
May 20, 2018
entropic thresholding, segmentation, 2D direction histogram, Rényi entropy, artificial bee colony algorithm

2D histogram-based thresholding methods, in which the histogram is computed from local image features, have better performance than 1D histogram-based methods, but they take much more computation time. In this paper, we present a Rényi entropic multilevel thresholding (REMT) method based on a 2D direction histogram constructed from pixel values and local directional features. In addition to presenting a fast recursive method for REMT, we propose the Rényi entropic artificial bee colony multilevel thresholding (REABCMT) method to quickly find the optimal threshold values. In order to demonstrate the efficacy of REABCMT, three versions of this method are compared in terms of computation time and optimal threshold values. In addition, the segmentation performance of REABCMT is also evaluated by comparing it with two other methods to show its effectiveness. Moreover, in order to evaluate the efficiency and stability of using the ABC algorithm in the search for threshold values, genetic algorithm (GA) and particle swarm optimization (PSO), two common optimization algorithms, are also compared with it.

Cite this article as:
A. Yimit and Y. Hagihara, “2D Direction Histogram-Based Rényi Entropic Multilevel Thresholding,” J. Adv. Comput. Intell. Intell. Inform., Vol.22 No.3, pp. 369-379, 2018.
Data files:
  1. [1] F. Y. Shih, “Image Processing and Pattern Recognition: Fundamentals and Techniques,” John Wiley & Sons, 2010.
  2. [2] W. Pratt, “Digital Image Processing: PIKS Scientific Inside,” 4th edition, Wiley-Inter science, 2007.
  3. [3] N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. on Systems, Man, and Cybernetics, Vol.9, No.1, pp. 62-66, 1979.
  4. [4] J. Kittler and J. Illingworth, “Minimum error thresholding,” Pattern Recognition, Vol.19, No.1, pp. 41-47, 1986.
  5. [5] J. N. Kapur, P. K. Sahoo, and A. K. C. Wong, “A new method for grey-level picture thresholding using the entropy of the histogram,” Computer Vision Graphics and Image Processing, Vol.29, No.3, pp. 273-285, 1985.
  6. [6] P. K. Sahoo, C. Willkins, and J. Yeager, “Threshold selection using Rényi’s entropy,” Pattern Recognition, Vol.30, No.1, pp. 71-84, 1997.
  7. [7] P. K. Sahoo, S. Soltani, and A. K. C. Wong, “A survey of thresholding techniques,” Computer Vision, Graphics, and Image Processing, Vol.41, No.2, pp. 233-260, 1988.
  8. [8] A. S. Abutaleb, “Automatic thresholding of gray-level picture using two-dimensional entropies,” Computer Vision, Graphics, and Image Processing, Vol.47, No.1, pp. 22-32, 1989.
  9. [9] J. Zhang and J. Hu, “Image segmentation based on 2D Otsu method with histogram analysis,” Int. Conf. on Computer Science and Software Engineering, Vol.6, pp. 105-108, 2008.
  10. [10] D. G. Lowe, “Distinctive image features from scale-invariant keypoints,” Int. J. Comput. Vis., Vol.60, No.2, pp. 91-110, 2004.
  11. [11] H. Bay, A. Ess, T. Tuytelaars, and L. V. Gool, “Speeded up robust features (SURF),” Comput. Vis. Image Underst. Vol.110, No.3, pp. 346-359, 2008.
  12. [12] L. Zhang and D. Zhang, “Robust visual knowledge transfer via extreme learning machine-based domain adaptation,” IEEE Trans. on Image Processing, Vol.25, No.10, pp. 4959-4973, 2016.
  13. [13] L. Zhang and D. Zhang, “Visual understanding via multi-feature shared learning with global consistency,” IEEE Trans. on Multimedia, Vol.18, No.2, pp. 247-259, 2016.
  14. [14] A. Yimit, Y. Hagihara, T. Miyoshi, and Y. Hagihara, “2-D direction histogram based entropic thresholding,” Neurocomputing, Vol.120, pp. 287-297, 2013.
  15. [15] F. Nie, C. Gao, Y. Guo, and M. Gan, “Two-dimensional minimum local cross-entropy thresholding based on co-occurrence matrix,” Computers & Electrical Engineering, Vol.37, No.5, pp. 757-767, 2011.
  16. [16] P.-S. Liao, T.-S. Chen, and P.-C. Chung, “A fast algorithm for multilevel thresholding,” J. of Information Science and Engineering, Vol.17, No.5, pp. 713-727, 2001.
  17. [17] H. Kiani, R. Safabakhsh, and E. Khadangi, “Fast recursive segmentation algorithm based on Kapur’s entropy,” 2nd Int. Conf. on Computer, Control and Communication, pp. 1-6, 2009.
  18. [18] Z. Ye, H. Chen, W. Li, and J. Zhang, “Automatic threshold selection based on Particle Swarm Optimization algorithm,” Int. Conf. on Intelligent Computation Technology and Automation, pp. 36-39, 2008.
  19. [19] P.-Y. Yin, “Multilevel minimum cross entropy threshold selection based on particle swarm optimization,” Applied Mathematics and Computation, Vol.184, No.2, pp. 503-513, 2007.
  20. [20] C. H. Li, and C. K. Lee, “Minimum cross entropy thresholding,” Pattern Recognition, Vol.26, No.4, pp. 617-625, 1993.
  21. [21] M. H. Horng, “Multilevel thresholding selection based on the artificial bee colony algorithm for image segmentation,” Expert Systems with Applications, Vol.38, No.11, pp. 13785-13791, 2011.
  22. [22] D. Karaboga and B. Basturk, “A powerful and efficient algorithm for numerical function optimization: Artificial bee colony (ABC) algorithm,” J. of Global Optimization, Vol.39, No.3, pp. 459-471, 2007.
  23. [23] B. Aaky and D. Karaboga, “A survey on the applications of artificial bee colony in signal, image, and video processing,” Signal, Image and Video Processing, Vol.9, No.4, pp. 967-990, 2015.
  24. [24] D. Karaboga and B. Akay, “A comparative study of artificial bee colony algorithm,” Applied Mathematics and Computation, Vol.214, No.1, pp. 108-132, 2009.
  25. [25] C. Xu, H. Duan, F. Liu, “Chaotic artificial bee colony approach to Uninhabited Combat Air Vehicle (UCAV) path planning,” Aerospace Science and Technology, Vol.14, No.8, pp. 535-541, 2010.
  26. [26] A. Rényi, “On measures of entropy and information,” 4th Berkeley Symp. on Mathematical Statistics and Probability, Vol.1, pp. 547-561, 1961.
  27. [27] Y. He, A. B. Hamza, and H. Krim, “A generalized divergence measure for robust image registration,” IEEE Trans.on Signal Processing, Vol.51, No.5, pp. 1211-1220, 2003.
  28. [28] T. Maszczyk and W. Duch, “Comparison of Shannon, Renyi and Tsallis entropy used in decision trees,” Int. Conf. on Artificial Intelligence and Soft Computing, pp. 643-651, 2008.
  29. [29] P. K. Sahoo and G. Arora, “A thresholding method based on 2D Renyi’s entropy,” Pattern Recognition, Vol.37, No.6, pp. 1149-1161, 2004.
  30. [30] A. Yimit, Y. Hagihara, T. Miyoshi, Y. Hagihara, and Q. Yimit, “Fast Method for Two-dimensional Renyi’s Entropy-based Thresholding,” IJCSE, Vol.4, No.2, pp. 176-183, 2012.
  31. [31] DIP 3/e Book Images, [accessed December 8, 2016]
  32. [32] B. Akay, “A study on particle swarm optimization and artificial bee colony algorithms for multilevel thresholding,” Applied Soft Computing, Vol.13, No.6, pp. 3066-3091, 2013.
  33. [33] C. Beck and F. Schögl, “Thermodynamics of Chaotic Systems: An Introduction,” Cambridge University Press, 1995.

*This site is desgined based on HTML5 and CSS3 for modern browsers, e.g. Chrome, Firefox, Safari, Edge, Opera.

Last updated on Jul. 12, 2024