Abstract
In this article, a granular computing based multi-level gray image thresholding algorithm is presented. An image is divided into spatial blocks called granules, and the classes of gray levels are represented using a fuzzy-rough collaborative approach, where the measure of roughness of a rough set is also modified from the classical definition of rough sets. This measure for each rough set is minimized simultaneously to obtain the optimal thresholds. Tchebycheff decomposition approach is employed to transform this multi-objective optimization problem to a single objective optimization problem. Differential Evolution (DE), one of the most efficient evolutionary optimizers of current interest, is used to optimize this single objective function, thus reducing the execution time. Superiority of the proposed method is presented by comparing it with some popular image thresholding techniques. MSSIM index and Probabilistic Rand Index (PRI) are used for quantitative comparison on the Berkley Image Segmentation Data Set (BSDS300).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bargiela, A., and Pedrycz, W.: Granular Computing - An Introduction. Kluwer Academic Publishers (2003)
Beauchemin, M.: Image thresholding based on semivariance. Pattern Recogn. Lett. 34(5), 456–462 (2013)
Benzid, R., Arar, D., Bentoumi, M.: A fast technique for gray level image thresholding and quantization based on the entropy maximization. In: 5th International Multi-Conference on Systems, Signals and Devices, pp. 1–4 (2008)
Bourjandi, M.: Image segmentation using thresholding by local fuzzy entropy-based competitive fuzzy edge detection. In: 2nd International Conference on Computer and Electrical Engineering, vol 2, pp. 298–301 (2009)
Bustince, H., Barrenechea, E., Pagola, M.: Image thresholding using restricted equivalence functions and maximizing the measures of similarity. Fuzzy Sets Syst. Elsevier 158, 496–516 (2007)
Chen, G., Hu, T., Guo, X., Meng, X.: A fast region-based image segmentation based on least square method. IEEE Intl. Conf. Syst. Man Cybern. 972–977 (2009)
Das, S., Suganthan, P.N.: Differential evolution: a survey of the state-of-the-art. IEEE Trans. Evol. Comput. 15(1), 4–31 (2011)
Deb, K., Anand, A., Joshi, D.: A computationally efficient evolutionary algorithm for real-parameter optimization. Evo. Comp. 10(4), 371–395 (2002)
Dubois, D., Prade, H.: Putting rough sets and fuzzy sets together. Intell. Decis. Support Theor. Decis. Libr. 11, 203–232 (1992)
Eriksson, A., Barr, O., Astrom, K.: Image segmentation using minimal graph cuts. Intl. J. Eng. Res. Technol. (IJERT) 1(6) (2012)
Feng, F.: Generalized rough fuzzy sets based on soft sets. In:. International Workshop on Intelligence Systems and Applications, pp. 1–4 (2009)
Ghosh, S., Das, S., Vasilakos, A.V., Suresh, K.: On convergence of differential evolution over a class of continuous functions with unique global optimum. IEEE Trans. SMC-B 42(1), 107–124 (2012)
Hsiao, Y.T., Chuang, C.L., Jiang, J.A., Chien, C.C.: A contour based image segmentation algorithm using morphological edge detection. IEEE Int. Conf. Syst. Man Cybern. 3, 2962–2967 (2005)
Hu, Q., Zhang, L., An, S., Zhang, D., Yu, D.: On robust fuzzy rough set models. IEEE Trans. Fuzzy Syst. 20(4), 636–651 (2012)
Kennedy, J., Eberhat, R.: Particle swarm optimization. IEEE Int. Conf. Neural Netw. 4, 1942–1948 (1995)
Marler, R.T., Arora, J.S.: Survey of multi-objective optimization methods for engineering. Struct. Multidisc. Optim. 26, 369–395 (2004)
Miettinen, K.: Nonlinear Multi-objective Optimization. International Series in Operations Research & Management Science, vol. 12. Springer, Norwell (1999)
Otsu, N.: A threshold selection method from gray level histograms. IEEE Trans. Syst. Man Cybern. 9, 62–66 (1972)
Pal, S.K., Shankar, B.U., Mitra, P.: Granular computing, rough entropy and object extraction. Pattern Recogn. Lett. 26, 2509–2517 (2005)
Pawlak, Z., Skowron, A.: Rudiments of rough sets. Info. Sci. 177, 3–27 (2007)
Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data, Kluwer Academic, Dordrecht (1991)
Sahoo, P.K., Arora, G.: A thresholding method based on two dimensional Renyis entropy. Pattern Recogn. 37, 1149–1161 (2004)
Sarkar, S., Das, S., Paul, S., Polley, S., Burman, R., Chaudhuri, S.S.: Multi-level image segmentation based on fuzzy - Tsallis entropy and differential evolution. IEEE Int. Conf. Fuzzy Syst. 1–8 (2013)
Sarkar, S., Das, S.: Multi-level image thresholding based on two-dimensional histogram and maximum Tsallis entropy - a differential evolution approach. IEEE Trans. Image Process. 22(12), 4788–4797 (2013)
Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27(3), 379423 (1948)
Storn, R., Price, K.: Differential evolution A simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341–359 (1997)
Steuer, R.E.: Multiple Criteria Optimization: Theory, Computation, and Application. Robert E. Krieger Publishing, Malabar (1989)
Tadaki, K.T.: The Tsallis entropy and Shannon entropy of a universal probability. IEEE International Symposium on Information Theory, pp. 2111–2115 (2008)
Tizhoosh, H.R.: Image thresholding using type II fuzzy sets. Pattern Recogn. 38, 2363–2372 (2008)
Tsang, E.C.C., Wang, C., Chen, C., Wu, C., Hu, Q.: Communication between information systems using fuzzy rough sets. IEEE Trans. Fuzzy Syst. 21(3), 527–540 (2013)
Unnikrishnan, R., Pantofaru, C., Hebert, M.: Towards objective evaluation of image segmentation algorithms. IEEE Trans. Pattern Anal. Mach. Intell. 29(6), 929–944 (2007)
Wang, Z., Bovik, A., Sheikh, H., Simoncelli, E.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)
Xiao, Y., Cao, Z., Yuan, J.: Entropic image thresholding based on GLGM histogram. Pattern Recogn. Lett. 40, 47–55 (2014)
Xu, Y.: Image decomposition based ultrasound image segmentation by using fuzzy clustering. IEEE Symp. Ind. Electron. Appl. 1, 6–10 (2009)
Xue, J.H., Zhang, Y.J.: Ridler and Calvards, Kittler and Illingworth’s and Otsu’s methods for image thresholding. Pattern Recogn. Lett. 33(6), 793–797 (2012)
The Berkeley Segmentation Dataset and Benchmark. http://www.eecs.berkeley.edu/Research/Projects/CS/vision/bsds/
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Paul, S., Datta, S., Das, S. (2015). Rough-Fuzzy Collaborative Multi-level Image Thresholding: A Differential Evolution Approach. In: Matoušek, R. (eds) Mendel 2015. ICSC-MENDEL 2016. Advances in Intelligent Systems and Computing, vol 378. Springer, Cham. https://doi.org/10.1007/978-3-319-19824-8_27
Download citation
DOI: https://doi.org/10.1007/978-3-319-19824-8_27
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19823-1
Online ISBN: 978-3-319-19824-8
eBook Packages: EngineeringEngineering (R0)