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Segmentation of Magnetic Resonance Brain Images Through the Self-Adaptive Differential Evolution Algorithm and the Minimum Cross-Entropy Criterion

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Applications of Hybrid Metaheuristic Algorithms for Image Processing

Part of the book series: Studies in Computational Intelligence ((SCI,volume 890))

Abstract

The segmentation is regarded as a vital step in preprocessing techniques for image analysis. Automatic segmentation of brain magnetic resonance images has been extensively investigated since with a precise segmentation can be identified and diagnosed several brain diseases. Thresholding is an important simple but efficient technique of image segmentation. Various strategies have been submitted to find optimal thresholds. Amongst those methods, the minimum cross-entropy (MCE) has been broadly implemented due to its simpleness. Although MCE is quite effective in bilevel thresholding, the computational cost increases exponentially the higher the number of thresholds (th) to find. This article introduces a new approach called MCE-SADE for multilevel thresholding using the Self-Adaptive Differential Evolution (SADE) algorithm. SADE is a robust metaheuristic algorithm (MA) that resolve general problems efficiently since, through evolution, the parameters and the proper learning strategy are continuously adjusted pursuant to prior knowledge. The optimum th values are found minimizing cross-entropy through SADE algorithm. The proposed method is tested in two groups of reference images; the primary group is formed of standard test images, while the following group consists of brain magnetic resonance images. In turn, MCE-SADE is compared with two metaheuristic algorithms, Grey Wolf Optimizer (GWO) and Competitive Imperialist Algorithm (ICA). From the experimental results, it is observed that MCE-SADE results improve in terms of consistency and quality in contrast to GWO and ICA based methods.

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References

  1. T. Budrys, V. Veikutis, S. Lukosevicius, et al., Artifacts in magnetic resonance imaging: how it can really affect diagnostic image quality and confuse clinical diagnosis? J. Vibroeng. 20, 1202–1213 (2018). https://doi.org/10.21595/jve.2018.19756

  2. S. Simu, S. Lal, A study about evolutionary and non-evolutionary segmentation techniques on hand radiographs for bone age assessment. Biomed. Signal Process. Control 33, 220–235 (2017). https://doi.org/10.1016/J.BSPC.2016.11.016

    Article  Google Scholar 

  3. S. González-Villà, A. Oliver, S. Valverde et al., A review on brain structures segmentation in magnetic resonance imaging. Artif. Intell. Med. 73, 45–69 (2016). https://doi.org/10.1016/j.artmed.2016.09.001

    Article  Google Scholar 

  4. T.X. Pham, P. Siarry, H. Oulhadj, Integrating fuzzy entropy clustering with an improved PSO for MRI brain image segmentation. Appl. Soft. Comput. J. 65, 230–242 (2018). https://doi.org/10.1016/j.asoc.2018.01.003

    Article  Google Scholar 

  5. Z. Yang, Y. Shufan, G. Li, D. Weifeng, Segmentation of MRI brain images with an improved harmony searching algorithm. Biomed. Res. Int. (2016). https://doi.org/10.1155/2016/4516376

  6. P. Moeskops, M.A. Viergever, A.M. Mendrik et al., Automatic segmentation of MR brain images with a convolutional neural network. IEEE Trans. Med. Imaging 35, 1252–1261 (2016). https://doi.org/10.1109/TMI.2016.2548501

    Article  Google Scholar 

  7. R. Hiralal, H.P. Menon, A survey of brain MRI image segmentation methods and the issues involved (Springer, Cham, 2016), pp. 245–259

    Google Scholar 

  8. N. Otsu, A threshold selection method FROM gray-level histograms. IEEE Trans. Syst. Man. Cybern. 9, 62–66 (1979). https://doi.org/10.1109/TSMC.1979.4310076

    Article  Google Scholar 

  9. J. Kittler, J. Illingworth, Minimum error thresholding. Pattern Recognit. 19, 41–47 (1986). https://doi.org/10.1016/0031-3203(86)90030-0

    Article  Google Scholar 

  10. N.R. Pal, On minimum cross-entropy thresholding. Pattern Recognit. 29, 575–580 (1996). https://doi.org/10.1016/0031-3203(95)00111-5

    Article  Google Scholar 

  11. A.G. Shanbhag, Utilization of information measure as a means of image thresholding. CVGIP Graph. Model Image Process. 56, 414–419 (1994). https://doi.org/10.1006/CGIP.1994.1037

    Article  Google Scholar 

  12. M. Sezgin, B. Sankur, Survey over image thresholding techniques and quantitative performance evaluation. J. Electron. Imaging 13, 146 (2004). https://doi.org/10.1117/1.1631315

    Article  Google Scholar 

  13. C.-I. Chang, Y. Du, J. Wang et al., Survey and comparative analysis of entropy and relative entropy thresholding techniques. IEEE Proc.—Vis. Image Signal Process. 153, 837 (2006). https://doi.org/10.1049/ip-vis:20050032

    Article  Google Scholar 

  14. M.L. Menendez, Shannon’s entropy in exponential families: statistical applications. Appl. Math. Lett. 13, 37–42 (2000). https://doi.org/10.1016/S0893-9659(99)00142-1

    Article  MathSciNet  MATH  Google Scholar 

  15. J.N. Kapur, P.K. Sahoo, A.K.C. Wong, A new method for gray-level picture thresholding using the entropy of the histogram. Comput. Vis. Graph. Image Process. 29, 273–285 (1985). https://doi.org/10.1016/0734-189X(85)90125-2

    Article  Google Scholar 

  16. C.H. Li, C.K. Lee, Minimum cross entropy thresholding. Pattern Recognit. 26, 617–625 (1993). https://doi.org/10.1016/0031-3203(93)90115-D

    Article  Google Scholar 

  17. C. Tsallis, Computational applications of nonextensive statistical mechanics. J. Comput. Appl. Math. 227, 51–58 (2009). https://doi.org/10.1016/J.CAM.2008.07.030

    Article  MathSciNet  MATH  Google Scholar 

  18. E. Beadle, J. Schroeder, B. Moran, S. Suvorova, An overview of Renyi Entropy and some potential applications, in 2008 42nd Asilomar Conference on Signals, Systems and Computers (IEEE, 2008), pp. 1698–1704

    Google Scholar 

  19. V. Osuna-Enciso, E. Cuevas, H. Sossa, A comparison of nature inspired algorithms for multi-threshold image segmentation. Expert Syst. Appl. 40, 1213–1219 (2013). https://doi.org/10.1016/J.ESWA.2012.08.017

    Article  Google Scholar 

  20. J. Zhang, H. Li, Z. Tang, et al., (2014) An improved quantum-inspired genetic algorithm for image multilevel thresholding segmentation. Math. Probl. Eng. (2014). https://doi.org/10.1155/2014/295402

  21. Y. Wang, Improved OTSU and adaptive genetic algorithm for infrared image segmentation, in 2018 Chinese Control and Decision Conference (CCDC) (IEEE, 2018), pp. 5644–5648

    Google Scholar 

  22. Y. Li, S. Wang, J. Xiao, Image segmentation based on dynamic particle swarm optimization for crystal growth. Sensors 18, 3878 (2018). https://doi.org/10.3390/s18113878

    Article  Google Scholar 

  23. M.F. Di, S. Sessa, PSO image thresholding on images compressed via fuzzy transforms. Inf. Sci. (Ny) 506, 308–324 (2020). https://doi.org/10.1016/J.INS.2019.07.088

    Article  MathSciNet  MATH  Google Scholar 

  24. H.V.H. Ayala, F.M. dos Santos, V.C. Mariani, L. dos Santos Coelho, Image thresholding segmentation based on a novel beta differential evolution approach. Expert Syst. Appl. 42, 2136–2142 (2015). https://doi.org/10.1016/J.ESWA.2014.09.043

    Article  Google Scholar 

  25. E. Cuevas, D.P.-C.M. Zaldivar, A novel multi-threshold segmentation approach based on differential evolution optimization. Expert Syst. Appl. 37, 5265–5271 (2010). https://doi.org/10.1016/j.eswa.2010.01.013

    Article  Google Scholar 

  26. U. Mlakar, B. Potočnik, J. Brest, A hybrid differential evolution for optimal multilevel image thresholding. Expert Syst. Appl. 65, 221–232 (2016). https://doi.org/10.1016/j.eswa.2016.08.046

    Article  Google Scholar 

  27. E. Cuevas, F. Sención, D. Zaldivar et al., A multi-threshold segmentation approach based on artificial bee colony optimization. Appl. Intell. 37, 321–336 (2012). https://doi.org/10.1007/s10489-011-0330-z

    Article  Google Scholar 

  28. S. Zhan, W. Jiang, S. Satoh, Multilevel thresholding color image segmentation using a modified artificial bee colony algorithm. IEICE Trans. Inf. Syst. 101, 2064–2071 (2018). https://doi.org/10.1587/transinf.2017EDP7183

  29. D. Oliva, E. Cuevas, G. Pajares, et al., Multilevel thresholding segmentation based on harmony search optimization. J. Appl. Math. (2013). https://doi.org/10.1155/2013/575414

  30. V. Tuba, M. Beko, M. Tuba, Color Image Segmentation by Multilevel Thresholding Based on Harmony Search Algorithm (Springer, Cham, 2017), pp. 571–579

    Google Scholar 

  31. T. Kaur, B.S. Saini, S. Gupta, Optimized Multi Threshold Brain Tumor Image Segmentation Using Two Dimensional Minimum Cross Entropy Based on Co-occurrence Matrix (Springer, Cham, 2016), pp. 461–486

    Google Scholar 

  32. D. Oliva, S. Hinojosa, E. Cuevas, G. Pajares, O.G.J. Avalos, Cross entropy based thresholding for magnetic resonance brain images using Crow Search Algorithm. Expert Syst. Appl. 79, 164–180 (2017). https://doi.org/10.1016/j.eswa.2017.02.042

    Article  Google Scholar 

  33. P.D. Sathya, R. Kayalvizhi, Amended bacterial foraging algorithm for multilevel thresholding of magnetic resonance brain images. Meas. J. Int. Meas. Confed. 44, 1828–1848 (2011). https://doi.org/10.1016/j.measurement.2011.09.005

    Article  Google Scholar 

  34. M. Ali, P. Siarry, M. Pant, Multi-level image thresholding based on hybrid differential evolution algorithm. Application on Medical Images (Springer, Berlin, Heidelberg, 2017), pp. 23–36

    Google Scholar 

  35. G. Chen, Z. Yang Z (2009) Preserving and exploiting genetic diversity in evolutionary programming algorithms. IEEE Trans. Evol. Comput. 13. https://doi.org/10.1109/TEVC.2008.2011742

  36. D.H. Wolpert, W.G. Macready, No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1, 67–82 (1997). https://doi.org/10.1109/4235.585893

    Article  Google Scholar 

  37. D. Shilane, J. Martikainen, S. Dudoit, S.J. Ovaska, A general framework for statistical performance comparison of evolutionary computation algorithms. Inf. Sci. (Ny) 178, 2870–2879 (2008). https://doi.org/10.1016/J.INS.2008.03.007

    Article  Google Scholar 

  38. S. Mirjalili, S.M. Mirjalili, A. Lewis, Grey wolf optimizer. Adv. Eng. Softw. 69, 46–61 (2014). https://doi.org/10.1016/j.advengsoft.2013.12.007

    Article  Google Scholar 

  39. A.E. Gargari, C. Lucas, Imperialist competitive algorithm : an algorithm for optimization inspires by imperialistic competition. IEEE Congr. Evol. Comput., 4661–4667 (2007)

    Google Scholar 

  40. S. Kullback, Information Theory and Statistics (Dover Publications, 1968)

    Google Scholar 

  41. R. Storn, K. Price, Differential evolution—A simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11, 341–359 (1997)

    Article  MathSciNet  Google Scholar 

  42. A.T. Buba, L.S. Lee, A differential evolution for simultaneous transit network design and frequency setting problem. Expert Syst. Appl. 106, 277–289 (2018). https://doi.org/10.1016/J.ESWA.2018.04.011

    Article  Google Scholar 

  43. B. Bošković, J. Brest, Protein folding optimization using differential evolution extended with local search and component reinitialization. Inf. Sci. (Ny) 454–455, 178–199 (2018). https://doi.org/10.1016/J.INS.2018.04.072

    Article  MathSciNet  Google Scholar 

  44. D.M. Diab, K. El Hindi, Using differential evolution for improving distance measures of nominal values. Appl. Soft. Comput. 64, 14–34 (2018). https://doi.org/10.1016/J.ASOC.2017.12.007

    Article  Google Scholar 

  45. M.G. Villarreal-Cervantes, E. Mezura-Montes, J.Y. Guzmán-Gaspar, Differential evolution based adaptation for the direct current motor velocity control parameters. Math. Comput. Simul. 150, 122–141 (2018). https://doi.org/10.1016/J.MATCOM.2018.03.007

    Article  MathSciNet  MATH  Google Scholar 

  46. S. Maggi, Estimating water retention characteristic parameters using differential evolution. Comput. Geotech. 86, 163–172 (2017). https://doi.org/10.1016/J.COMPGEO.2016.12.025

    Article  Google Scholar 

  47. A.K. Qin, V.L. Huang, P.N. Suganthan, Differential evolution Algorithm with strategy adaptation for global numerical optimization. IEEE Commun. Mag. 13, 398–417 (2009). https://doi.org/10.1109/TEVC.2008.927706

    Article  Google Scholar 

  48. J.E. Baker, Reducing bias and inefficiency in the selection algorithm, in Proceedings of the Second International Conference on Genetic Algorithms, 28–31 July 1987, Massachusetts Institute of Technology, MA (1987)

    Google Scholar 

  49. S. Sarkar, S. Paul, R. Burman et al., A Fuzzy Entropy Based Multi-Level Image Thresholding Using Differential Evolution (Springer, Cham, 2015), pp. 386–395

    Google Scholar 

  50. A.K.M. Khairuzzaman, S. Chaudhury, Multilevel thresholding using grey wolf optimizer for image segmentation. Expert Syst. Appl. 86, 64–76 (2017). https://doi.org/10.1016/j.eswa.2017.04.029

    Article  Google Scholar 

  51. M. Nejad, M. Fartash, Applying chaotic imperialist competitive algorithm for multi-level image thresholding based on Kapur’s entropy. Adv. Sci. Technol. Res. J. 10, 125–131 (2016). https://doi.org/10.12913/22998624/61940

  52. B. Sankur, B. Sankur, K. Sayood, Statistical evaluation of image quality measures. J Electron. Imaging 11, 206 (2002). https://doi.org/10.1117/1.1455011

    Article  Google Scholar 

  53. Z. Wang, A.C. Bovik, H.R. Sheikh, E.P. Simoncelli, Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13, 600–612 (2004). https://doi.org/10.1109/TIP.2003.819861

    Article  Google Scholar 

  54. L. Zhang, L. Zhang, X. Mou, D. Zhang, FSIM: a feature similarity index for image quality assessment. IEEE Trans. Image Process. 20, 2378–2386 (2011). https://doi.org/10.1109/TIP.2011.2109730

    Article  MathSciNet  MATH  Google Scholar 

  55. P. Ghamisi, M.S. Couceiro, J.A. Benediktsson, N.M.F. Ferreira, An efficient method for segmentation of images based on fractional calculus and natural selection. Expert Syst. Appl. 39, 12407–12417 (2012). https://doi.org/10.1016/J.ESWA.2012.04.078

    Article  Google Scholar 

  56. F. Wilcoxon, Individual comparisons by ranking methods. Biometrics Bull. 1, 80–83 (1945)

    Article  Google Scholar 

  57. S. García, D. Molina, M. Lozano, F. Herrera, A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 Special Session on Real Parameter Optimization. J. Heuristics 15, 617–644 (2009). https://doi.org/10.1007/s10732-008-9080-4

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. División de Electrónica y Computación, Universidad de Guadalajara, CUCEI, Guadalajara, Jalisco, México

    Itzel Aranguren, Arturo Valdivia & Marco A. Pérez

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  1. Itzel Aranguren
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  2. Arturo Valdivia
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  3. Marco A. Pérez
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Correspondence to Itzel Aranguren .

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Editors and Affiliations

  1. CUCEI, University of Guadalajara, Guadajalara, Mexico

    Diego Oliva

  2. CUCEI, University of Guadalajara, Guadajalara, Mexico

    Salvador Hinojosa

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Aranguren, I., Valdivia, A., Pérez, M.A. (2020). Segmentation of Magnetic Resonance Brain Images Through the Self-Adaptive Differential Evolution Algorithm and the Minimum Cross-Entropy Criterion. In: Oliva, D., Hinojosa, S. (eds) Applications of Hybrid Metaheuristic Algorithms for Image Processing. Studies in Computational Intelligence, vol 890. Springer, Cham. https://doi.org/10.1007/978-3-030-40977-7_14

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