Soft Computing

, Volume 23, Issue 2, pp 431–450 | Cite as

Image segmentation by minimum cross entropy using evolutionary methods

  • Diego OlivaEmail author
  • Salvador Hinojosa
  • Valentín Osuna-Enciso
  • Erik Cuevas
  • Marco Pérez-Cisneros
  • Gildardo Sanchez-Ante
Methodologies and Application


The segmentation of digital images is one of the most important steps in an image processing or computer vision system. It helps to classify the pixels in different regions according to their intensity level. Several segmentation techniques have been proposed, and some of them use complex operators. The techniques based on thresholding are the easiest to implement; the problem is to select correctly the best threshold that divides the pixels. An interesting method to choose the best thresholds is the minimum cross entropy (MCET), which provides excellent results for bi-level thresholding. Nevertheless, the extension of the segmentation problem into multiple thresholds increases significantly the computational effort required to find optimal threshold values. Each new threshold adds complexity to the formulation of the problem. Classic methods for image thresholding perform extensive searches, while new approaches take advantage of heuristics to reduce the search. Evolutionary algorithms use heuristics to optimize criteria over a finite number of iterations. The correct selection of an evolutionary algorithm to minimize the MCET directly impacts the performance of the method. Current approaches take a large number of iterations to converge and a high rate of MCET function evaluations. The electromagnetism-like optimization (EMO) algorithm is an evolutionary technique which emulates the attraction–repulsion mechanism among charges for evolving the individuals of a population. Such technique requires only a small number of evaluations to find the optimum. This paper proposes the use of EMO to search for optimal threshold values by minimizing the cross entropy function while reducing the amount of iterations and function evaluations. The approach is tested on a set of benchmark images to demonstrate that is able to improve the convergence and velocity; additionally, it is compared with similar state-of-the-art optimization approaches.


Image processing Segmentation Evolutionary algorithms Cross entropy Electromagnetism optimization 


Compliance with ethical standards

Ethical standards

None of the authors of this paper has a financial or personal relationship with other people or organizations that could inappropriately influence or bias the content of the paper.

Conflict of interest

It is to specifically state that “No Competing interests are at stake and there is No Conflict of Interest” with other people or organizations that could inappropriately influence or bias the content of the paper.

Human and animal rights

This article does not contain any studies with human participants or animals performed by any of the authors.


  1. Agrawal S, Panda R, Bhuyan S, Panigrahi BK (2013) Tsallis entropy based optimal multilevel thresholding using cuckoo search algorithm. Swarm Evol Comput 11:16–30. doi: 10.1016/j.swevo.2013.02.001 CrossRefGoogle Scholar
  2. Akay B (2013) A study on particle swarm optimization and artificial bee colony algorithms for multilevel thresholding. Appl Soft Comput 13:3066–3091. doi: 10.1016/j.asoc.2012.03.072 CrossRefGoogle Scholar
  3. Bhandari AK, Singh VK, Kumar A, Singh GK (2014) Cuckoo search algorithm and wind driven optimization based study of satellite image segmentation for multilevel thresholding using Kapur’s entropy. Expert Syst Appl 41:3538–3560. doi: 10.1016/j.eswa.2013.10.059 CrossRefGoogle Scholar
  4. Birbil ŞI, Fang SC (2003) An electromagnetism-like mechanism for global optimization. J Glob Optim 25:263–282. doi: 10.1023/A:1022452626305 MathSciNetCrossRefzbMATHGoogle Scholar
  5. Birbil ŞI, Fang SC, Sheu RL (2004) On the convergence of a population-based global optimization algorithm. J Glob Optim 30:301–318MathSciNetCrossRefzbMATHGoogle Scholar
  6. Cao X, Li Q, Du X et al (2014) Exploring effect of segmentation scale on orient-based crop identification using HJ CCD data in Northeast China. IOP Conf Ser Earth Environ Sci 17:12047. doi: 10.1088/1755-1315/17/1/012047 CrossRefGoogle Scholar
  7. De Castro LN, Von Zuben FJ (2002) Learning and optimization using the clonal selection principle. IEEE Trans Evol Comput 6:239–251. doi: 10.1109/TEVC.2002.1011539 CrossRefGoogle Scholar
  8. De Jong K (1988) Learning with genetic algorithms: an overview. Mach Learn 3:121–138. doi: 10.1007/BF00113894 Google Scholar
  9. Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern B Cybern 26(1):29–41. doi: 10.1109/3477.484436 CrossRefGoogle Scholar
  10. García S, Molina D, Lozano M, Herrera F (2009) 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. doi: 10.1007/s10732-008-9080-4 CrossRefzbMATHGoogle Scholar
  11. Ghamisi P, Couceiro MS, Benediktsson JA, Ferreira NMF (2012) An efficient method for segmentation of images based on fractional calculus and natural selection. Expert Syst Appl 39:12407–12417. doi: 10.1016/j.eswa.2012.04.078 CrossRefGoogle Scholar
  12. Gonzalez RC, Woods RE (1992) Digital image processing. Pearson, Prentice-Hall, New JerseyGoogle Scholar
  13. Hammouche K, Diaf M, Siarry P (2008) A multilevel automatic thresholding method based on a genetic algorithm for a fast image segmentation. Comput Vis Image Underst 109:163–175. doi: 10.1016/j.cviu.2007.09.001 CrossRefGoogle Scholar
  14. Horng M-H (2010) Multilevel minimum cross entropy threshold selection based on the honey bee mating optimization. Expert Syst Appl 37:4580–4592. doi: 10.1016/j.eswa.2009.12.050 CrossRefGoogle Scholar
  15. Horng M-H (2011) Multilevel thresholding selection based on the artificial bee colony algorithm for image segmentation. Expert Syst Appl 38:13785–13791. doi: 10.1016/j.eswa.2011.04.180 Google Scholar
  16. Horng M-H, Liou R-J (2011) Multilevel minimum cross entropy threshold selection based on the firefly algorithm. Expert Syst Appl 38:14805–14811. doi: 10.1016/j.eswa.2011.05.069 CrossRefGoogle Scholar
  17. Hung HL, Huang YF (2011) Peak to average power ratio reduction of multicarrier transmission systems using electromagnetism-like method. Int J Innov Comput Inf Control 7:2037–2050Google Scholar
  18. Il-Seok O, Lee J-S, Moon B-R (2004) Hybrid genetic algorithms for feature selection. IEEE Trans Pattern Anal Mach Intell 26:1424–1437. doi: 10.1109/TPAMI.2004.105 CrossRefGoogle Scholar
  19. Jhang JY, Lee KC (2009) Array pattern optimization using electromagnetism-like algorithm. AEU Int J Electron Commun 63:491–496. doi: 10.1016/j.aeue.2008.04.001 CrossRefGoogle Scholar
  20. Kapur JN, Sahoo PK, Wong AKC (1985) A new method for gray-level picture thresholding using the entropy of the histogram. Comput Vis Graph Image Process 29:273–285. doi: 10.1016/0734-189X(85)90125-2 CrossRefGoogle Scholar
  21. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39:459–471. doi: 10.1007/s10898-007-9149-x MathSciNetCrossRefzbMATHGoogle Scholar
  22. Kaur T, Saini BS, Gupta S (2016) Optimized multi threshold brain tumor image segmentation using two dimensional minimum cross entropy based on co-occurrence matrix. Springer, Berlin, pp 461–486Google Scholar
  23. Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Neural Networks, 1995 proceedings, IEEE international conference, vol. 4, pp 1942–1948. doi: 10.1109/ICNN.1995.488968
  24. Khairuzzaman AKM, Chaudhury S (2017) Multilevel thresholding using grey wolf optimizer for image segmentation. Expert Syst Appl. doi: 10.1016/j.eswa.2017.04.029 Google Scholar
  25. Kong Y, Deng Y, Dai Q (2015) Discriminative clustering and feature selection for brain MRI segmentation. IEEE Signal Process Lett 22:573–577CrossRefGoogle Scholar
  26. Kullback S (1968) Information theory and statistics. Dover, New YorkzbMATHGoogle Scholar
  27. Lee CH, Chang FK (2010) Fractional-order PID controller optimization via improved electromagnetism-like algorithm. Expert Syst Appl 37:8871–8878. doi: 10.1016/j.eswa.2010.06.009 CrossRefGoogle Scholar
  28. Li CH, Lee CK (1993) Minimum cross entropy thresholding. Pattern Recognit 26:617–625. doi: 10.1016/0031-3203(93)90115-D CrossRefGoogle Scholar
  29. Liu Y, Mu C, Kou W, Liu J (2015) Modified particle swarm optimization-based multilevel thresholding for image segmentation. Soft Comput 19:1311–1327. doi: 10.1007/s00500-014-1345-2 CrossRefGoogle Scholar
  30. Loganathan GVV, Geem ZW, Kim JH, Loganathan GVV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76:60–68. doi: 10.1177/003754970107600201 CrossRefGoogle Scholar
  31. Naderi B, Tavakkoli-Moghaddam R, Khalili M (2010) Electromagnetism-like mechanism and simulated annealing algorithms for flowshop scheduling problems minimizing the total weighted tardiness and makespan. Knowl Based Syst 23:77–85. doi: 10.1016/j.knosys.2009.06.002 CrossRefGoogle Scholar
  32. Oliva D, Hinojosa S, Cuevas E et al (2017) Cross entropy based thresholding for magnetic resonance brain images using Crow Search Algorithm. Expert Syst Appl. doi: 10.1016/j.eswa.2017.02.042
  33. Olugbara OO, Adetiba E, Oyewole SA (2015) Pixel intensity clustering algorithm for multilevel image segmentation. Math Probl Eng. doi: 10.1155/2015/649802 Google Scholar
  34. Otsu N (1979) A threshold selection method from gray-level histograms. IEEE Trans Syst Man Cybern 9:62–66. doi: 10.1109/TSMC.1979.4310076 CrossRefGoogle Scholar
  35. Pal N (1996) On minimum cross-entropy thresholding. Pattern Recognit 29:575–580. doi: 10.1016/0031-3203(95)00111-5 CrossRefGoogle Scholar
  36. Rocha AMAC, Fernandes EMGP (2009a) Hybridizing the electromagnetism-like algorithm with descent search for solving engineering design problems. Int J Comput Math 86:1932–1946. doi: 10.1080/00207160902971533 CrossRefzbMATHGoogle Scholar
  37. Rocha AMAC, Fernandes EMGP (2009b) Modified movement force vector in an electromagnetism-like mechanism for global optimization. Optim Methods Softw 24:253–270MathSciNetCrossRefzbMATHGoogle Scholar
  38. Sarkar S, Das S, Chaudhuri SS (2015) A multilevel color image thresholding scheme based on minimum cross entropy and differential evolution. Pattern Recognit Lett 54:27–35. doi: 10.1016/j.patrec.2014.11.009 CrossRefGoogle Scholar
  39. Sarkar S, Patra GR, Das S (2011) A differential evolution based approach for multilevel image segmentation using minimum cross entropy thresholding. In: Swarm, evolutionary, and memetic computing, pp 51–58Google Scholar
  40. Sathya PD, Kayalvizhi R (2011) Optimal multilevel thresholding using bacterial foraging algorithm. Expert Syst Appl 38:15549–15564. doi: 10.1016/j.eswa.2011.06.004 CrossRefGoogle Scholar
  41. Storn R, Price K (1997) Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim. doi: 10.1023/A:1008202821328
  42. Tang K, Yuan X, Sun T et al (2011) An improved scheme for minimum cross entropy threshold selection based on genetic algorithm. Knowl Based Syst 24:1131–1138. doi: 10.1016/j.knosys.2011.02.013 CrossRefGoogle Scholar
  43. Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13:600–612. doi: 10.1109/TIP.2003.819861 CrossRefGoogle Scholar
  44. Wu P, Yang W-H, Wei N-C (2004) An electromagnetism algorithm of neural network analysis-an application to textile retail operation. J Chin Inst Ind Eng 21:59–67. doi: 10.1080/10170660409509387 Google Scholar
  45. Yang X-S (2014) Cuckoo search and firefly algorithm: overview and analysis. In: Yang X-S (ed) Cuckoo search and firefly algorithm. Springer, Berlin, Heidelberg, pp 1–26Google Scholar
  46. Yin P-Y (2007) Multilevel minimum cross entropy threshold selection based on particle swarm optimization. Appl Math Comput 184:503–513. doi: 10.1016/j.amc.2006.06.057 MathSciNetzbMATHGoogle Scholar
  47. Yu JJQ, Li VOK (2015) A social spider algorithm for global optimization. Appl Soft Comput 30:614–627. doi: 10.1016/j.asoc.2015.02.014 CrossRefGoogle Scholar
  48. Yurtkuran A, Emel E (2010) A new hybrid electromagnetism-like algorithm for capacitated vehicle routing problems. Expert Syst Appl 37:3427–3433. doi: 10.1016/j.eswa.2009.10.005 CrossRefGoogle Scholar
  49. Zhang L, Zhang L, XuanqinMou DZ (2011) FSIM: a feature similarity index for image. IEEE Trans Image Process 20:2378–2386MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.División de Electrónica y Computación, CUCEIUniversidad de GuadalajaraGuadalajaraMexico
  2. 2.Departamento de Ingeniería del Software e Inteligencia Artificial, Facultad InformáticaUniversidad Complutense de MadridMadridSpain
  3. 3.Departamento de Ciencias de la Información y Desarrollos Tecnológicos, CUTONALAUniversidad de GuadalajaraTonaláMexico
  4. 4.Universidad Politécnica de YucatánUcúMexico

Personalised recommendations