Nature-Inspired Optimization Algorithms and Their Application in Multi-Thresholding Image Segmentation

Abstract

In the field of image processing, there are several problems where an efficient search of the solutions has to be performed within a complex search domain to find an optimal solution. Multi-thresholding which is a very important image segmentation technique is one of them. The multi-thresholding problem is simply an exponential combinatorial optimization process which traditionally is formulated based on complex objective function criterion which can be solved using only nondeterministic methods. Under such circumstances, there is also no unique measurement which quantitatively judges the quality of a given segmented image. Therefore, researchers are solving those issues by using Nature-Inspired Optimization Algorithms (NIOAs) as alternative methodologies for the multi-thresholding problem. This study presents an up-to-date review on all most important NIOAs employed in multi-thresholding based image segmentation domain. The key issues which are involved during the formulation of NIOAs based image multi-thresholding models are also discussed here.

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References

  1. 1.

    El Aziz MA, Ewees AA, Hassanien AE (2016) Hybrid swarms optimization based image segmentation. In: Bhattacharyya S, Dutta P, De S, Klepac G (eds) Hybrid soft computing for image segmentation. Springer, Cham

    Google Scholar 

  2. 2.

    Ngambeki SS, Ding X, Nachipyangu MD (2015) Real time face recognition using region-based segmentation algorithm. Int J Eng Res Technol 4(4):875–878

    Google Scholar 

  3. 3.

    Zhao F, Xie X (2013) An overview of interactive medical image segmentation. Ann BMVA 2013(7):1–22

    Google Scholar 

  4. 4.

    Kim SH, An KJ, Jang SW, Kim GY (2016) Texture feature-based text region segmentation in social multimedia data. Multimed Tools Appl 75(20):12815–12829

    Article  Google Scholar 

  5. 5.

    Pare S, Bhandari AK, Kumar A, Singh GK, Khare S (2015) Satellite image segmentation based on different objective functions using genetic algorithm: a comparative study. In: 2015 IEEE international conference on digital signal processing (DSP). IEEE, pp 730–734

  6. 6.

    Bong CW, Rajeswari M (2012) Multiobjective clustering with metaheuristic: current trends and methods in image segmentation. IET Image Process 6(1):1–10

    MathSciNet  Article  Google Scholar 

  7. 7.

    Bhanu B, Lee S, Das S (1993) Adaptive image segmentation using multi-objective evaluation and hybrid search methods. Mach Learn Comput Vis. AAAI Technical Report FS-93-04, pp 30-34

  8. 8.

    Bhanu B, Lee S, Das S (1995) Adaptive image segmentation using genetic and hybrid search methods. IEEE Trans Aerosp Electron Syst 31(4):1268–1291

    Article  Google Scholar 

  9. 9.

    Liang Y, Zhang M, Browne WN (2014) Image segmentation: a survey of methods based on evolutionary computation. In: Asia-Pacific conference on simulated evolution and learning. Springer, Cham, pp 847–859

    Google Scholar 

  10. 10.

    Senthilkumaran N, Rajesh R (2009) Edge detection techniques for image segmentation—a survey of soft computing approaches. Int J Recent Trends Eng 1(2):250–254

    Google Scholar 

  11. 11.

    Jiao L (2011) Evolutionary-based image segmentation methods. In: Ho P-G (ed) Image segmentation. IntechOpen. https://doi.org/10.5772/16106. Available from: https://www.intechopen.com/books/imagesegmentation/evolutionary-based-image-segmentation-methods

    Google Scholar 

  12. 12.

    Kaur D, Kaur Y (2014) Various image segmentation techniques: a review. Int J Comput Sci Mob Comput 3(5):809–814

    Google Scholar 

  13. 13.

    Pathegama M, Göl Ö (2007) Edge-end pixel extraction for edge-based image segmentation. World Acad Sci Eng Technol 2:657–660

    Google Scholar 

  14. 14.

    Gonzalez RC, Woods RE (2002) Digital image processing, 2nd edn. Prentice Hall, Upper Saddle River

    Google Scholar 

  15. 15.

    Fister Jr I (2013) A comprehensive review of bat algorithms and their hybridization. Masters thesis. University of Maribor, Slovenia

  16. 16.

    Darwin C (1859) On the origin of species. Reprinted by Harvard University Press (1964)

  17. 17.

    Kulkarni AJ, Krishnasamy G, Abraham A (2017) Cohort intelligence: a socio-inspired optimization method. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-44254-9_1

    Google Scholar 

  18. 18.

    Fister Jr I, Yang XS, Fister I, Brest J, Fister D (2013) A brief review of nature-inspired algorithms for optimization. arXiv preprint arXiv:1307.4186

  19. 19.

    Yang XS (2012) Flower pollination algorithm for global optimization. In: International conference on unconventional computing and natural computation. Springer, Berlin, pp 240–249

    Google Scholar 

  20. 20.

    Fister Jr I, Mlakar U, Brest J, Fister I (2016) A new population-based nature-inspired algorithm every month: is the current era coming to the end. In: StuCoSReC: proceedings of the 2016 3rd student computer science research conference, University of Primorskapp, Koper, pp 33–37

  21. 21.

    Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evolut Comput 1(1):67–82

    Article  Google Scholar 

  22. 22.

    Fister I, Yang XS, Ljubič K, Fister D, Brest J (2014) Towards the novel reasoning among particles in PSO by the use of RDF and SPARQL. Sci World J 2014:1–10

    Google Scholar 

  23. 23.

    Colorni A, Dorigo M, Maniezzo V (1992) Distributed optimization by ant colonies. In: Toward a practice of autonomous systems: proceedings of the first European conference on artificial life. MIT Press, p 134

  24. 24.

    Mirjalili S (2015) The ant lion optimizer. Adv Eng Softw 83:80–98

    Article  Google Scholar 

  25. 25.

    Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39(3):459–471

    MathSciNet  MATH  Article  Google Scholar 

  26. 26.

    Rosenberg LB (2015) Human swarming, a real-time method for parallel distributed intelligence. In: 2015 swarm/human blended intelligence workshop (SHBI), pp 1–7, ISBN 978-1-4673-6522-2. https://doi.org/10.1109/shbi.2015.7321685

  27. 27.

    Passino KM (2002) Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Syst 22(3):52–67

    MathSciNet  Article  Google Scholar 

  28. 28.

    Chen TC, Tsai PW, Chu SC, Pan JS (2007) A novel optimization approach: bacterial-GA foraging. In: Second international conference on innovative computing, information and control, 2007, ICICIC’07, IEEE, p 391

  29. 29.

    Yang XS (2010) A new metaheuristic bat-inspired algorithm. In: Nature inspired cooperative strategies for optimization (NICSO 2010), pp 65–74

    Google Scholar 

  30. 30.

    Teodorovic D, Dell’Orco M (2005) Bee colony optimization–a cooperative learning approach to complex transportation problems. Advanced OR and AI methods in transportation, 51–60

  31. 31.

    Wedde HF, Farooq M, Zhang Y (2004) BeeHive: an efficient fault-tolerant routing algorithm inspired by honey bee behavior. In: International workshop on ant colony optimization and swarm intelligence. Springer, Berlin, pp 83–94

    Google Scholar 

  32. 32.

    Lucic P, Teodorović D (2001) Bee system: Modeling combinatorial optimization transportation engineering problems by swarm intelligence. In: Preprints of the TRISTAN IV triennial symposium on transportation analysis, pp 441–445

  33. 33.

    Pham DT, Ghanbarzadeh A, Koc E, Otri S, Rahim S, Zaidi M (2011) The bees algorithm—a novel tool for complex optimisation. In: Intelligent production machines and systems-2nd I*PROMS virtual international conference, 3–14 July 2006

  34. 34.

    Drias H, Sadeg S, Yahi S (2005) Cooperative bees swarm for solving the maximum weighted satisfiability problem. In: International work-conference on artificial neural networks. Springer, Berlin, pp 318–325

    Google Scholar 

  35. 35.

    Comellas F, Martinez-Navarro J (2009) Bumblebees: a multiagent combinatorial optimization algorithm inspired by social insect behaviour. In: Proceedings of the first ACM/SIGEVO summit on genetic and evolutionary computation. ACM, pp 811–814

  36. 36.

    Chu S-A, Tsai P-W, Pan J-S (2006) Cat swarm optimization. Lecture notes in computer science (including subseries Lecture notes in artificial intelligence and lecture notes in bioinformatics), LNAI, vol 4099, pp 854–858. cited by (since 1996) 8

  37. 37.

    Iordache S (2010) Consultant-guided search: a new metaheuristic for combinatorial optimization problems. In: Proceedings of the 12th annual conference on genetic and evolutionary computation. ACM, pp 225–232

  38. 38.

    Askarzadeh A (2016) A novel metaheuristic method for solving constrained engineering optimization problems: crow search algorithm. Comput Struct 169:1–12

    Article  Google Scholar 

  39. 39.

    Yang XS, Deb S (2009) Cuckoo search via Lévy flights. In: World congress on nature and biologically inspired computing, 2009, NaBIC 2009. IEEE, pp 210–214

  40. 40.

    Mirjalili S (2016) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Appl 27(4):1053–1073

    Article  Google Scholar 

  41. 41.

    Topal AO, Altun O (2014) A novel meta-heuristic algorithm: dynamic virtual bats algorithm. Inf Sci 354:222–235

    Article  Google Scholar 

  42. 42.

    Yang XS, Deb S (2010) Eagle strategy using Lévy walk and firefly algorithms for stochastic optimization. In: Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, Berlin, pp 101–111

    Google Scholar 

  43. 43.

    Chu Y, Mi H, Liao H, Ji Z, Wu QH (2008) A fast bacterial swarming algorithm for high-dimensional function optimization. In: IEEE congress on evolutionary computation, 2008. CEC 2008 (IEEE world congress on computational intelligence). IEEE, pp 3135–3140

  44. 44.

    Yang XS (2010) Firefly algorithm, stochastic test functions and design optimisation. Int J Bio-Inspir Comput 2(2):78–84

    Article  Google Scholar 

  45. 45.

    Li LX, Shao ZJ, Qian JX (2002) An optimizing method based on autonomous animals: fish-swarm algorithm systems engineering. Theory Pract 22:32–38

    Google Scholar 

  46. 46.

    Krishnanand KN, Ghose D (2005) Detection of multiple source locations using a glowworm metaphor with applications to collective robotics. In: Proceedings of swarm intelligence symposium, 2005. SIS 2005. IEEE, pp 84–91

  47. 47.

    Krishnanand KN, Ghose D (2009) Glowworm swarm optimisation: a new method for optimising multi-modal functions. Int J Comput Intell Stud 1(1):93–119

    Article  Google Scholar 

  48. 48.

    Su S, Wang J, Fan W, Yin X (2007) Good lattice swarm algorithm for constrained engineering design optimization. In: International conference on wireless communications, networking and mobile computing, 2007, WiCom 2007. IEEE, pp 6421–6424

  49. 49.

    Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30–47

    Article  Google Scholar 

  50. 50.

    Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    Article  Google Scholar 

  51. 51.

    Chen H, Zhu Y, Hu K, He X (2010) Hierarchical swarm model: a new approach to optimization. Discrete Dyn Nat Soc 2010:1–30

    MathSciNet  MATH  Google Scholar 

  52. 52.

    Oftadeh R, Mahjoob MJ (2009) A new meta-heuristic optimization algorithm: Hunting search. In: Fifth international conference on soft computing, computing with words and perceptions in system analysis, decision and control, 2009, ICSCCW 2009. IEEE, pp 1–5

  53. 53.

    Biyanto TR, Irawan S, Febrianto HY, Afdanny N, Rahman AH, Gunawan KS, Pratama JA, Bethiana TN (2017) Killer whale algorithm: an algorithm inspired by the life of killer whale. Procedia Comput Sci 124:151–157

    Article  Google Scholar 

  54. 54.

    Gandomi AH, Alavi AH (2012) Krill herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci Numer Simul 17(12):4831–4845

    MathSciNet  MATH  Article  Google Scholar 

  55. 55.

    Mucherino A, Seref O (2007) Monkey search: a novel metaheuristic search for global optimization. In: AIP conference proceedings, vol 953, No. 1, pp 162–173. AIP

  56. 56.

    Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowledge-Based Syst 89:228–249

    Article  Google Scholar 

  57. 57.

    Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science, 1995, MHS’95. IEEE, pp 39–43

  58. 58.

    Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191

    Article  Google Scholar 

  59. 59.

    Abedinia O, Amjady N, Ghasemi A (2016) A new metaheuristic algorithm based on shark smell optimization. Complexity 21(5):97–116

    MathSciNet  Article  Google Scholar 

  60. 60.

    Yang XS, Lees JM, Morley CT (2006) Application of virtual ant algorithms in the optimization of cfrp shear strengthened precracked structures. In: International conference on computational science. Springer, Berlin, pp 834–837

    Google Scholar 

  61. 61.

    Yang XS (2005) Engineering optimizations via nature-inspired virtual bee algorithms. In: International work-conference on the interplay between natural and artificial computation. Springer, Berlin, pp 317–323

    Google Scholar 

  62. 62.

    Ting TO, Man KL, Guan SU, Nayel M, Wan K (2012) Weightless swarm algorithm (WSA) for dynamic optimization problems. In: NPC, pp 508–515

  63. 63.

    Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67

    Article  Google Scholar 

  64. 64.

    Tang R, Fong S, Yang XS, Deb S (2012) Wolf search algorithm with ephemeral memory. In: 2012 seventh international conference on digital information management (ICDIM). IEEE, pp 165–172

  65. 65.

    Yan GW, Hao ZJ (2013) A novel optimization algorithm based on atmosphere clouds model. Int J Comput Intell Appl 12(01):1350002

    Article  Google Scholar 

  66. 66.

    Simon D (2008) Biogeography-based optimization. IEEE Trans Evolut Comput 12(6):702–713

    Article  Google Scholar 

  67. 67.

    Shi Y (2015) An optimization algorithm based on brainstorming process. In: Emerging research on swarm intelligence and algorithm optimization. IGI Global, pp 1–35

  68. 68.

    Eesa AS, Brifcani AMA, Orman Z (2013) Cuttlefish algorithm—a novel bio-inspired optimization algorithm. Int J Sci Eng Res 4(9):1978–1986

    Google Scholar 

  69. 69.

    Kaveh A, Farhoudi N (2013) A new optimization method: dolphin echolocation. Adv Eng Softw 59:53–70

    Article  Google Scholar 

  70. 70.

    Biyanto TR, Fibrianto HY, Nugroho G, Hatta AM, Listijorini E, Budiati T, Huda H (2016) Duelist algorithm: an algorithm inspired by how duelist improve their capabilities in a duel. In: International conference in swarm intelligence. Springer, pp 39–47

  71. 71.

    Zheng YJ, Ling HF, Xue JY (2014) Ecogeography-based optimization: enhancing biogeography-based optimization with ecogeographic barriers and differentiations. Comput Oper Res 50:115–127

    MATH  Article  Google Scholar 

  72. 72.

    Parpinelli RS, Lopes HS (2011) An eco-inspired evolutionary algorithm applied to numerical optimization. In: 2011 third world congress on nature and biologically inspired computing (NaBIC). IEEE, pp 466–471

  73. 73.

    Sur C, Sharma S, Shukla A (2013) Egyptian vulture optimization algorithm—a new nature inspired meta-heuristics for knapsack problem. In: The 9th international conference on computing and information technology (IC2IT2013), Springer, Berlin, pp 227–237

    Google Scholar 

  74. 74.

    Bastos Filho CJ, de Lima Neto FB, Lins AJ, Nascimento AI, Lima MP (2008) A novel search algorithm based on fish school behavior. In: IEEE international conference on systems, man and cybernetics, 2008, SMC 2008. IEEE, pp 2646–2651

  75. 75.

    Filho CJAB, de Lima Neto FB, Lins AJCC, Nascimento AIS, Lima MP (2009) Fish school search. In: Chiong R (ed) Nature-inspired algorithms for optimisation. Studies in computational intelligence, vol 193. Springer, Berlin, pp 261–277

    Google Scholar 

  76. 76.

    Yang XS, Karamanoglu M, He X (2013) Multi-objective flower algorithm for optimization. Procedia Comput Sci 18:861–868

    Article  Google Scholar 

  77. 77.

    Ferreira C (2001) Gene expression programming: a new adaptive algorithm for solving problems. arXiv preprint https://arxiv.org/pdf/cs/0102027

  78. 78.

    Mozaffari A, Fathi A, Behzadipour S (2012) The great salmon run: a novel bio-inspired algorithm for artificial system design and optimisation. Int J Bio-Inspir Comput 4(5):286–301

    Article  Google Scholar 

  79. 79.

    He S, Wu QH, Saunders JR (2009) Group search optimizer: an optimization algorithm inspired by animal searching behavior. IEEE Trans Evolut Comput 13(5):973–990

    Article  Google Scholar 

  80. 80.

    Zhang LM, Dahlmann C, Zhang Y (2009) Human-inspired algorithms for continuous function optimization. In: IEEE international conference on intelligent computing and intelligent systems, 2009, ICIS 2009, vol 1. IEEE, pp 318–321

  81. 81.

    Mehrabian AR, Lucas C (2006) A novel numerical optimization algorithm inspired from weed colonization. Ecol Inform 1(4):355–366

    Article  Google Scholar 

  82. 82.

    Hernández H, Blum C (2012) Distributed graph colouring: an approach based on the calling behavior of Japanese tree frogs. Swarm Intell 6(2):117–150

    Article  Google Scholar 

  83. 83.

    Yazdani M, Jolai F (2016) Lion optimization algorithm (LOA): a nature-inspired metaheuristic algorithm. J Comput Des Eng 3(1):24–36

    Google Scholar 

  84. 84.

    Abbass HA (2001) MBO: marriage in honey bees optimization—a haplometrosis polygynous swarming approach. In: Proceedings of the 2001 congress on evolutionary computation, vol 1. IEEE, pp 207–214

  85. 85.

    Asil Gharebaghi S, ArdalanAsl M (2017) New meta-heuristic optimization algorithm using neuronal communication. Iran Univ Sci Technol 7(3):413–431

    Google Scholar 

  86. 86.

    Maia RD, de Castro LN, Caminhas WM (2012) Bee colonies as model for multimodal continuous optimization: the OptBees algorithm. In: 2012 IEEE congress on evolutionary computation (CEC). IEEE, pp 1–8

  87. 87.

    Premaratne U, Samarabandu J, Sidhu T (2009) A new biologically inspired optimization algorithm. In: 2009 international conference on industrial and information systems (ICIIS). IEEE, pp 279–284

  88. 88.

    Jung SH (2003) Queen-bee evolution for genetic algorithms. Electron Lett 39(6):575–576

    Article  Google Scholar 

  89. 89.

    Havens TC, Spain CJ, Salmon NG, Keller JM (2008) Roach infestation optimization. In: Swarm intelligence symposium, 2008, SIS 2008. IEEE, pp 1–7

  90. 90.

    Eusuff MM, Lansey KE (2003) Optimization of water distribution network design using the shuffled frog leaping algorithm. J Water Resour Plan Manag 129(3):210–225

    Article  Google Scholar 

  91. 91.

    Ebrahimi A, Khamehchi E (2016) Sperm whale algorithm: an effective metaheuristic algorithm for production optimization problems. J Nat Gas Sci Eng 29:211–222

    Article  Google Scholar 

  92. 92.

    Dhiman G, Kumar V (2017) Spotted hyena optimizer: a novel bio-inspired based metaheuristic technique for engineering applications. Adv Eng Softw 114:48–70

    Article  Google Scholar 

  93. 93.

    Pattnaik SS, Bakwad KM, Sohi BS, Ratho RK, Devi S (2013) Swine influenza models based optimization (SIMBO). Appl Soft Comput 13(1):628–653

    Article  Google Scholar 

  94. 94.

    Cheng MY, Prayogo D (2014) Symbiotic organisms search: a new metaheuristic optimization algorithm. Comput Struct 139:98–112

    Article  Google Scholar 

  95. 95.

    Hedayatzadeh R, Salmassi FA, Keshtgari M, Akbari R, Ziarati K (2010) Termite colony optimization: a novel approach for optimizing continuous problems. In: 2010 18th Iranian conference on electrical engineering (ICEE). IEEE, pp 553–558

  96. 96.

    Jaderyan M, Khotanlou H (2016) Virulence optimization algorithm. Appl Soft Comput 43:596–618

    Article  Google Scholar 

  97. 97.

    Li MD, Zhao H, Weng XW, Han T (2016) A novel nature-inspired algorithm for optimization: virus colony search. Adv Eng Softw 92:65–68

    Article  Google Scholar 

  98. 98.

    Pelikan M (2005) Hierarchical Bayesian optimization algorithm. In: Hierarchical Bayesian optimization algorithm. Springer, Berlin, pp 105–129

    Google Scholar 

  99. 99.

    Zandi Z, Afjei E, Sedighizadeh M (2012) Reactive power dispatch using big bang-big crunch optimization algorithm for voltage stability enhancement. In: 2012 IEEE international conference on power and energy (PECon). IEEE, pp 239–244

  100. 100.

    Hatamlou A (2013) Black hole: a new heuristic optimization approach for data clustering. Inf Sci 222:175–184

    MathSciNet  Article  Google Scholar 

  101. 101.

    Formato RA (2007) Central force optimization: a new metaheuristic with applications in applied electromagnetics. Prog Electromagn Res 77:425–491

    Article  Google Scholar 

  102. 102.

    Kaveh A, Talatahari S (2010) A novel heuristic optimization method: charged system search. Acta Mech 213(3–4): 267–289

    MATH  Article  Google Scholar 

  103. 103.

    Salmani MH, Eshghi K (2017) A metaheuristic algorithm based on chemotherapy science: CSA. J Optim 2017:1–13

    MathSciNet  MATH  Google Scholar 

  104. 104.

    Kaveh A, Mahdavi VR (2014) Colliding bodies optimization: a novel meta-heuristic method. Comput Struct 139:18–27

    Article  Google Scholar 

  105. 105.

    Cuevas E, Oliva D, Zaldivar D, Pérez-Cisneros M, Sossa H (2012) Circle detection using electro-magnetism optimization. Inf Sci 182(1):40–55

    MathSciNet  Article  Google Scholar 

  106. 106.

    Kaedi M (2017) Fractal-based algorithm: a new metaheuristic method for continuous optimization. Int J Artif Intell 15(1):76–92

    Google Scholar 

  107. 107.

    Shah-Hosseini H (2011) Principal components analysis by the galaxy-based search algorithm: a novel metaheuristic for continuous optimisation. Int J Comput Sci Eng 6(1–2):132–140

    Google Scholar 

  108. 108.

    Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248

    MATH  Article  Google Scholar 

  109. 109.

    Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68

    Article  Google Scholar 

  110. 110.

    Wedyan A, Whalley J, Narayanan A (2017) Hydrological cycle algorithm for continuous optimization problems. J Optim 2017:1–25

    MathSciNet  MATH  Google Scholar 

  111. 111.

    Hosseini HS (2007) Problem solving by intelligent water drops. In: IEEE congress on evolutionary computation, 2007, CEC 2007. IEEE, pp 3226–3231

  112. 112.

    Javidy B, Hatamlou A, Mirjalili S (2015) Ions motion algorithm for solving optimization problems. Appl Soft Comput 32:72–79

    Article  Google Scholar 

  113. 113.

    https://en.wikiversity.org/wiki/Algorithms/Mass_and_Energy_Balances_Algorithm

  114. 114.

    Kashan AH (2015) A new metaheuristic for optimization: optics inspired optimization (OIO). Comput Oper Res 55:99–125

    MathSciNet  MATH  Article  Google Scholar 

  115. 115.

    Biyanto TR, Syamsi MN, Fibrianto HY, Afdanny N, Rahman AH, Gunawan KS, Pratama JAD, Malwindasari A, Abdillah AI, Bethiana TN, Putra YA (2017) Optimization of energy efficiency and conservation in green building design using duelist, Killer-Whale and Rain-Water Algorithms. In: IOP conference series: materials science and engineering, vol 267, No. 1, p 012036. IOP Publishing

    Article  Google Scholar 

  116. 116.

    Kaboli SHA, Selvaraj J, Rahim NA (2017) Rain-fall optimization algorithm: a population based algorithm for solving constrained optimization problems. J Comput Sci 19:31–42

    Article  Google Scholar 

  117. 117.

    Rabanal P, Rodríguez I, Rubio F (2007) Using river formation dynamics to design heuristic algorithms. In: Unconventional computation, pp 163–177

  118. 118.

    Vicsek T, Czirók A, Ben-Jacob E, Cohen I, Shochet O (1995) Novel type of phase transition in a system of self-driven particles. Phys Rev Lett 75(6):1226

    MathSciNet  Article  Google Scholar 

  119. 119.

    Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680

    MathSciNet  MATH  Article  Google Scholar 

  120. 120.

    Ibrahim A, Rahnamayan S, Martin MV (2014) Simulated raindrop algorithm for global optimization. In: 2014 IEEE 27th Canadian conference on electrical and computer engineering (CCECE). IEEE, pp 1–8

  121. 121.

    Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowledge-Based Syst 96:120–133

    Article  Google Scholar 

  122. 122.

    Tzanetos A, Dounias G (2017) A new metaheuristic method for optimization: sonar inspired optimization. In: Boracchi G, Iliadis L, Jayne C, Likas A (eds) Engineering applications of neural networks. EANN 2017 communications in computer and information science, vol 744. Springer, Cham

    Google Scholar 

  123. 123.

    Tamura K, Yasuda K (2011) Spiral dynamics inspired optimization. J Adv Comput Intell Intell Inform 15(8):1116–1122

    Article  Google Scholar 

  124. 124.

    Bishop JM (1989) Stochastic searching networks. In: First IEE international conference on artificial neural networks (Conf. Publ. No. 313). IET, pp 329–331

  125. 125.

    Kaveh A, Dadras A (2017) A novel meta-heuristic optimization algorithm: thermal exchange optimization. Adv Eng Softw 110:69–84

    Article  Google Scholar 

  126. 126.

    Doğan B, Ölmez T (2015) A new metaheuristic for numerical function optimization: vortex search algorithm. Inf Sci 293:125–145

    Article  Google Scholar 

  127. 127.

    Eskandar H, Sadollah A, Bahreininejad A, Hamdi M (2012) Water cycle algorithm—a novel metaheuristic optimization method for solving constrained engineering optimization problems. Comput Struct 110:151–166

    Article  Google Scholar 

  128. 128.

    Zheng YJ (2015) Water wave optimization: a new nature-inspired metaheuristic. Comput Oper Res 55:1–11

    MathSciNet  MATH  Article  Google Scholar 

  129. 129.

    Friedl G, Kuczmann M (2015) A new metaheuristic optimization algorithm, the weighted attraction method. Acta Technica Jaurinensis 8(3):257–266

    Article  Google Scholar 

  130. 130.

    Hasançebi O, Azad SK (2015) Adaptive dimensional search: a new metaheuristic algorithm for discrete truss sizing optimization. Comput Struct 154:1–16

    Article  Google Scholar 

  131. 131.

    Shayeghi H, Dadashpour J (2012) Anarchic society optimization based PID control of an automatic voltage regulator (AVR) system. Electr Electron Eng 2(4):199–207

    Article  Google Scholar 

  132. 132.

    Civicioglu P (2013) Artificial cooperative search algorithm for numerical optimization problems. Inf Sci 229:58–76

    MATH  Article  Google Scholar 

  133. 133.

    Civicioglu P (2013) Backtracking search optimization algorithm for numerical optimization problems. Appl Math Comput 219(15):8121–8144

    MathSciNet  MATH  Google Scholar 

  134. 134.

    Kim JH, Choi YH, Ngo TT, Choi J, Lee HM, Choo YM, Lee EH, Yoo DG, Sadollah A, Jung D (2016) KU battle of metaheuristic optimization algorithms 1: development of six new/improved algorithms. In: Kim J, Geem Z (eds) Harmony search algorithm. Advances in intelligent systems and computing, vol 382. Springer, Berlin

    Google Scholar 

  135. 135.

    Civicioglu P (2012) Transforming geocentric cartesian coordinates to geodetic coordinates by using differential search algorithm. Comput Geosci 46:229–247

    Article  Google Scholar 

  136. 136.

    Azad SK, Hasançebi O (2014) An elitist self-adaptive step-size search for structural design optimization. Appl Soft Comput 19:226–235

    Article  Google Scholar 

  137. 137.

    Fadakar E, Ebrahimi M (2016) A new metaheuristic football game inspired algorithm. In: 2016 1st conference on swarm intelligence and evolutionary computation (CSIEC). IEEE, pp 6–11

  138. 138.

    Ryan C, Collins JJ, Neill MO (1998) Grammatical evolution: evolving programs for an arbitrary language. In: European conference on genetic programming. Springer, Berlin, pp 83–96

    Google Scholar 

  139. 139.

    Azad SK, Hasançebi O, Saka MP (2014) Guided stochastic search technique for discrete sizing optimization of steel trusses: a design-driven heuristic approach. Comput Struct 134:62–74

    Article  Google Scholar 

  140. 140.

    Atashpaz-Gargari E, Lucas C (2007) Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. In: IEEE congress on evolutionary computation, 2007, CEC 2007. IEEE, pp 4661–4667

  141. 141.

    Kashan AH (2009) League championship algorithm: a new algorithm for numerical function optimization. In: International conference of soft computing and pattern recognition, 2009, SOCPAR’09. IEEE, pp 43–48

  142. 142.

    Savsani P, Savsani V (2016) Passing vehicle search (PVS): a novel metaheuristic algorithm. Appl Math Modell 40(5):3951–3978

    MATH  Article  Google Scholar 

  143. 143.

    Gonçalves MS, Lopez RH, Miguel LFF (2015) Search group algorithm: a new metaheuristic method for the optimization of truss structures. Comput Struct 153:165–184

    Article  Google Scholar 

  144. 144.

    Xu Y, Cui Z, Zeng J (2010) Social emotional optimization algorithm for nonlinear constrained optimization problems. In: SEMCCO, pp 583–590

  145. 145.

    Glover F (1989) Tabu search—part I. ORSA J Comput 1(3):190–206

    MATH  Article  Google Scholar 

  146. 146.

    Glover F (1990) Tabu search—part II. ORSA J Comput 2(1):4–32

    MATH  Article  Google Scholar 

  147. 147.

    Rao RV, Savsani VJ, Vakharia DP (2012) Teaching–learning-based optimization: an optimization method for continuous non-linear large scale problems. Inf Sci 183(1):1–15

    MathSciNet  Article  Google Scholar 

  148. 148.

    Razmjooy N, Khalilpour M, Ramezani M (2016) A new meta-heuristic optimization algorithm inspired by FIFA World Cup Competitions: theory and its application in PID designing for AVR system. J Control Autom Electr Syst 27(4):419–440

    Article  Google Scholar 

  149. 149.

    Punnathanam V, Kotecha P (2016) Yin-Yang-pair optimization: a novel lightweight optimization algorithm. Eng Appl Artif Intell 54:62–79

    Article  Google Scholar 

  150. 150.

    Price KV (1999) An introduction to differential evolution. In: Corne D, Dorigo M, Glover F, Dasgupta D, Moscato P, Poli R, Price KV (eds) New ideas in optimization. McGraw-Hill Ltd, UK, pp 79–108

    Google Scholar 

  151. 151.

    Price KV, Storn RM, Lampinen JA (2005) Differential evolution a practical approach to global optimization. Springer, Berlin

    Google Scholar 

  152. 152.

    Storn R, Price K (1997) Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359

    MathSciNet  MATH  Article  Google Scholar 

  153. 153.

    Beyer HG, Schwefel HP (2002) Evolution strategies - a comprehensive introduction. Nat Comput 1(1):3–52

    MathSciNet  MATH  Article  Google Scholar 

  154. 154.

    Michalewicz Z (ed) (1996) Evolution strategies and other methods. In: Genetic algorithms + data structures = evolution programs. Springer, pp 159–177

  155. 155.

    Back T, Fogel DB, Michalewicz Z (1997) Handbook of evolutionary computation. IOP Publishing Ltd, Bristol

    Google Scholar 

  156. 156.

    Fogel DB (1993) Applying evolutionary programming to selected traveling salesman problems. Cybern Syst 24(1):27–36

    MathSciNet  Article  Google Scholar 

  157. 157.

    Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evolut Comput 3(2):82–102

    Article  Google Scholar 

  158. 158.

    Goldberg DE, Holland JH (1988) Genetic algorithms and machine learning. Mach Learn 3(2):95–99

    Article  Google Scholar 

  159. 159.

    Holland JH (1992) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control and artificial intelligence. MIT Press, Cambridge

    Google Scholar 

  160. 160.

    Koza JR (1992) Genetic programming: vol. 1, on the programming of computers by means of natural selection. MIT Press, Cambridge

    Google Scholar 

  161. 161.

    Koza JR (1994) Genetic programming as a means for programming computers by natural selection. Stat Comput 4(2):87–112

    Article  Google Scholar 

  162. 162.

    Koza JR, Bennett FH III, Stiffelman O (1999) Genetic programming as a Darwinian invention machine. Springer, Berlin

    Google Scholar 

  163. 163.

    Fister I, Yang XS, Brest J, Fister I Jr (2014) On the randomized firefly algorithm. In: Yang X-S (ed) Cuckoo search and firefly algorithm. Springer, Berlin, pp 27–48

    Google Scholar 

  164. 164.

    Črepinšek M, Liu SH, Mernik M (2013) Exploration and exploitation in evolutionary algorithms: a survey. ACM Comput Surv 45(3):35

    MATH  Article  Google Scholar 

  165. 165.

    Črepinšek M, Mernik M, Liu SH (2011) Analysis of exploration and exploitation in evolutionary algorithms by ancestry trees. Int J Innov Comput Appl 3(1):11–19

    MATH  Article  Google Scholar 

  166. 166.

    Eiben AE, Schippers CA (1998) On evolutionary exploration and exploitation. Fundam Inform 35(1–4):35–50

    MATH  Article  Google Scholar 

  167. 167.

    Walton S, Hassan O, Morgan K, Brown MR (2011) Modified cuckoo search: a new gradient free optimisation algorithm. Chaos, Solitons Fractals 44(9):710–718

    Article  Google Scholar 

  168. 168.

    Walton S, Hassan O, Morgan K, Brown MR (2013) A review of the development and applications of the Cuckoo search algorithm. In: Swarm intelligence and bio-inspired computation. Elsevier, pp 257–271

  169. 169.

    Bansal JC, Singh PK, Saraswat M, Verma A, Jadon SS, Abraham A (2011) Inertia weight strategies in particle swarm optimization. In: Third world congress on nature and biologically inspired computing, pp 640–647

  170. 170.

    Yang X, Yuan J, Yuan J, Mao H (2007) A modified particle swarm optimizer with dynamic adaptation. Appl Math Comput 189(2):1205–1213

    MathSciNet  MATH  Google Scholar 

  171. 171.

    Fister I, Yang XS, Brest J, Fister Jr I (2013) Memetic self-adaptive firefly algorithm. In: Swarm intelligence and bio-inspired computation: theory and applications, pp 73–102. https://doi.org/10.1016/b978-0-12-405163-8.00004-1

    Google Scholar 

  172. 172.

    Dhal KG, Das S (2017) Local search based dynamically adapted Bat algorithm in image enhancement domain. Int J Comput Sci Math (publication house). https://www.inderscience.com/info/ingeneral/forthcoming.php?jcode=ijcsm

  173. 173.

    Dhal KG, Das S (2017) Cuckoo search with search strategies and proper objective function for brightness preserving image enhancement. Pattern Recognit Image Anal 27(4):695–712

    Article  Google Scholar 

  174. 174.

    Khan W (2013) Image segmentation techniques: a survey. J Image Graph 1(4):166–170

    Google Scholar 

  175. 175.

    Bhandarkar SM, Zhang H (1999) Image segmentation using evolutionary computation. IEEE Trans Evolut Comput 3:1–21

    Article  Google Scholar 

  176. 176.

    Zhang J, Zhan ZH, Lin Y, Chen N, Gong YJ, Zhong JH, Shi YH (2011) Evolutionary computation meets machine learning: a survey. IEEE Comput Intell Mag 6(4):68–75

    Article  Google Scholar 

  177. 177.

    Riseman EM, Arbib MA (1977) Survey: computational techniques in the visual segmentation of static scenes. Comput Vis Graph Image Process 6:221–276

    Article  Google Scholar 

  178. 178.

    Weszka JS (1978) A survey of threshold selection techniques. CGIP 7(2):259–265

    Google Scholar 

  179. 179.

    Fu KS, Mui JK (1981) A survey on image segmentation. Pattern Recogn 13:3–16

    MathSciNet  Article  Google Scholar 

  180. 180.

    Haralharick RM, Shapiro LG (1985) Survey: image segmentation techniques. CVGIP 29:100–132

    Google Scholar 

  181. 181.

    Borisenko VI, Zlatotol AA, Muchnik IB (1987) Image segmentation (state of the art survey). Automat Remote Control 48:837–879

    MATH  Google Scholar 

  182. 182.

    Sahoo PK, Soltani S, Wong AKC, Chen YC (1988) A survey of thresholding techniques. CVGIP 41:233–260

    Google Scholar 

  183. 183.

    Pal NR, Pal SK (1993) A review on image segmentation. Pattern Recognit 26(9):1277–1294

    Article  Google Scholar 

  184. 184.

    Sarkar S, Das S, Chaudhuri SS (2017) Multi-level thresholding with a decomposition-based multi-objective evolutionary algorithm for segmenting natural and medical images. Appl Soft Comput 50:142–157

    Article  Google Scholar 

  185. 185.

    Tuba M (2014) Multilevel image thresholding by nature-inspired algorithms: a short review. Comput Sci J Moldova 22(3):318–338

    MathSciNet  Google Scholar 

  186. 186.

    El Joumani S, Mechkouri SE, Zennouhi R, El Kadmiri O, Masmoudi L (2017) Segmentation method based on multiobjective optimization for very high spatial resolution satellite images. EURASIP J Image Video Process 2017(1):26

    Article  Google Scholar 

  187. 187.

    Zhang J, Li H, Tang Z, Lu Q, Zheng X, Zhou J (2014) An improved quantum-inspired genetic algorithm for image multilevel thresholding segmentation. Math Probl Eng 2014:1–12

    Google Scholar 

  188. 188.

    Mala C, Sridevi M (2016) Multilevel threshold selection for image segmentation using soft computing techniques. Soft Comput 20(5):1793–1810

    Article  Google Scholar 

  189. 189.

    Pare S, Kumar A, Bajaj V, Singh GK (2016) A multilevel color image segmentation technique based on cuckoo search algorithm and energy curve. Appl Soft Comput 47:76–102

    Article  Google Scholar 

  190. 190.

    Hamdaoui F, Sakly A, Mtibaa A (2015) An efficient multilevel thresholding method for image segmentation based on the hybridization of modified PSO and Otsu’s method. In: Azar AT, Vaidyanathan S (eds) Computational intelligence applications in modeling and control. Springer, pp 343–367

  191. 191.

    Liu Y, Mu C, Kou W, Liu J (2015) Modified particle swarm optimization-based multilevel thresholding for image segmentation. Soft Comput 19(5):1311–1327

    Article  Google Scholar 

  192. 192.

    Ghamisi P, Couceiro MS, Benediktsson JA, Ferreira NM (2012) An efficient method for segmentation of images based on fractional calculus and natural selection. Expert Syst Appl 39(16):12407–12417

    Article  Google Scholar 

  193. 193.

    Ghamisi P, Couceiro MS, Martins FM, Benediktsson JA (2013) Multilevel image segmentation based on fractional-order Darwinian particle swarm optimization. IEEE Trans Geosci Remote Sens 52(5):2382–2394

    Article  Google Scholar 

  194. 194.

    Dey S, Bhattacharyya S, Maulik U (2016) New quantum inspired meta-heuristic techniques for multi-level colour image thresholding. Appl Soft Comput 46:677–702

    Article  Google Scholar 

  195. 195.

    Ayala HVH, dos Santos FM, Mariani VC, dos Santos Coelho L (2015) Image thresholding segmentation based on a novel beta differential evolution approach. Expert Syst Appl 42(4):2136–2142

    Article  Google Scholar 

  196. 196.

    Bakhshali MA, Shamsi M (2014) Segmentation of color lip images by optimal thresholding using bacterial foraging optimization (BFO). J Comput Sci 5(2):251–257

    Article  Google Scholar 

  197. 197.

    Fan C, Ouyang H, Zhang Y, Xiao L (2014) Optimal multilevel thresholding using molecular kinetic theory optimization algorithm. Appl Math Comput 239:391–408

    MathSciNet  MATH  Google Scholar 

  198. 198.

    Hussein WA, Sahran S, Abdullah SNHS (2016) A fast scheme for multilevel thresholding based on a modified bees algorithm. Knowledge-Based Syst 101:114–134

    Article  Google Scholar 

  199. 199.

    Kumar S, Kumar P, Sharma TK, Pant M (2013) Bi-level thresholding using PSO, artificial bee colony and MRLDE embedded with Otsu method. Memet Comput 5(4):323–334

    Article  Google Scholar 

  200. 200.

    Horng MH (2010) A multilevel image thresholding using the honey bee mating optimization. Appl Math Comput 215(9):3302–3310

    MathSciNet  MATH  Google Scholar 

  201. 201.

    Ouadfel S, Taleb-Ahmed A (2016) Social spiders optimization and flower pollination algorithm for multilevel image thresholding: a performance study. Expert Syst Appl 55:566–584

    Article  Google Scholar 

  202. 202.

    Sathya PD, Kayalvizhi R (2011) Optimal multilevel thresholding using bacterial foraging algorithm. Expert Syst Appl 38(12):15549–15564

    Article  Google Scholar 

  203. 203.

    Sathya PD, Kayalvizhi R (2011) Modified bacterial foraging algorithm based multilevel thresholding for image segmentation. Eng Appl Artif Intell 24:595–615

    Article  Google Scholar 

  204. 204.

    Sun G, Zhang A, Yao Y, Wang Z (2016) A novel hybrid algorithm of gravitational search algorithm with genetic algorithm for multi-level thresholding. Appl Soft Comput 46:703–730

    Article  Google Scholar 

  205. 205.

    Brajevic I, Tuba M (2014) Cuckoo search and firefly algorithm applied to multilevel image thresholding. In: Yang X-S (ed) Cuckoo search and firefly algorithm. Springer, Cham, pp 115–139

    Google Scholar 

  206. 206.

    Marciniak A, Kowal M, Filipczuk P, Korbicz J (2014) Swarm intelligence algorithms for multi-level image thresholding. In: Korbicz J, Kowal M (eds) Intelligent systems in technical and medical diagnostics. Advances in intelligent systems and computing, vol 230. Springer, Berlin

    Google Scholar 

  207. 207.

    Ouadfel S, Meshoul S (2014) Bio-inspired algorithms for multilevel image thresholding. Int J Comput Appl Technol 49(3–4):207–226

    Article  Google Scholar 

  208. 208.

    Tuba M, Bacanin N, Alihodzic A (2015) Multilevel image thresholding by fireworks algorithm. In: 2015 25th international conference on radioelektronika (RADIOELEKTRONIKA). IEEE, pp 326–330

  209. 209.

    Ye ZW, Wang MW, Liu W, Chen SB (2015) Fuzzy entropy based optimal thresholding using bat algorithm. Appl Soft Comput 31:381–395

    Article  Google Scholar 

  210. 210.

    Li JY, Zhao YD, Li JH, Liu XJ (2015) Artificial bee colony optimizer with bee-to-bee communication and multipopulation coevolution for multilevel threshold image segmentation. Math Probl Eng 2015:1–23

    MATH  Google Scholar 

  211. 211.

    Jiang Y, Tsai P, Hao Z, Cao L (2015) Automatic multilevel thresholding for image segmentation using stratified sampling and Tabu search. Soft Comput 19(9):2605–2617

    Article  Google Scholar 

  212. 212.

    Ma M, Liang J, Guo M, Fan Y, Yin Y (2011) SAR image segmentation based on artificial bee colony algorithm. Appl Soft Comput 11(8):5205–5214

    Article  Google Scholar 

  213. 213.

    Bhandari AK, Kumar A, Singh GK (2015) Modified artificial bee colony based computationally efficient multilevel thresholding for satellite image segmentation using Kapur’s, Otsu and Tsallis functions. Expert Syst Appl 42(3):1573–1601

    Article  Google Scholar 

  214. 214.

    Kurban T, Civicioglu P, Kurban R, Besdok E (2014) Comparison of evolutionary and swarm based computational techniques for multilevel color image thresholding. Appl Soft Comput 23:128–143

    Article  Google Scholar 

  215. 215.

    Sarkar S, Paul S, Burman R, Das S, Chaudhuri SS (2014) A fuzzy entropy based multi-level image thresholding using differential evolution. In: International conference on swarm, evolutionary, and memetic computing. Springer International Publishing, pp 386–395

  216. 216.

    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

    Article  Google Scholar 

  217. 217.

    Yang AY, Wright J, Ma Y, Sastry SS (2008) Unsupervised segmentation of naturalimages via lossy data compression. Comput Vis Image Underst 110(2):212–225

    Article  Google Scholar 

  218. 218.

    Comaniciu D, Meer P (2002) Mean shift: a robust approach toward feature space analysis. IEEE Trans Pattern Anal Mach Intell 24(5):603–619

    Article  Google Scholar 

  219. 219.

    Shi J, Malik J (2000) Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intell 22(8):888–905

    Article  Google Scholar 

  220. 220.

    Felzenszwalb PF, Huttenlocher DP (2004) Efficient graph-based image segmentation. Int J Comput Vis 59(2):167–181

    Article  Google Scholar 

  221. 221.

    Bhandari AK, Kumar A, Singh GK (2015) Tsallis entropy based multilevel thresholding for colored satellite image segmentation using evolutionary algorithms. Expert Syst Appl 42(22):8707–8730

    Article  Google Scholar 

  222. 222.

    Sarkar S, Das S, Chaudhuri SS (2016) Hyper-spectral image segmentation using Rényi entropy based multi-level thresholding aided with differential evolution. Expert Syst Appl 50:120–129

    Article  Google Scholar 

  223. 223.

    Sarkar S, Das S, Paul S, Polley S, Burman R, Chaudhuri SS (2013) Multi-level image segmentation based on fuzzy-Tsallis entropy and differential evolution. In: 2013 IEEE international conference on fuzzy systems (FUZZ). IEEE, pp 1–8

  224. 224.

    Sarkar S, Das S (2013) Multilevel image thresholding based on 2D histogram and maximum Tsallis entropy—a differential evolution approach. IEEE Trans Image Process 22(12):4788–4797

    MathSciNet  MATH  Article  Google Scholar 

  225. 225.

    Cuevas E, Zaldivar D, Pérez-Cisneros M (2010) A novel multi-threshold segmentation approach based on differential evolution optimization. Expert Syst Appl 37(7):5265–5271

    Article  Google Scholar 

  226. 226.

    Peng H, Wang J, Pérez-Jiménez MJ (2015) Optimal multi-level thresholding with membrane computing. Digit Signal Process 37:53–64

    Article  Google Scholar 

  227. 227.

    Raja N, Rajinikanth V, Latha K (2014) Otsu based optimal multilevel image thresholding using firefly algorithm. Model Simul Eng 2014:37

    Google Scholar 

  228. 228.

    Hamdaoui F, Sakly A, Mtibaa A (2015) An efficient multi level thresholding method for image segmentation based on the hybridization of modified PSO and Otsu’s method. In: Azar AT, Vaidyanathan S (eds) Computational intelligence applications in modeling and control. Springer, Berlin, pp 343–367

    Google Scholar 

  229. 229.

    Oliva D, Cuevas E, Pajares G, Zaldivar D, Perez-Cisneros M (2013) Multilevel thresholding segmentation based on harmony search optimization. J Appl Math 2013:1–24

    MathSciNet  Article  Google Scholar 

  230. 230.

    Oliva D, Cuevas E, Pajares G, Zaldivar D, Osuna V (2014) A multilevel thresholding algorithm using electromagnetism optimization. Neurocomputing 139:357–381

    Article  Google Scholar 

  231. 231.

    Agarwal P, Singh R, Kumar S, Bhattacharya M (2016) Social spider algorithm employed multi-level thresholding segmentation approach. In: Proceedings of first international conference on information and communication technology for intelligent systems, vol 2. Springer, Berlin, pp 249–259

    Google Scholar 

  232. 232.

    Ludwig SA (2016) Improved glowworm swarm optimization algorithm applied to multi-level thresholding. In: 2016 IEEE congress on evolutionary computation (CEC). IEEE, pp 1533–1540

  233. 233.

    Alihodzic A, Tuba M (2014) Improved bat algorithm applied to multilevel image thresholding. Sci World J 2014:1–26

    Article  Google Scholar 

  234. 234.

    Satapathy SC, Raja NSM, Rajinikanth V, Ashour AS, Dey N (2016) Multi-level image thresholding using Otsu and chaotic bat algorithm. Neural Comput Appl 29:1–23

    Google Scholar 

  235. 235.

    Naidu MSR, Kumar PR (2017) Multilevel image thresholding for image segmentation by optimizing fuzzy entropy using firefly algorithm. Int J Eng Technol 9(2):472–488

    Article  Google Scholar 

  236. 236.

    Naidu MSR, Kumar PR, Chiranjeevi K (2017) Shannon and fuzzy entropy based evolutionary image thresholding for image segmentation. Alex Eng J 57:1643–1655

    Article  Google Scholar 

  237. 237.

    Mousavirad SJ, Ebrahimpour-Komleh H (2017) Multilevel image thresholding using entropy of histogram and recently developed population-based metaheuristic algorithms. Evolut Intell 10(1–2):45–75

    Article  Google Scholar 

  238. 238.

    Li L, Sun L, Guo J, Qi J, Xu B, Li S (2017) Modified discrete grey wolf optimizer algorithm for multilevel image thresholding. Comput Intell Neurosci 2017:1–16

    Google Scholar 

  239. 239.

    El Aziz MA, Ewees AA, Hassanien AE (2017) Whale optimization algorithm and moth-flame optimization for multilevel thresholding image segmentation. Expert Syst Appl 83:242–256

    Article  Google Scholar 

  240. 240.

    Dhal KGG, Sen M, Das S (2018) Multi-thresholding of histopathological images using fuzzy entropy and parameterless cuckoo search. In: Shi Y (ed) Critical developments and applications of swarm intelligence. IGI Global, pp 339–356

  241. 241.

    Pare S, Bhandari AK, Kumar A, Singh GK (2017) An optimal color image multilevel thresholding technique using grey-level co-occurrence matrix. Expert Syst Appl 87:335–362

    Article  Google Scholar 

  242. 242.

    Mlakar U, Potočnik B, Brest J (2016) A hybrid differential evolution for optimal multilevel image thresholding. Expert Syst Appl 65:221–232

    Article  Google Scholar 

  243. 243.

    Rajinikanth V, Raja NSM, Satapathy SC (2016) Robust color image multi-thresholding using between-class variance and cuckoo search algorithm. In: Satapathy S, Mandal J, Udgata S, Bhateja V (eds) Information systems design and intelligent applications. Advances in intelligent systems and computing, vol 433. Springer, New Delhi, pp 379–386

    Google Scholar 

  244. 244.

    Pal SS, Kumar S, Kashyap M, Choudhary Y, Bhattacharya M (2016) Multi-level thresholding segmentation approach based on spider monkey optimization algorithm. In: Proceedings of the second international conference on computer and communication technologies. Springer, New Delhi, pp 273–287

    Google Scholar 

  245. 245.

    Chen K, Zhou Y, Zhang Z, Dai M, Chao Y, Shi J (2016) Multilevel image segmentation based on an improved firefly algorithm. Math Probl Eng 2016:1–12

    Google Scholar 

  246. 246.

    Gao H, Pun CM, Kwong S (2016) An efficient image segmentation method based on a hybrid particle swarm algorithm with learning strategy. Inf Sci 369:500–521

    MathSciNet  Article  Google Scholar 

  247. 247.

    Ye Z, Yin H, Ye Y (2018) Comparative analysis of two leading evolutionary intelligence approaches for multilevel thresholding. Int J Signal Imaging Syst Eng 11(1):20–30

    Article  Google Scholar 

  248. 248.

    He L, Huang S (2016) Improved glowworm swarm optimization algorithm for multilevel color image thresholding problem. Math Probl Eng 2016:1–24

    Google Scholar 

  249. 249.

    Li L, Sun L, Kang W, Guo J, Han C, Li S (2016) Fuzzy multilevel image thresholding based on modified discrete grey wolf optimizer and local information aggregation. IEEE Access 4:6438–6450

    Article  Google Scholar 

  250. 250.

    Chao Y, Dai M, Chen K, Chen P, Zhang Z (2016) Fuzzy entropy based multilevel image thresholding using modified gravitational search algorithm. In: 2016 IEEE international conference on industrial technology (ICIT). IEEE, pp 752–757

  251. 251.

    Singh VP, Prakash T, Rathore NS, Singh Chauhan DP, Singh SP (2016) Multilevel thresholding with membrane computing inspired TLBO. Int J Artif Intell Tools 25(06):1650030

    Article  Google Scholar 

  252. 252.

    Kotte S, Kumar PR, Injeti SK (2016) An efficient approach for optimal multilevel thresholding selection for gray scale images based on improved differential search algorithm. Ain Shams Eng J 9:1043–1067

    Article  Google Scholar 

  253. 253.

    Pan J, Zheng XW, Sun L, Yang LN, Wang YL, Luo HW, Wang PSP (2016) Image segmentation based on 2D OTSU and simplified swarm optimization. In: 2016 international conference on machine learning and cybernetics (ICMLC), vol 2. IEEE, pp 1026–1030

  254. 254.

    Cao LL, Ding S, Fu XW, Chen L (2016) Otsu multilevel thresholding segmentation based on quantum particle swarm optimisation algorithm. Int J Wirel Mobile Comput 10(3):272–277

    Article  Google Scholar 

  255. 255.

    Fan CD, Ren K, Zhang YJ, Yi LZ (2016) Optimal multilevel thresholding based on molecular kinetic theory optimization algorithm and line intercept histogram. J Cent South Univ 23(4):880–890

    Article  Google Scholar 

  256. 256.

    Ouadfel S, Taleb-Ahmed A (2016) Performance study of harmony search algorithm for multilevel thresholding. J Intell Syst 25(4):473–513

    Google Scholar 

  257. 257.

    He L, Huang S (2017) Modified firefly algorithm based multilevel thresholding for color image segmentation. Neurocomputing 240:152–174

    Article  Google Scholar 

  258. 258.

    Khairuzzaman AKM, Chaudhury S (2017) Multilevel thresholding using grey wolf optimizer for image segmentation. Expert Syst Appl 86:64–76

    Article  Google Scholar 

  259. 259.

    Tang K, Xiao X, Wu J, Yang J, Luo L (2017) An improved multilevel thresholding approach based modified bacterial foraging optimization. Appl Intell 46(1):214–226

    Article  Google Scholar 

  260. 260.

    Pare S, Kumar A, Bajaj V, Singh GK (2017) An efficient method for multilevel color image thresholding using cuckoo search algorithm based on minimum cross entropy. Appl Soft Comput 61:570–592

    Article  Google Scholar 

  261. 261.

    Tuba E, Alihodzic A, Tuba M (2017) Multilevel image thresholding using elephant herding optimization algorithm. In: 2017 14th international conference on engineering of modern electric systems (EMES). IEEE, pp 240–243

  262. 262.

    Ishak AB (2017) A two-dimensional multilevel thresholding method for image segmentation. Appl Soft Comput 52:306–322

    Article  Google Scholar 

  263. 263.

    Abdel-Khalek S, Ishak AB, Omer OA, Obada AS (2017) A two-dimensional image segmentation method based on genetic algorithm and entropy. Optik Int J Light Electron Opt 131:414–422

    Article  Google Scholar 

  264. 264.

    Oliva D, Hinojosa S, Elaziz MA, Ortega-Sánchez N (2018) Context based image segmentation using antlion optimization and sine cosine algorithm. Multimed Tools Appl 77:1–37

    Article  Google Scholar 

  265. 265.

    Maurya L, Sharma E, Mahapatra P, Doegar A (2018) A hybrid of fireworks and harmony search algorithm for multilevel image thresholding. In: Choudhary RK, Mandal JK, Bhattacharyya D (eds) Advanced computing and communication technologies. Springer, Singapore, pp 11–21

    Google Scholar 

  266. 266.

    Zhou Y, Yang X, Ling Y, Zhang J (2018) Meta-heuristic moth swarm algorithm for multilevel thresholding image segmentation. Multimed Tools Appl 77(18):23699–23727

    Article  Google Scholar 

  267. 267.

    Gao Y, Li X, Dong M, Li HP (2018) An enhanced artificial bee colony optimizer and its application to multi-level threshold image segmentation. J Cent South Univ 25(1):107–120

    Article  Google Scholar 

  268. 268.

    Dhar S, Kundu MK (2018) A novel method for image thresholding using interval type-2 fuzzy set and bat algorithm. Appl Soft Comput 63:154–166

    Article  Google Scholar 

  269. 269.

    Hinojosa S, Pajares G, Cuevas E, Ortega-Sanchez N (2018) Thermal image segmentation using evolutionary computation techniques. In: Hassanien AE, Oliva DA (eds) Advances in soft computing and machine learning in image processing. Studies in Computational Intelligence, vol 730. Springer, Cham, pp 63–88

    Google Scholar 

  270. 270.

    Mittal H, Saraswat M (2018) An optimum multi-level image thresholding segmentation using non-local means 2D histogram and exponential Kbest gravitational search algorithm. Eng Appl Artif Intell 71:226–235

    Article  Google Scholar 

  271. 271.

    Bohat VK, Arya KV (2018) A new heuristic for multilevel thresholding of images. Expert Syst Appl 117:176-203

    Article  Google Scholar 

  272. 272.

    Resma KB, Nair MS (2018) Multilevel thresholding for image segmentation using Krill Herd Optimization algorithm. J King Saud Univ Comput Inf Sci. https://doi.org/10.1016/j.jksuci.2018.04.007

    Article  Google Scholar 

  273. 273.

    Merzban MH, Elbayoumi M (2018) Efficient solution of Otsu multilevel image thresholding: a comparative study. Expert Syst Appl 116:299–309

    Article  Google Scholar 

  274. 274.

    Pare S, Bhandari AK, Kumar A, Singh GK (2018) Rényi’s entropy and bat algorithm based color image multilevel thresholding. In: Tanveer M, Pachori RB (eds) Machine intelligence and signal analysis. Springer, Singapore, pp 71–84

    Google Scholar 

  275. 275.

    Agrawal S, Panda R, Abraham A (2018) A novel diagonal class entropy-based multilevel image thresholding using coral reef optimization. IEEE Trans Syst Man Cybern Syst 99:1–9

    Google Scholar 

  276. 276.

    Pare S, Bhandari AK, Kumar A, Bajaj V (2018) Backtracking search algorithm for color image multilevel thresholding. Signal Image Video Process 12(2):385–392

    Article  Google Scholar 

  277. 277.

    Zhang S, Jiang W, Satoh SI (2018) Multilevel thresholding color image segmentation using a modified artificial bee colony algorithm. IEICE Trans Inf Syst 101(8):2064–2071

    Article  Google Scholar 

  278. 278.

    Li J, Tang W, Wang J, Zhang X (2018) Multilevel thresholding selection based on variational mode decomposition for image segmentation. Signal Process 147:80–91

    Article  Google Scholar 

  279. 279.

    Bouteldja MA, Baadeche M, Batouche M (2018) Multilevel thresholding for image segmentation based on cellular metaheuristics. Int J Appl Metaheur Comput 9(4):1–32

    Article  Google Scholar 

  280. 280.

    Hinojosa S, Oliva D, Cuevas E, Pérez-Cisneros M, Pájares G (2018) Real-time video thresholding using evolutionary techniques and cross entropy. In: 2018 IEEE conference on evolving and adaptive intelligent systems (EAIS). IEEE, pp 1–8

  281. 281.

    Yimit A, Hagihara Y (2018) 2D direction histogram-based Rényi entropic multilevel thresholding. J Adv Comput Intell Intell Inform 22(3):369–379

    Article  Google Scholar 

  282. 282.

    Deuri J, Sathya SS (2018) Multilevel thresholding for image segmentation using cricket chirping algorithm. In: Acharjya DP, Santhi V (eds) Bio-inspired computing for image and video processing. Chapman and Hall/CRC, pp 31–58

  283. 283.

    Chakraborty R, Sushil R, Garg ML (2018) An improved PSO-based multilevel image segmentation technique using minimum cross-entropy thresholding. Arab J Sci Eng. https://doi.org/10.1007/s13369-018-3400-2

    Article  Google Scholar 

  284. 284.

    Suresh K, Sakthi U (2018) Robust multi-thresholding in noisy grayscale images using Otsu’s function and harmony search optimization algorithm. In: Kalam A, Das S, Sharma K (eds) Advances in electronics, communication and computing. Springer, Singapore, pp 491–499

    Google Scholar 

  285. 285.

    Shen L, Fan C, Huang X (2018) Multi-level Image thresholding using modified flower pollination algorithm. IEEE Access 6:30508–30519

    Article  Google Scholar 

  286. 286.

    Santos ACS, Pedrini H (2018) Image thresholding based on fuzzy particle swarm optimization. In: Bhattacharyya S (ed) Hybrid metaheuristics for image analysis. Springer, Cham, pp 187–207

    Google Scholar 

  287. 287.

    Mishra S, Panda M (2018) Bat algorithm for multilevel colour image segmentation using entropy-based thresholding. Arab J Sci Eng 43:1–30

    Article  Google Scholar 

  288. 288.

    Akay B (2013) A study on particle swarm optimization and artificial bee colony algorithms for multilevel thresholding. Appl Soft Comput 13(6):3066–3091

    Article  Google Scholar 

  289. 289.

    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(7):3538–3560

    Article  Google Scholar 

  290. 290.

    Sezgin M, Sankur B (2004) Survey over image thresholding techniques and quantitative performance evaluation. J Electron Imaging 13(1):146–165

    Article  Google Scholar 

  291. 291.

    Rodrigues PS, Wachs-Lopes GA, Erdmann HR, Ribeiro MP, Giraldi GA (2017) Improving a firefly meta-heuristic for multilevel image segmentation using Tsallis entropy. Pattern Analysis and Applications 20(1):1–20

    MathSciNet  MATH  Article  Google Scholar 

  292. 292.

    Suresh S, Lal S (2017) Multilevel thresholding based on Chaotic Darwinian Particle Swarm Optimization for segmentation of satellite images. Appl Soft Comput 55:503–522

    Article  Google Scholar 

  293. 293.

    Luca AD, Termini S (1972) Definition of a non probabilistic entropy in the setting of fuzzy sets theory. Inf Control 20:301–315

    MATH  Article  Google Scholar 

  294. 294.

    Zhao X, Turk M, Li W, Lien KC, Wang G (2016) A multilevel image thresholding segmentation algorithm based on two-dimensional K-L divergence and modified particle swarm optimization. Appl Soft Comput 48:151–159

    Article  Google Scholar 

  295. 295.

    Wang W, Duan L, Wang Y (2017) Fast image segmentation using two-dimensional Otsu based on estimation of distribution algorithm. J Electr Comput Eng 2017:1–12

    Google Scholar 

  296. 296.

    Aja-Fernández S, San José Estépar R, Alberola-López C, Westin CF (2006) Image quality assessment based on local variance. In: EMBC 2006, New York

  297. 297.

    Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13(4):600–612

    Article  Google Scholar 

  298. 298.

    Hore A, Ziou D (2010) Image quality metrics: PSNR vs. SSIM. In: 2010 20th international conference on pattern recognition (ICPR). IEEE, pp 2366–2369

  299. 299.

    Zhang L, Zhang L, Mou X, Zhang D (2011) FSIM: a feature similarity index for image quality assessment. IEEE Trans Image Process 20(8):2378–2386

    MathSciNet  MATH  Article  Google Scholar 

  300. 300.

    Yin PY, Wu TH (2017) Multi-objective and multi-level image thresholding based on dominance and diversity criteria. Appl Soft Comput 54:62–73

    Article  Google Scholar 

  301. 301.

    Nakib A, Oulhadj H, Siarry P (2010) Image thresholding based on Pareto multiobjective optimization. Eng Appl Artif Intell 23(3):313–320

    MATH  Article  Google Scholar 

  302. 302.

    Djerou L, Khelil N, Dehimi NH, Batouche M (2012) Automatic multi-level thresholding segmentation based on multi-objective optimization. J Appl Comput Sci Math 6(13):24–31

    Google Scholar 

  303. 303.

    Arulraj M, Nakib A, Cooren Y, Siarry P (2014) Multicriteria image thresholding based on multiobjective particle swarm optimization. Appl Math Sci 8(3):131–137

    Google Scholar 

  304. 304.

    El Aziz MA, Ewees AA, Hassanien AE, Mudhsh M, Xiong S (2018) Multi-objective whale optimization algorithm for multilevel thresholding segmentation. In: Hassanien AE, Oliva DA (eds) Advances in soft computing and machine learning in image processing. Springer, Cham, pp 23–39

    Google Scholar 

  305. 305.

    Hinojosa S, Avalos O, Oliva D, Cuevas E, Pajares G, Zaldivar D, Gálvez J (2018) Unassisted thresholding based on multi-objective evolutionary algorithms. Knowledge-Based Syst 159:221–232

    Article  Google Scholar 

  306. 306.

    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. In: Dey N, Bhateja V, Hassanien AE (eds) Medical imaging in clinical applications. Springer, Cham, pp. 461–486

    Google Scholar 

  307. 307.

    Mozaffari MH, Lee WS (2016) Multilevel thresholding segmentation of T2 weighted brain MRI images using convergent heterogeneous particle swarm optimization. arXiv preprint arXiv:1605.04806

  308. 308.

    Cuevas E, Sención F, Zaldivar D, Pérez-Cisneros M, Sossa H (2012) A multi-threshold segmentation approach based on artificial bee colony optimization. Appl Intell 37(3):321–336

    Article  Google Scholar 

  309. 309.

    Harrabi R, Braiek EB (2012) Color image segmentation using multi-level thresholding approach and data fusion techniques: application in the breast cancer cells images. EURASIP J Image Video Process 2012(1):11

    Article  Google Scholar 

  310. 310.

    Manikandan S, Ramar K, Iruthayarajan MW, Srinivasagan KG (2014) Multilevel thresholding for segmentation of medical brain images using real coded genetic algorithm. Measurement 47:558–568

    Article  Google Scholar 

  311. 311.

    Raja NSM, Sukanya SA, Nikita Y (2015) Improved PSO based multi-level thresholding for cancer infected breast thermal images using Otsu. Procedia Comput Sci 48:524–529

    Article  Google Scholar 

  312. 312.

    Wang R, Zhou Y, Zhao C, Wu H (2015) A hybrid flower pollination algorithm based modified randomized location for multi-threshold medical image segmentation. Bio-med Mater Eng 26(s1):S1345–S1351

    Article  Google Scholar 

  313. 313.

    Oliva D, Hinojosa S, Cuevas E, Pajares G, Avalos O, Gálvez J (2017) Cross entropy based thresholding for magnetic resonance brain images using Crow Search Algorithm. Expert Syst Appl 79:164–180

    Article  Google Scholar 

  314. 314.

    Sandhya G, Babu Kande G, Savithri TS (2017) Multilevel thresholding method based on electromagnetism for accurate brain MRI segmentation to detect white matter, gray matter, and CSF. BioMed Res Int 2017:1–17

    Article  Google Scholar 

  315. 315.

    Li Y, Bai X, Jiao L, Xue Y (2017) Partitioned-cooperative quantum-behaved particle swarm optimization based on multilevel thresholding applied to medical image segmentation. Appl Soft Comput 56:345–356

    Article  Google Scholar 

  316. 316.

    Krishnan T, Balasubramanian P, Krishnan C (2016) Segmentation of brain regions by integrating meta heuristic multilevel threshold with markov random field. Curr Med Imaging Rev 12(1):4–12

    Article  Google Scholar 

  317. 317.

    Li Y, Jiao L, Shang R, Stolkin R (2015) Dynamic-context cooperative quantum-behaved particle swarm optimization based on multilevel thresholding applied to medical image segmentation. Inf Sci 294:408–422

    MathSciNet  Article  Google Scholar 

  318. 318.

    Jothi JAA, Rajam VMA (2015) Segmentation of nuclei from breast histopathology images using PSO-based Otsu’s multilevel thresholding. In: Artificial intelligence and evolutionary algorithms in engineering systems. Springer, New Delhi, pp 835–843

    Google Scholar 

  319. 319.

    Panda R, Agrawal S, Samantaray L, Abraham A (2017) An evolutionary gray gradient algorithm for multilevel thresholding of brain MR images using soft computing techniques. Appl Soft Comput 50:94–108

    Article  Google Scholar 

  320. 320.

    Raja NSM, Kavitha G, Ramakrishnan S (2012) Analysis of vasculature in human retinal images using particle swarm optimization based Tsallis multi-level thresholding and similarity measures. In: International conference on swarm, evolutionary, and memetic computing. Springer, Berlin, pp 380–387

    Google Scholar 

  321. 321.

    Sathya PD, Kayalvizhi R (2011) Amended bacterial foraging algorithm for multilevel thresholding of magnetic resonance brain images. Measurement 44(10):1828–1848

    Article  Google Scholar 

  322. 322.

    Beevi S, Nair MS, Bindu GR (2016) Automatic segmentation of cell nuclei using Krill Herd optimization based multi-thresholding and localized active contour model. Biocybern Biomed Eng 36(4):584–596

    Article  Google Scholar 

  323. 323.

    Jothi JAA, Rajam VMA (2016) Effective segmentation and classification of thyroid histopathology images. Appl Soft Comput 46:652–664

    Article  Google Scholar 

  324. 324.

    Tosta TAA, Faria PR, Neves LA, do Nascimento MZ (2017) Computational method for unsupervised segmentation of lymphoma histological images based on fuzzy 3-partition entropy and genetic algorithm. Expert Syst Appl 81:223–243

    Article  Google Scholar 

  325. 325.

    Phoulady HA, Goldgof DB, Hall LO, Mouton PR (2016) Nucleus segmentation in histology images with hierarchical multilevel thresholding. In: Medical imaging 2016: digital pathology, vol 9791. International Society for Optics and Photonics, p 979111

  326. 326.

    Saleh MD, Eswaran C (2012) An efficient algorithm for retinal blood vessel segmentation using h-maxima transform and multilevel thresholding. Comput Methods Biomech Biomed Eng 15(5):517–525

    Article  Google Scholar 

  327. 327.

    Chakraborty J, Midya A, Mukhopadhyay S, Rangayyan RM, Sadhu A, Singla V, Khandelwal N (2018) Computer-aided detection of mammographic masses using hybrid region growing controlled by multilevel thresholding. J Med Biol Eng. https://doi.org/10.1007/s40846-018-0415-9

    Article  Google Scholar 

  328. 328.

    Kaur T, Saini BS, Gupta S (2018) A comparative study on Kapur’s and Tsallis entropy for multilevel thresholding of MR images via particle swarm optimisation technique. Int J Comput Syst Eng 4(2–3):156–164

    Article  Google Scholar 

  329. 329.

    Kumar PR, Kumar IS (2018) Optimal multilevel thresholding selection for brain MRI image segmentation based on adaptive wind driven optimization. Measurement 130:340–361

    Article  Google Scholar 

  330. 330.

    Kaur T, Saini BS, Gupta S (2018) A novel fully automatic multilevel thresholding technique based on optimized intuitionistic fuzzy sets and tsallis entropy for MR brain tumor image segmentation. Australas Phys Eng Sci Med 41(1):41–58

    Article  Google Scholar 

  331. 331.

    Mohamed ST, Ebeid HM, Hassanien AE, Tolba MF (2018) Automatic white blood cell counting approach based on flower pollination optimization multilevel thresholoding algorithm. In: International conference on advanced intelligent systems and informatics. Springer, Cham, pp 313–323

    Google Scholar 

  332. 332.

    Hassan G, Hassanien AE (2018) Retinal fundus vasculature multilevel segmentation using whale optimization algorithm. Signal Image Video Process 12(2):263–270

    Article  Google Scholar 

  333. 333.

    Khorram B, Yazdi M (2018) A new optimized thresholding method using ant colony algorithm for MR brain image segmentation. J Digit Imag 32:1–13

    Google Scholar 

  334. 334.

    Díaz-Cortés MA, Ortega-Sánchez N, Hinojosa S, Oliva D, Cuevas E, Rojas R, Demin A (2018) A multi-level thresholding method for breast thermograms analysis using Dragonfly algorithm. Infrared Phys Technol 93:346–361

    Article  Google Scholar 

  335. 335.

    Hinojosa S, Dhal KG, Elaziz MA, Oliva D, Cuevas E (2018) Entropy-based imagery segmentation for breast histology using the Stochastic Fractal Search. Neurocomputing. https://doi.org/10.1016/j.neucom.2018.09.034

    Article  Google Scholar 

  336. 336.

    Muangkote N, Sunat K, Chiewchanwattana S (2016) Multilevel thresholding for satellite image segmentation with moth-flame based optimization. In: 2016 13th international joint conference on computer science and software engineering (JCSSE). IEEE, pp 1–6

  337. 337.

    Bhandari AK, Kumar A, Chaudhary S, Singh GK (2016) A novel color image multilevel thresholding based segmentation using nature inspired optimization algorithms. Expert Syst Appl 63:112–133

    Article  Google Scholar 

  338. 338.

    Suresh S, Lal S (2016) An efficient cuckoo search algorithm based multilevel thresholding for segmentation of satellite images using different objective functions. Expert Syst Appl 58:184–209

    Article  Google Scholar 

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Dhal, K.G., Das, A., Ray, S. et al. Nature-Inspired Optimization Algorithms and Their Application in Multi-Thresholding Image Segmentation. Arch Computat Methods Eng 27, 855–888 (2020). https://doi.org/10.1007/s11831-019-09334-y

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