An accurate Cluster chaotic optimization approach for digital medical image segmentation


Image segmentation is a crucial stage in digital image processing used to obtain a more straightforward representation of images. Although classic bi-level segmentation is a relatively simple task, it only suffices to analyze rather simple images. More complex real-life scenarios such as medical imaging processing usually require multi-level segmentation to differentiate between the many regions of interest present in the original images. Traditional histogram-based approaches for multi-level segmentation tend to perform suboptimally, with the best performing being computationally expensive. This difficult compromise between performance and computational cost has led to the proposal of new approaches mixing a variety of optimization algorithms and statistical criteria. Despite the success of these new approaches, there is still room for improvement. It is under these circumstances that evolutionary algorithms like the cluster chaotic optimization (CCO) become relevant. The CCO takes advantage of the classification procedures of clustering techniques and the randomness of chaotic sequences for encouraging the search strategy. This paper proposes a novel method based on the CCO algorithm named minimum cross-entropy multi-level segmentation CCO (CEMS-CCO). The CEMS-CCO employs the cross-entropy as its fitness function and the CCO capabilities to deal with multimodal functions to search for the optimal solution to the multi-level segmentation problem. The CEMS-CCO shows competitive results for medical images multi-level segmentation regarding different quality metrics. Furthermore, its robustness and effectiveness are tested through the analysis of well-known benchmark images. Statistical analysis of the experimental results shows that the proposed CEMS-CCO technique outperforms state-of-the-art algorithms.

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  1. 1.

    Purri M, Xue J, Dana K, et al (2019) Material segmentation of multi-view satellite imagery. arXiv

  2. 2.

    Jia H, Sun K, Song W et al (2019) Multi-strategy emperor penguin optimizer for RGB histogram-based color satellite image segmentation using masi entropy. IEEE Access 7:134448–134474.

    Article  Google Scholar 

  3. 3.

    Shubham S, Bhandari AK (2019) A generalized Masi entropy based efficient multi-level thresholding method for color image segmentation. Multimed Tools Appl 78:17197–17238.

    Article  Google Scholar 

  4. 4.

    Wan M, Gu G, Sun J et al (2018) A level set method for infrared image segmentation using global and local information. Remote Sens 10:1039.

    Article  Google Scholar 

  5. 5.

    Mutlu K, Rabell JE, Martin del Olmo P, Haesler S (2018) IR thermography-based monitoring of respiration phase without image segmentation. J Neurosci Methods 301:1–8.

    Article  Google Scholar 

  6. 6.

    Lu TT, Huyen A, Payumo K et al. (2018) Deep neural network for precision multi-band infrared image segmentation. In: Alam MS (ed) Pattern recognition and tracking XXIX. SPIE, p 3

  7. 7.

    Zhao A, Balakrishnan G, Durand F et al. (2019) Data augmentation using learned transformations for one-shot medical image segmentation. In: Proceedings of the IEEE computer society conference on computer vision and pattern recognition. pp 8535–8545

  8. 8.

    Chen X, Williams BM, Vallabhaneni SR et al. (2019) Learning active contour models for medical image segmentation. In: Proceedings of the IEEE computer society conference on computer vision and pattern recognition. pp 11624–11632

  9. 9.

    Hesamian MH, Jia W, He X, Kennedy P (2019) Deep learning techniques for medical image segmentation: achievements and challenges. J Digit Imag 32:582–596.

    Article  Google Scholar 

  10. 10.

    Weng Y, Zhou T, Li Y, Qiu X (2019) NAS-Unet: nural architecture search for medical image segmentation. IEEE Access 7:44247–44257.

    Article  Google Scholar 

  11. 11.

    Santosh KC, Wendling L, Antani S, Thoma GR (2016) Overlaid arrow detection for labeling regions of interest in biomedical images. IEEE Intell Syst 31:66–75.

    Article  Google Scholar 

  12. 12.

    Vaidya SP, Mouli PVSSRC, Santosh KC (2019) Imperceptible watermark for a game-theoretic watermarking system. Int J Mach Learn Cybern 10:1323–1339.

    Article  Google Scholar 

  13. 13.

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

    Article  Google Scholar 

  14. 14.

    Dirami A, Hammouche K, Diaf M, Siarry P (2013) Fast multi-level thresholding for image segmentation through a multiphase level set method. Signal Process 93:139–153.

    Article  Google Scholar 

  15. 15.

    Otsu N (1979) A threshold selection method from gray-level histograms. IEEE Trans Syst Man Cybern 9:62–66.

    Article  Google Scholar 

  16. 16.

    Tsai WH (1985) Moment-preserving thresholding: a new approach. Comput Vision Graph Image Process 29:377–393.

    Article  Google Scholar 

  17. 17.

    Kapur JN, Sahoo PK, Wong AKC (1985) A new method for gray-level picture thresholding using the entropy of the histogram. Comput Vision Graph Image Process 29:273–285.

    Article  Google Scholar 

  18. 18.

    Li CH, Lee CK (1993) Minimum cross entropy thresholding. Pattern Recognit 26:617–625.

    Article  Google Scholar 

  19. 19.

    Laurenceau J, Meaux M (2008) Comparison of gradient and response surface based optimization frameworks using adjoint method. American Institute of Aeronautics and Astronautics (AIAA)

  20. 20.

    Dwight RP, Brezillon J (2006) Effect of approximations of the discrete adjoint on gradient-based optimization. AIAA J 44:3022–3031.

    Article  Google Scholar 

  21. 21.

    Wetter M, Wright J (2004) A comparison of deterministic and probabilistic optimization algorithms for nonsmooth simulation-based optimization. Building and environment. Elsevier BV, Amsterdam, pp 989–999

    Google Scholar 

  22. 22.

    Wiley: Evolutionary optimization algorithms: Dan Simon. Accessed 23 Jul 2020

  23. 23.

    Holland JH (1992) Genetic algorithms: computer programs that “evolve” in ways that resemble natural selection can solve complex problems even their creators do not fully understand. Sci Am 267:66–72

    Article  Google Scholar 

  24. 24.

    Angeline PJ (1994) Genetic programming: on the programming of computers by means of natural selection. Biosystems 33:69–73.

    Article  Google Scholar 

  25. 25.

    Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Neural networks, 1995 proceedings, IEEE international conference 4:1942–1948 vol 4.

  26. 26.

    Karaboga D, Basturk B (2007) Artificial Bee Colony (ABC) optimization algorithm for solving constrained optimization problems. In: Melin P, Castillo O, Aguilar LT, et al (eds) Foundations of fuzzy logic and soft computing: 12th international fuzzy systems association world congress, IFSA 2007, Cancun, Mexico, June 18–21, 2007. Proceedings. Springer, Berlin, pp 789–798

  27. 27.

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

    Article  Google Scholar 

  28. 28.

    Yang XS, Deb S (2009) Cuckoo search via Lévy flights. In: 2009 world congress on nature and biologically inspired computing NABIC 2009-Proc 210–214.

  29. 29.

    Dorigo M, on GDC-P of the 1999 congress, 1999 undefined Ant colony optimization: a new meta-heuristic.

  30. 30.

    Zaldivar D, Morales B, Rodríguez A et al (2018) A novel bio-inspired optimization model based on yellow saddle goatfish behavior. Elsevier, Amsterdam

    Google Scholar 

  31. 31.

    Cuevas E, Cienfuegos M, Zaldívar D, Pérez-Cisneros M (2013) A swarm optimization algorithm inspired in the behavior of the social-spider. Expert Syst Appl 40:6374–6384.

    Article  Google Scholar 

  32. 32.

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

    Article  Google Scholar 

  33. 33.

    Rai GNH, Nair TRG (2010) Gradient based seeded region grow method for CT angiographic image segmentation. InterJRI Comput Sci Netw 1(1)

  34. 34.

    Akram MU, Nasir S, Tariq A et al. (2008) Improved fingerprint image segmentation using new modified gradient based technique. In: Canadian conference on electrical and computer engineering. pp 1967–1971

  35. 35.

    Hill PR, Nishan Canagarajah C, Bull DR (2003) Image segmentation using a texture gradient based watershed transform. IEEE Trans Image Process 12:1618–1633.

    MathSciNet  Article  Google Scholar 

  36. 36.

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

    Article  Google Scholar 

  37. 37.

    Rajinikanth V, Sri Madhava Raja N, Satapathy SC (2016) Robust color image multi-thresholding using between-class variance and cuckoo search algorithm. Advances in intelligent systems and computing. Springer, Berlin, pp 379–386

    Google Scholar 

  38. 38.

    Pare S, Bhandari AK, Kumar A, Singh GK (2018) A new technique for multi-level color image thresholding based on modified fuzzy entropy and Lévy flight firefly algorithm. Comput Electr Eng 70:476–495.

    Article  Google Scholar 

  39. 39.

    Dey S, Bhattacharyya S, Maulik U (2017) Efficient quantum inspired meta-heuristics for multi-level true colour image thresholding. Appl Soft Comput J 56:472–513.

    Article  Google Scholar 

  40. 40.

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

    Article  Google Scholar 

  41. 41.

    Agrawal S, Panda R, Abraham A (2018) A novel diagonal class entropy-based multi-level image thresholding using coral reef optimization. IEEE Trans Syst Man, Cybern Syst.

    Article  Google Scholar 

  42. 42.

    Shahabi F, Pourahangarian F, Beheshti H (2019) A multi-level image thresholding approach based on crow search algorithm and Otsu method. Decis Oper Res 4:33–41

    Google Scholar 

  43. 43.

    Alwerfali HSN, Abd Elaziz M, Al-Qaness MAA et al (2019) A Multi-level image thresholding based on hybrid salp swarm algorithm and fuzzy entropy. IEEE Access 7:181405–181422.

    Article  Google Scholar 

  44. 44.

    Huang X, Shen L, Fan C et al. (2020) Multilevel image thresholding using a fully informed cuckoo search algorithm. arXiv

  45. 45.

    Shahabi F, Poorahangaryan F, Edalatpanah SA, Beheshti H (2020) A multi-level image thresholding approach based on crow search algorithm and Otsu method. Int J Comput Intell Appl 19:2050015.

    Article  Google Scholar 

  46. 46.

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

    Article  Google Scholar 

  47. 47.

    Gálvez J, Cuevas E, Becerra H, Avalos O (2020) A hybrid optimization approach based on clustering and chaotic sequences. Int J Mach Learn Cybern 11:359–401.

    Article  Google Scholar 

  48. 48.

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

    Article  Google Scholar 

  49. 49.

    Elaziz MA, Lu S (2019) Many-objectives multi-level thresholding image segmentation using knee evolutionary algorithm. Expert Syst Appl 125:305–316.

    Article  Google Scholar 

  50. 50.

    Rodríguez-Esparza E, Zanella-Calzada LA, Oliva D et al (2020) An efficient Harris hawks-inspired image segmentation method. Expert Syst Appl 155:113428.

    Article  Google Scholar 

  51. 51.

    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 79:164–180.

    Article  Google Scholar 

  52. 52.

    Labati RD, Piuri V, Scotti F (2011) All-IDB: the acute lymphoblastic leukemia image database for image processing. In: 2011 18th IEEE international conference on image processing. IEEE, pp 2045–2048

  53. 53.

    Li Y, Zhu R, Mi L et al (2016) Segmentation of white blood cell from acute lymphoblastic leukemia images using dual-threshold method. Comput Math Methods Med 2016:9514707.

    Article  Google Scholar 

  54. 54.

    USF Digital Mammography Home Page. Accessed 6 Jul 2020

  55. 55.

    Horé A, Ziou D (2010) Image quality metrics: PSNR vs. SSIM. In: Proceedings-international conference on pattern recognition. pp 2366–2369

  56. 56.

    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.

    Article  Google Scholar 

  57. 57.

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

    MathSciNet  Article  MATH  Google Scholar 

  58. 58.

    Yin PY (2007) Multi-level minimum cross entropy threshold selection based on particle swarm optimization. Appl Math Comput 184:503–513.

    MathSciNet  Article  MATH  Google Scholar 

  59. 59.

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

    MathSciNet  Article  MATH  Google Scholar 

  60. 60.

    Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 762:60–68

    Article  Google Scholar 

  61. 61.

    Gonzalez RC, Woods RE, Eddins SL (2004) Digital image processing using MATLAB. Upper Saddle River, NJ, Pearson/Prentice Hall

    Google Scholar 

  62. 62.

    Murtagh F, Legendre P (2014) Ward’s hierarchical agglomerative clustering method: which algorithms implement ward’s criterion? J Classif 31:274–295.

    MathSciNet  Article  MATH  Google Scholar 

  63. 63.

    Ward JH (1963) Hierarchical grouping to optimize an objective function. J Am Stat Assoc 58:236–244.

    MathSciNet  Article  Google Scholar 

  64. 64.

    Ewees AA, Abd Elaziz M, Al-Qaness MAA et al (2020) Improved artificial bee colony using sine-cosine algorithm for multi-level thresholding image segmentation. IEEE Access 8:26304–26315.

    Article  Google Scholar 

  65. 65.

    Mousavirad SJ, Ebrahimpour-Komleh H (2019) Human mental search-based multi-level thresholding for image segmentation. Appl Soft Comput J.

    Article  Google Scholar 

  66. 66.

    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.

    Article  Google Scholar 

  67. 67.

    Flynn JR, Ward S, Abich J, Poole D (2013) Image quality assessment using the SSIM and the just noticeable difference paradigm. In: Harris D (ed) Engineering psychology and cognitive ergonomics. Understanding human cognition. EPCE 2013. Lecture Notes in Computer Science, vol 8019. Springer, Berlin, Heidelberg.

  68. 68.

    Yue X, Zhang H (2020) A multi-level image thresholding approach using Otsu based on the improved invasive weed optimization algorithm. Signal Image Video Process 14:575–582.

    Article  Google Scholar 

  69. 69.

    Di MF, Sessa S (2020) PSO image thresholding on images compressed via fuzzy transforms. Inf Sci (NY) 506:308–324.

    MathSciNet  Article  Google Scholar 

  70. 70.

    Monisha R, Mrinalini R, Nithila Britto M et al. (2019) Social group optimization and Shannon’s function-based RGB image multi-level thresholding. In: Smart Innovation, Systems and Technologies. Springer Science and Business Media Deutschland GmbH, pp 123–132

  71. 71.

    Abdel-Basset M, Chang V, Mohamed R (2020) A novel equilibrium optimization algorithm for multi-thresholding image segmentation problems. Neural Comput Appl.

    Article  Google Scholar 

  72. 72.

    Loizou CP, Pantziaris M, Seimenis I, Pattichis CS (2009) Brain MR image normalization in texture analysis of multiple sclerosis. In: final program and abstract Book-9th international conference on information technology and applications in biomedicine, ITAB 2009

  73. 73.

    Loizou CP, Kyriacou EC, Seimenis I et al (2011) Brain white matter lesions classification in multiple sclerosis subjects for the prognosis of future disability. IFIP advances in information and communication technology. Springer, New York, pp 400–409

    Google Scholar 

  74. 74.

    Loizou CP, Murray V, Pattichis MS et al (2011) Multiscale amplitude-modulation frequency-modulation (AMFM) texture analysis of multiple sclerosis in brain MRI images. IEEE Trans Inf Technol Biomed 15:119–129.

    Article  Google Scholar 

  75. 75.

    Loizou CP, Petroudi S, Seimenis I et al (2015) Quantitative texture analysis of brain white matter lesions derived from T2-weighted MR images in MS patients with clinically isolated syndrome. J Neuroradiol 42:99–114.

    Article  Google Scholar 

  76. 76.

    Wang X, Peng Y, Lu L et al. (2017) ChestX-ray8: hospital-scale chest X-ray database and benchmarks on weakly-supervised classification and localization of common thorax diseases. arXiv

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Avalos, O., Ayala, E., Wario, F. et al. An accurate Cluster chaotic optimization approach for digital medical image segmentation. Neural Comput & Applic (2021).

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  • Cluster chaotic optimization
  • Multi-level segmentation
  • Digital medical image
  • Minimum cross-entropy
  • Optimization process
  • Digital image segmentation