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An adaptive multilevel thresholding method with chaotically-enhanced Rao algorithm

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Abstract

Multilevel image thresholding is a well-known technique for image segmentation. Recently, various metaheuristic methods have been proposed for the determination of the thresholds for multilevel image segmentation. These methods are mainly based on metaphors and they have high complexity and their convergences are comparably slow. In this paper, a multilevel image thresholding approach is proposed that simplifies the thresholding problem by using a simple optimization technique instead of metaphor-based algorithms. More specifically, in this paper, Chaotic enhanced Rao (CER) algorithms are developed where eight chaotic maps namely Logistic, Sine, Sinusoidal, Gauss, Circle, Chebyshev, Singer, and Tent are used. Besides, in the developed CER algorithm, the number of thresholds is determined automatically, instead of manual determination. The performances of the developed CER algorithms are evaluated based on different statistical analysis metrics namely BDE, PRI, VOI, GCE, SSIM, FSIM, RMSE, PSNR, NK, AD, SC, MD, and NAE. The experimental works and the related evaluations are carried out on the BSDS300 dataset. The obtained experimental results demonstrate that the proposed CER algorithm outperforms the compared methods based on PRI, SSIM, FSIM, PSNR, RMSE, AD, and NAE metrics. In addition, the proposed method provides better convergence regarding speed and accuracy.

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References

  1. Abdel-Basset M, Mohamed R, AbdelAziz NM, Abouhawwash M (2022) HWOA: a hybrid whale optimization algorithm with a novel local minima avoidance method for multi-level thresholding color image segmentation. Expert Syst Appl 190:116145. https://doi.org/10.1016/j.eswa.2021.116145

    Article  Google Scholar 

  2. Achanta R, Estrada F, Wils P, Süsstrunk S (2008) Salient region detection and segmentation. In: Computer vision systems. Springer Berlin Heidelberg, Berlin, pp 66–75

    Chapter  Google Scholar 

  3. Agrawal S, Panda R, Abraham A (2020) A novel diagonal class entropy-based multilevel image thresholding using coral reef optimization. IEEE Trans Syst Man Cybern Syst 50:4688–4696. https://doi.org/10.1109/TSMC.2018.2859429

    Article  Google Scholar 

  4. Bao X, Jia H, Lang C (2019) A novel hybrid Harris hawks optimization for color image multilevel thresholding segmentation. IEEE Access 7:76529–76546

    Article  Google Scholar 

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

    Article  Google Scholar 

  6. 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

    Article  Google Scholar 

  7. Feoktistov V (2006) Differential Evolution. In: Differential evolution: in search of solutions. Springer US, Boston, pp 1–24

    MATH  Google Scholar 

  8. Grzywiński M, Atmaca B, Dede T, Venkata Rao R (2020) The size optimization of steel braced barrel vault structure by using Rao-1 algorithm. Sigma J Eng Nat Sci 38:1415–1425

    Google Scholar 

  9. Hosny M, Kamel S, El-Dabah M et al (2021) Optimal reactive power dispatch with time-varying demand and renewable energy uncertainty using Rao-3 algorithm. IEEE Access PP:1–1. https://doi.org/10.1109/ACCESS.2021.3056423

    Article  Google Scholar 

  10. Houssein EH, Helmy BE, Oliva D, Jangir P, Premkumar M, Elngar AA, Shaban H (2022) An efficient multi-thresholding based COVID-19 CT images segmentation approach using an improved equilibrium optimizer. Biomed Signal Process Control 73:103401. https://doi.org/10.1016/j.bspc.2021.103401

    Article  Google Scholar 

  11. Jet colormap array - MATLAB jet. https://www.mathworks.com/help/matlab/ref/jet.html. Accessed 31 Dec 2021

  12. Jia H, Ma J, Song W (2019) Multilevel thresholding segmentation for color image using modified moth-flame optimization. IEEE Access 7:44097–44134

    Article  Google Scholar 

  13. Karaboga D, Basturk B (2007) Artificial bee colony (ABC) optimization algorithm for solving constrained optimization problems. In: Foundations of fuzzy logic and soft computing. Springer, Berlin, Heidelberg, pp 789–798

    Chapter  MATH  Google Scholar 

  14. Li M-W, Wang Y-T, Geng J, Hong W-C (2021) Chaos cloud quantum bat hybrid optimization algorithm. Nonlinear Dyn 103:1167–1193. https://doi.org/10.1007/s11071-020-06111-6

    Article  Google Scholar 

  15. Luo TL, Eisenberg MC, Hayashi MAL, Gonzalez-Cabezas C, Foxman B, Marrs CF, Rickard AH (2018) A sensitive thresholding method for confocal laser scanning microscope image stacks of microbial biofilms. Sci Rep 8:13013. https://doi.org/10.1038/s41598-018-31012-5

    Article  Google Scholar 

  16. Manda MP, Kim HS (2020) A fast image thresholding algorithm for infrared images based on histogram approximation and circuit theory. Algorithms 13:207. https://doi.org/10.3390/a13090207

    Article  MathSciNet  Google Scholar 

  17. Maolood IY, Al-Salhi YEA, Lu S (2018) Thresholding for medical image segmentation for Cancer using fuzzy entropy with level set algorithm. Open Med (Wars) 13:374–383. https://doi.org/10.1515/med-2018-0056

    Article  Google Scholar 

  18. 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 

  19. Mittal H, Pal R, Kulhari A, Saraswat M (2016) Chaotic Kbest gravitational search algorithm (CKGSA). In: 2016 ninth international conference on contemporary computing. Noida, India, pp 1–6

    Google Scholar 

  20. Naji Alwerfali HS, Al-qaness AA, Abd Elaziz M et al (2020) Multi-level image thresholding based on modified spherical search optimizer and fuzzy entropy. Entropy 22:328. https://doi.org/10.3390/e22030328

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  22. Pare S, Kumar A, Singh GK (2017) Color multilevel thresholding using gray-level co-occurrence matrix and differential evolution algorithm. In: 2017 international conference on communication and signal processing (ICCSP), pp 0096–0100

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

    Article  Google Scholar 

  24. Pare S, Kumar A, Bajaj V, Singh GK (2019) A context sensitive multilevel thresholding using swarm based algorithms. IEEE/CAA J Autom Sin 6:1471–1486. https://doi.org/10.1109/JAS.2017.7510697

    Article  MathSciNet  Google Scholar 

  25. Raj A, Gautam G, Sheikh Abdullah S et al (2019) Multi-level thresholding based on differential evolution and Tsallis Fuzzy entropy. Image Vis Comput 91. https://doi.org/10.1016/j.imavis.2019.07.004

  26. Rao RV (2020) Rao algorithms: three metaphor-less simple algorithms for solving optimization problems. Int J Ind Eng Comput 11:107–130. https://doi.org/10.5267/j.ijiec.2019.6.002

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  28. Ravipudi J (2020) Synthesis of linear, planar, and concentric circular antenna arrays using Rao algorithms. Int J Appl Evol Comput 11:31–49. https://doi.org/10.4018/IJAEC.2020070103

    Article  Google Scholar 

  29. Sathya BS, Manavalan R (2011) Image segmentation by clustering methods: performance analysis. Int J Comput Appl 29:27–32. https://doi.org/10.5120/3688-5127

    Article  Google Scholar 

  30. Shao D, Xu C, Xiang Y, Gui P, Zhu X, Zhang C, Yu Z (2019) Ultrasound image segmentation with multilevel threshold based on differential search algorithm. IET Image Process 13:998–1005

    Article  Google Scholar 

  31. Sharma S, Singh B, Aneja M (2021) Classification of Parkinson disease using binary Rao optimization algorithms. Expert Syst. https://doi.org/10.1111/exsy.12674

  32. Shen L, Huang X, Fan C (2018) Double-group particle swarm optimization and its application in remote sensing image segmentation. Sensors 18:1393. https://doi.org/10.3390/s18051393

    Article  Google Scholar 

  33. Sörensen K (2015) Metaheuristics—the metaphor exposed. Int Trans Oper Res 22:3–18. https://doi.org/10.1111/itor.12001

    Article  MathSciNet  MATH  Google Scholar 

  34. Srikanth R, Bikshalu K (2021) Multilevel thresholding image segmentation based on energy curve with harmony search algorithm. Ain Shams Eng J 12:1–20. https://doi.org/10.1016/j.asej.2020.09.003

    Article  Google Scholar 

  35. Srinivasu PN, Norwawi N, Amiripalli SS, Deepalakshmi P (2021) Secured compression for 2D medical images through the manifold and fuzzy trapezoidal correlation function. Gazi Univ J Sci. https://doi.org/10.35378/gujs.884880

  36. Swain M, Tripathy TT, Panda R, Agrawal S, Abraham A (2022) Differential exponential entropy-based multilevel threshold selection methodology for colour satellite images using equilibrium-cuckoo search optimizer. Eng Appl Artif Intell 109:104599. https://doi.org/10.1016/j.engappai.2021.104599

    Article  Google Scholar 

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

    MathSciNet  Google Scholar 

  38. Varnan SC, Jagan A, Kaur J, Jyoti D, Rao DS (2011) Image quality assessment techniques pn spatial domain. Int J Comput Sci Technol 2:177–184

    Google Scholar 

  39. Venkata Rao R, Keesari H (2020) Rao algorithms for multi-objective optimization of selected thermodynamic cycles. Eng Comput 37:3409–3437. https://doi.org/10.1007/s00366-020-01008-9

    Article  Google Scholar 

  40. 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 

  41. Wang L, Wang Z, Liang H, Huang C (2019) Parameter estimation of photovoltaic cell model with Rao-1 algorithm. Optik 210:163846. https://doi.org/10.1016/j.ijleo.2019.163846

    Article  Google Scholar 

  42. Wunnava A, Kumar Naik M, Panda R, Jena B, Abraham A (2020) A differential evolutionary adaptive Harris hawks optimization for two dimensional practical Masi entropy-based multilevel image thresholding. J King Saud Univ – Comput Inf Sci 34:3011–3024. https://doi.org/10.1016/j.jksuci.2020.05.001

    Article  Google Scholar 

  43. Xing Z (2020) An improved emperor penguin optimization based multilevel thresholding for color image segmentation. Knowl-Based Syst 194:105570. https://doi.org/10.1016/j.knosys.2020.105570

    Article  Google Scholar 

  44. Yue X, Zhang H (2020) Modified hybrid bat algorithm with genetic crossover operation and smart inertia weight for multilevel image segmentation. Appl Soft Comput 90:106157. https://doi.org/10.1016/j.asoc.2020.106157

    Article  Google Scholar 

  45. Zhang Z, Hong W-C (2021) Application of variational mode decomposition and chaotic grey wolf optimizer with support vector regression for forecasting electric loads. Know-Based Syst 228:107297. https://doi.org/10.1016/j.knosys.2021.107297

    Article  Google Scholar 

  46. 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

    Article  MathSciNet  MATH  Google Scholar 

  47. Zhaoa X, Turk M, Li W et al (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 

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Olmez, Y., Sengur, A., Koca, G.O. et al. An adaptive multilevel thresholding method with chaotically-enhanced Rao algorithm. Multimed Tools Appl 82, 12351–12377 (2023). https://doi.org/10.1007/s11042-022-13671-9

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