Spatial context-based optimal multilevel energy curve thresholding for image segmentation using soft computing techniques


Image segmentation using multilevel thresholding (MT) is one of the leading methods. Although, as most techniques are based on the image histogram to be segmented, MT approaches only include the occurrence frequency of particular intensity range disregarding each spatial information. Energy curve-based contextual information can help to improve the quality of the thresholded image as it computes not only the value of the pixel but also its vicinity. Therefore, the energy curve is intended to carry spatial information into a curve with the same properties as the histogram. In this paper, classical Otsu’s method (between-class variance) is combined with energy curve for multilevel thresholding to perform segmentation of colored images. The energy curve-based Otsu (Energy-Otsu) uses an exhaustive search process to determine the optimal threshold values. However, due to the multidimensionality and multimodal nature of the color images, it becomes challenging and highly complex to obtain optimal thresholds. Therefore, the cuckoo search (CS) algorithm is coupled with Otsu thresholding criteria to perform MT over the energy curve. The proposed Energy-Otsu-CS method produces better-segmented results as compared to other well-known optimization algorithms such as differential evolution, particle swarm optimization, firefly algorithm, bacterial foraging optimization, and artificial bee colony algorithm. The proposed approach is examined intensively regarding quality, and the numerical parameter analysis is presented to compare the segmented results of the algorithms against closely related current approaches such as gray-level co-occurrence matrix and Renyi’ entropy-based thresholding approaches.

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  1. 1.

    Tuan TM (2016) A cooperative semi-supervised fuzzy clustering framework for dental X-ray image segmentation. Expert Syst Appl 46:380–393

    Article  Google Scholar 

  2. 2.

    Choy SK, Lam SY, Yu KW, Lee WY, Leung KT (2017) Fuzzy model-based clustering and its application in image segmentation. Pattern Recogn 68:141–157

    Article  Google Scholar 

  3. 3.

    Deng YL, Xu SP, Chen HQ, Liang ZH, Yu CL (2018) Inspection of extremely slight aesthetic defects in a polymeric polarizer using the edge of light between black and white stripes. Polym Test 65:169–175

    Article  Google Scholar 

  4. 4.

    Barth R, IJsselmuiden J, Hemming J, Van Henten EJ (2018) Data synthesis methods for semantic segmentation in agriculture: a Capsicum annuum dataset. Comput Electron Agric 144:284–296

    Article  Google Scholar 

  5. 5.

    Sahoo PK, Soltani SAKC, Wong AK (1988) A survey of thresholding techniques. Comput Vis Graph Image Process 41(2):233–260

    Article  Google Scholar 

  6. 6.

    Gonzalez RC, Woods RE (2002) Digital image processing, 2nd edn. Pearson Prentice Hall, Singapore

    Google Scholar 

  7. 7.

    Sezgin M, Sankur B (2004) Survey over image thresholding techniques and quantitative performance evaluation. J Electron Imaging 13:146–168

    Article  Google Scholar 

  8. 8.

    Pun T (1980) New method for gray-level picture thresholding using the entropy of the histogram. Signal Process 2:223–237

    Article  Google Scholar 

  9. 9.

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

    Article  Google Scholar 

  10. 10.

    Kittler J, Illingworth J (1986) Minimum error thresholding. Pattern Recogn 19(1):41–47

    Article  Google Scholar 

  11. 11.

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

    Article  Google Scholar 

  12. 12.

    de Albuquerque MP, Esquef IA, Mello AG (2004) Image thresholding using Tsallis entropy. Pattern Recogn Lett 25(9):1059–1065

    Article  Google Scholar 

  13. 13.

    Li CH, Lee CK (1993) Minimum cross entropy thresholding. Pattern Recogn 26(4):617–625

    Article  Google Scholar 

  14. 14.

    Lim YK, Lee SU (1990) On the color image segmentation algorithm based on the thresholding and the fuzzy c-means techniques. Pattern Recogn 23:935–952

    Article  Google Scholar 

  15. 15.

    Sahoo PK, Arora G (2004) A thresholding method based on two-dimensional Renyi’s entropy. Pattern Recogn 37(6):1149–1161

    MATH  Article  Google Scholar 

  16. 16.

    Chang EJ, Yen JC, Chang S (1995) A new criterion for automatic multilevel thresholding. IEEE Trans Image Process 4:370–378

    Article  Google Scholar 

  17. 17.

    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 

  18. 18.

    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 

  19. 19.

    Sağ T, Çunkaş M (2015) Color image segmentation based on multi-objective artificial bee colony optimization. Appl Soft Comput 34:389–401

    Article  Google Scholar 

  20. 20.

    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 

  21. 21.

    Rajinikanth V, Couceiro MS (2015) RGB histogram based color image segmentation using firefly algorithm. Procedia Comput Sci 46:1449–1457

    Article  Google Scholar 

  22. 22.

    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 

  23. 23.

    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 

  24. 24.

    Dey S, Bhattacharyya S, Maulik U (2013) Quantum inspired meta-heuristic algorithms for multi-level thresholding for true colour images. Proc IEEE Indicon 2013:1–6

    Google Scholar 

  25. 25.

    Dey S, Bhattacharyya S, Maulik U (2014) New quantum inspired tabu search for multi-level colour image thresholding. In: Proceedings of 8th international conference on computing for sustainable global development (INDIACom-2014), pp 311–316

  26. 26.

    Dey S, Bhattacharyya S, Maulik U (2017) Efficient quantum inspired meta-heuristics for multi-level true colour image thresholding. Appl Soft Comput 56:47–2513

    Article  Google Scholar 

  27. 27.

    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 

  28. 28.

    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 

  29. 29.

    Ghamisi P, Couceiro MS, Martins FM, Benediktsson JA (2014) Multilevel image segmentation based on fractional-order Darwinian particle swarm optimization. IEEE Trans Geosci Remote Sens 52(5):2382–2394

    Article  Google Scholar 

  30. 30.

    Sarkar S, Das S, Chaudhuri SS (2015) A multilevel color image thresholding scheme based on minimum cross entropy and differential evolution. Pattern Recogn Lett 54:27–35

    Article  Google Scholar 

  31. 31.

    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: IEEE international conference on digital signal processing (DSP), pp 730–734

  32. 32.

    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 

  33. 33.

    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 

  34. 34.

    Pare S, Kumar A, Bajaj V, Singh GK (2017) A context sensitive multilevel thresholding using swarm based algorithms. IEEE/CAA J Autom Sin.

    Article  Google Scholar 

  35. 35.

    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 

  36. 36.

    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 

  37. 37.

    Pare S, Bhandari AK, Kumar A, Singh GK (2017) 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 

  38. 38.

    Pare S, Bhandari AK, Kumar A, Bajaj V (2017) Backtracking search algorithm for color image multilevel thresholding. Signal Image Video Process 12:1–8

    Google Scholar 

  39. 39.

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

    Article  Google Scholar 

  40. 40.

    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 

  41. 41.

    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 

  42. 42.

    Bianconi F, Fernandez A (2014) Rotation invariant co-occurrence features based on digital circles and discrete Fourier transform. Pattern Recogn Lett 48:34–41

    Article  Google Scholar 

  43. 43.

    Panda R, Agrawal S, Bhuyan S (2013) Edge magnitude based multilevel thresholding using cuckoo search technique. Expert Syst Appl 40(18):7617–7628

    Article  Google Scholar 

  44. 44.

    Sahoo P, Wilkins C, Yeager J (1997) Threshold selection using Rényi’s entropy. Pattern Recogn 30(1):71–84

    MATH  Article  Google Scholar 

  45. 45.

    Patra S, Gautam R, Singla A (2014) A novel context sensitive multilevel thresholding for image segmentation. Appl Soft Comput 23:122–127

    Article  Google Scholar 

  46. 46.

    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(19):25761–25797

    Article  Google Scholar 

  47. 47.

    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 

  48. 48.

    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 

  49. 49.

    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 

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Correspondence to Ashish Kumar Bhandari.

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Kandhway, P., Bhandari, A.K. Spatial context-based optimal multilevel energy curve thresholding for image segmentation using soft computing techniques. Neural Comput & Applic 32, 8901–8937 (2020).

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  • Multilevel thresholding
  • Renyi’s entropy
  • Spatial context sensitive
  • Energy-Otsu method
  • Gray-level co-occurrence matrix
  • Soft computing techniques