Skip to main content
Log in

Variational Mode Decomposition-Based Multilevel Threshold Selection Scheme for Color Image Segmentation

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

Image segmentation is a method of subdividing an image into numerous meaningful regions or objects, which makes the image more informative and easy to analyze. Thresholding-based approaches are extensively employed for segmenting the image due to their low computational cost and are easy implementation. However, histogram-based thresholding schemes suffer from high variation that leads to abnormalities and sharp specifics. In this paper, we propose a technique for multilevel color image segmentation through variational mode decomposition (VMD) and Kapur’s entropy. Initially, the VMD is employed in order to decompose the histogram into corresponding submodes of analysis and attributes extraction, which leads to the removal of the unfavorable effects. Then, Kapur’s entropy is incorporated in order to generate accurate and optimal thresholds for segmentation. For the performance evaluation of the presented VMD–Kapur algorithm, various qualitative metrics have been used such as probability rand index, mean-square error, peak signal-to-noise ratio, variation of information, structural similarity index, dice error, feature similarity index, entropy, Jaccard/Tanimoto error, and normalized absolute error. The experimental results show that the proposed technique produces best-segmented images compared to Kapur’s, Tsallis, Masi, and fuzzy entropies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32
Fig. 33
Fig. 34
Fig. 35
Fig. 36

Similar content being viewed by others

References

  1. A.S. Abutaleb, Automatic thresholding of gray-level pictures using two-dimensional entropy. Comput. Vis. Graph. Image Process. 47(1), 22–32 (1989)

    Google Scholar 

  2. J. Acharya, A. Orlitsky, A.T. Suresh, H. Tyagi, Estimating Rényi entropy of discrete distributions. IEEE Trans. Inf. Theory 63(1), 38–56 (2017)

    MATH  Google Scholar 

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

    Google Scholar 

  4. P. Arbelaez, M. Maire, C. Fowlkes, J. Malik, Contour detection and hierarchical image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 33(5), 898–916 (2011)

    Google Scholar 

  5. I. Avcibas, B. Sankur, K. Sayood, Statistical evaluation of image quality measures. J. Electron. Imaging 11(2), 206–224 (2002)

    Google Scholar 

  6. A.K. Bhandari, I.V. Kumar, K. Srinivas, Cuttleish algorithm based multilevel 3D Otsu function for color image segmentation. IEEE Trans. Instrum. Meas. 1–10 (2019). https://doi.org/10.1109/TIM.2019.2922516

  7. A.K. Bhandari, K. Rahul, A context sensitive Masi entropy for multilevel image segmentation using Moth Swarm algorithm. Infrared Phys. Technol. 98, 132–154 (2019)

    Google Scholar 

  8. A.K. Bhandari, V.K. Singh, A. Kumar, G.K. Singh, 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 (2014)

    Google Scholar 

  9. A.K. Bhandari, A. Kumar, G.K. Singh, 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 (2015)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  12. S.M. Bhuiyan, R.R. Adhami, J.F. Khan, A novel approach of fast and adaptive bidimensional empirical mode decomposition. In 2008 IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2008), pp. 1313–1316

  13. S. Borjigin, P.K. Sahoo, Color image segmentation based on multi-level Tsallis–Havrda–Charvát entropy and 2D histogram using PSO algorithms. Pattern Recognit. 92, 107–118 (2019)

    Google Scholar 

  14. E.J. Candes, D.L. Donoho, Curvelets: A Surprisingly Effective Nonadaptive Representation for Objects with Edges (Stanford University CA Dept of Statistics, 2000)

  15. M.J. Dahan, N. Chen, A. Shamir, D. Cohen-Or, Combining color and depth for enhanced image segmentation and retargeting. Vis. Comput. 28(12), 1181–1193 (2012)

    Google Scholar 

  16. I. Daubechies, Orthonormal bases of compactly supported wavelets. Commun. Pure Appl. Math. 41(7), 909–996 (1988)

    MathSciNet  MATH  Google Scholar 

  17. M.P. De Albuquerque, I.A. Esquef, A.G. Mello, Image thresholding using Tsallis entropy. Pattern Recognit. Lett. 25(9), 1059–1065 (2004)

    Google Scholar 

  18. L.R. Dice, Measures of the amount of ecologic association between species. Ecology 26(3), 297–302 (1945)

    Google Scholar 

  19. M.N. Do, M. Vetterli, Pyramidal directional filter banks and curvelets, in Proceedings 2001 International Conference on Image Processing (Cat. No. 01CH37205), vol. 3 (IEEE, 2001), pp. 158–161

  20. K. Dragomiretskiy, D. Zosso, Two-dimensional variational mode decomposition, in International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition (Springer, Cham, 2015), pp. 197–208

  21. K. Dragomiretskiy, D. Zosso, Variational mode decomposition. IEEE Trans. Signal Process. 62(3), 531–544 (2014)

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  23. M. Feldman, Time-varying vibration decomposition and analysis based on the Hilbert transform. J. Sound Vib. 295(3–5), 518–530 (2006)

    MATH  Google Scholar 

  24. B. Goyal, A. Dogra, S. Agrawal, B.S. Sohi, A three stage integrated denoising approach for grey scale images. J. Ambient Intell. Humaniz. Comput. 1–16 (2018). https://doi.org/10.1007/s12652-018-1019-5

  25. K. Guo, D. Labate, Optimally sparse multidimensional representation using shearlets. SIAM J. Math. Anal. 39(1), 298–318 (2007)

    MathSciNet  MATH  Google Scholar 

  26. D. Hao, Q. Li, C. Li, Histogram-based image segmentation using variational mode decomposition and correlation coefficients. Signal Image Video Process. 11(8), 1411–1418 (2017)

    Google Scholar 

  27. R.M. Haralick, L.G. Shapiro, Image segmentation techniques. Comput. Vis. Graph. Image Process. 29(1), 100–132 (1985)

    Google Scholar 

  28. L.K. Huang, M.J.J. Wang, Image thresholding by minimizing the measures of fuzziness. Pattern Recognit. 28(1), 41–51 (1995)

    Google Scholar 

  29. A.B. Ishak, Choosing parameters for Rényi and Tsallis entropies within a two-dimensional multilevel image segmentation framework. Phys. A Stat. Mech. Appl. 466, 521–536 (2017)

    Google Scholar 

  30. P. Jaccard, Nouvelles recherches sur la distribution florale. Bull. Soc. Vaud. Sci. Nat. 44, 223–270 (1908)

    Google Scholar 

  31. S. Jiang, X. Mu, H. Cheng, Q. Song, Image thresholding segmentation of generalized fuzzy entropy based on double adaptive ant colony algorithm. J. Intell. Fuzzy Syst. 35(2), 1979–1990 (2018)

    Google Scholar 

  32. P. Kandhway, A.K. Bhandari, A water cycle algorithm-based multilevel thresholding system for color image segmentation using Masi entropy. Circuits Syst. Signal Process. 38, 1–49 (2018)

    Google Scholar 

  33. J.N. Kapur, P.K. Sahoo, A.K. Wong, A new method for gray-level picture thresholding using the entropy of the histogram. Comput. Vis. Graph. Image Process. 29(3), 273–285 (1985)

    Google Scholar 

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

    Google Scholar 

  35. D. Labate, W.Q. Lim, G. Kutyniok, G. Weiss, Sparse multidimensional representation using shearlets, in Wavelets XI, vol. 5914 (International Society for Optics and Photonics, 2005), p. 59140U

  36. T.S. Lee, Image representation using 2D Gabor wavelets. IEEE Trans. Pattern Anal. Mach. Intell. 18(10), 959–971 (1996)

    Google Scholar 

  37. C.H. Li, C.K. Lee, Minimum cross entropy thresholding. Pattern Recognit. 26(4), 617–625 (1993)

    Google Scholar 

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

    Google Scholar 

  39. J. Lin, Divergence measures based on the Shannon entropy. IEEE Trans. Inf. Theory 37(1), 145–151 (1991)

    MathSciNet  MATH  Google Scholar 

  40. Q. Lin, C. Ou, Tsallis entropy and the long-range correlation in image thresholding. Signal Process. 92(12), 2931–2939 (2012)

    Google Scholar 

  41. W. Liu, S. Cao, Y. Chen, Seismic time–frequency analysis via empirical wavelet transform. IEEE Geosci. Remote Sens. Lett. 13(1), 28–32 (2016)

    Google Scholar 

  42. R. Malik, R. Dhir, S.K. Mittal, Remote sensing and landsat image enhancement using multiobjective PSO based local detail enhancement. J. Ambient Intell. Humaniz. Comput. 10, 1–9 (2018)

    Google Scholar 

  43. S.G. Mallat, A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. Mach. Intell. 7, 674–693 (1989)

    MATH  Google Scholar 

  44. M. Masi, A step beyond Tsallis and Rényi entropies. Phys. Lett. A 338(3–5), 217–224 (2005)

    MathSciNet  MATH  Google Scholar 

  45. M. Meilă, Comparing clusterings—an information based distance. J. Multivar. Anal. 98(5), 873–895 (2007)

    MathSciNet  MATH  Google Scholar 

  46. M.S.R. Naidu, P.R. Kumar, K. Chiranjeevi, Shannon and fuzzy entropy based evolutionary image thresholding for image segmentation. Alex. Eng. J. 57(3), 1643–1655 (2018)

    Google Scholar 

  47. F. Nie, P. Zhang, J. Li, D. Ding, A novel generalized entropy and its application in image thresholding. Signal Process. 134, 23–34 (2017)

    Google Scholar 

  48. N. Nikbakhsh, Y. Baleghi, H. Agahi, Maximum mutual information and Tsallis entropy for unsupervised segmentation of tree leaves in natural scenes. Comput. Electron. Agric. 162, 440–449 (2019)

    Google Scholar 

  49. J.C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, P. Bunel, Image analysis by bidimensional empirical mode decomposition. Image Vis. Comput. 21(12), 1019–1026 (2003)

    MATH  Google Scholar 

  50. D. Oliva, M.A. Elaziz, S. Hinojosa, Fuzzy entropy approaches for image segmentation, in Metaheuristic Algorithms for Image Segmentation: Theory and Applications (Springer, Cham, 2019), pp. 141–147

  51. N. Otsu, A threshold selection method from gray-level histograms. IEEE Trans. Syst. Man Cybern. 9(1), 62–66 (1979)

    Google Scholar 

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

    Google Scholar 

  53. P.K. Sahoo, G. Arora, A thresholding method based on two-dimensional Renyi’s entropy. Pattern Recognit. 37(6), 1149–1161 (2004)

    MATH  Google Scholar 

  54. P.K. Sahoo, G. Arora, Image thresholding using two-dimensional Tsallis–Havrda–Charvát entropy. Pattern Recognit. Lett. 27(6), 520–528 (2006)

    Google Scholar 

  55. P.K. Sahoo, S.A.K.C. Soltani, A.K. Wong, A survey of thresholding techniques. Comput. Vis. Graph. Image Process. 41(2), 233–260 (1988)

    Google Scholar 

  56. P. Sahoo, C. Wilkins, J. Yeager, Threshold selection using Renyi’s entropy. Pattern Recognit. 30(1), 71–84 (1997)

    MATH  Google Scholar 

  57. M. Sezgin, B. Sankur, Survey over image thresholding techniques and quantitative performance evaluation. J. Electron. Imaging 13(1), 146–166 (2004)

    Google Scholar 

  58. A. Sheeba, S. Manikandan, Image segmentation using bi-level thresholding, in 2014 International Conference on Electronics and Communication Systems (ICECS) (IEEE, 2014), pp. 1–5

  59. A. K. Bhandari, A. Singh, I. V. Kumar, Spatial context energy curve-based multilevel 3-D Otsu algorithm for image segmentation. IEEE Trans. Syst. Man Cybern. Syst. 1–14 (2019). https://doi.org/10.1109/TSMC.2019.2916876

  60. S. Shubham, A.K. Bhandari, A generalized Masi entropy based efficient multilevel thresholding method for color image segmentation. Multimed. Tools Appl. 78(12), 17197–17238 (2019)

    Google Scholar 

  61. J. Sullivan, S. Carlsson, Recognizing and tracking human action, in European Conference on Computer Vision (Springer, Berlin, 2002), pp. 629–644

  62. W. Tao, H. Jin, L. Liu, Object segmentation using ant colony optimization algorithm and fuzzy entropy. Pattern Recognit. Lett. 28(7), 788–796 (2007)

    Google Scholar 

  63. The Berkeley Segmentation Dataset and Benchmark (2018), https://www2.eecs.berkeley.edu/Research/Projects/CS/vision/bsds/. Accessed 29 Mar 2019

  64. J. Tou, R. Gonzalez, Pattern recognition principles (Addison-Wesley, London, 1974)

    MATH  Google Scholar 

  65. W.H. Tsai, Moment-preserving thresolding: a new approach. Comput. Vis. Graph. Image Process. 29(3), 377–393 (1985)

    Google Scholar 

  66. R. Unnikrishnan, C. Pantofaru, M. Hebert, Toward objective evaluation of image segmentation algorithms. IEEE Trans. Pattern Anal. Mach. Intell. 6, 929–944 (2007)

    Google Scholar 

  67. P. Upadhyay, J.K. Chhabra, Kapur’s entropy based optimal multilevel image segmentation using Crow Search algorithm. Appl. Soft Comput. 105522 (2019). https://doi.org/10.1016/j.asoc.2019.105522

  68. Z. Wang, A.C. Bovik, H.R. Sheikh, E.P. Simoncelli, Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)

    Google Scholar 

  69. Y. Zhang, L. Wu, Optimal multi-level thresholding based on maximum Tsallis entropy via an artificial bee colony approach. Entropy 13(4), 841–859 (2011)

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ashish Kumar Bhandari.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Singh, N., Bhandari, A.K. & Singh, A. Variational Mode Decomposition-Based Multilevel Threshold Selection Scheme for Color Image Segmentation. Circuits Syst Signal Process 39, 3978–4020 (2020). https://doi.org/10.1007/s00034-020-01349-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-020-01349-2

Keywords

Navigation