Simultaneous segmentation and correction model for color medical and natural images with intensity inhomogeneity


In this paper, a new level set formulation that can simultaneously segment and correct color images is proposed by combining the illumination and reflectance estimation (IRE) model, the level set method and the split Bregman method. The advantages of our model are mainly summarized in three aspects. First, our model can effectively extract the intensity change information in the images, regarded as the bias field. Based on the accurate segmentation results, our model can correct the inhomogeneous color images by removing the estimated bias field from the original images. Second, the application of the split Bregman method accelerates the iterative process and computational speed, making our model more efficient. Third, the use of the edge detection function in the energy functional makes it easier for our model to detect the target boundary. Perfectly absorbing the above three advantages, our model is applied to segment color medical and natural images with intensity inhomogeneity. Experimental results demonstrate that our model can accurately segment color images and get satisfactory correction images with intensity homogeneity. In addition, numerical comparison results further indicate that the performance of our model for segmentation and correction is significantly superior to the IRE model.

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

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


  1. 1.

    Bi, L., Kim, J., Kumar, A., Fulham, M., Feng, D.G.: Stacked fully convolutional networks with multi-channel learning: application to medical image segmentation. Visual Comput. 33(6–8), 1061–1071 (2017)

    Article  Google Scholar 

  2. 2.

    Cai, Q., Liu, H.Y., Zhou, S.P., Sun, J.F., Li, J.: An adaptive-scale active contour model for inhomogeneous image segmentation and bias field estimation. Pattern Recognit. 82, 79–93 (2018)

    Article  Google Scholar 

  3. 3.

    Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. Int. J. Comput. Vis. 22(1), 61–79 (1997)

    MATH  Article  Google Scholar 

  4. 4.

    Chan, T.E., Sandberg, B.Y., Vese, L.A.: Active contours without edges for vector-valued images. J. Vis. Commun. Image Represent. 11(2), 130–141 (2000)

    Article  Google Scholar 

  5. 5.

    Chan, T.F., Nikolova, M.: Algorithms for finding global minimizers of image segmentation and denoising models. SIAM J. Appl. Math. 66(5), 1632–1648 (2006)

    MathSciNet  MATH  Article  Google Scholar 

  6. 6.

    Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Trans. Image Process. 10(2), 266–277 (2001)

    MATH  Article  Google Scholar 

  7. 7.

    Feng, C.L., Zhao, D.Z., Huang, M.: Image segmentation and bias correction using local inhomogeneous intensity clustering (LINC): a region-based level set method. Neurocomputing 219, 107–129 (2017)

    Article  Google Scholar 

  8. 8.

    Goldstein, T., Bresson, X., Osher, S.: Geometric applications of the split Bregman method: segmentation and surface reconstruction. J. Sci. Comput. 45(1–3), 272–293 (2010)

    MathSciNet  MATH  Article  Google Scholar 

  9. 9.

    Goldstein, T., Osher, S.: The split Bregman method for L1-regularized problems. SIAM J. Imaging Sci. 2(2), 323–343 (2009)

    MathSciNet  MATH  Article  Google Scholar 

  10. 10.

    Hettiarachchi, R., Peters, J.F.: Voronoi region-based adaptive unsupervised color image segmentation. Pattern Recognit. 65, 119–135 (2017)

    Article  Google Scholar 

  11. 11.

    Kass, M., Witkin, A., Terzopoulos, D.: Snakes: active contour models. Int. J. Comput. Vis. 1(4), 321–331 (1988)

    MATH  Article  Google Scholar 

  12. 12.

    Le, Y., Xu, X.Z., Zha, L., Zhao, W.C., Zhu, Y.Y.: Tumour localisation in ultrasound-guided high-intensity focused ultrasound ablation using improved gradient and direction vector flow. IET Image Process. 9(10), 857–865 (2015)

    Article  Google Scholar 

  13. 13.

    Li, C., Gore, J.C., Davatzikos, C.: Multiplicative intrinsic component optimization (MICO) for MRI bias field estimation and tissue segmentation. Magn. Reson. Imaging 32(7), 913–923 (2014)

    Article  Google Scholar 

  14. 14.

    Li, C., Kao, C.Y., Gore, J.C., Ding, Z.: Minimization of region-scalable fitting energy for image segmentation. IEEE Trans. Image Process. 17(10), 1940–1949 (2008)

    MathSciNet  MATH  Article  Google Scholar 

  15. 15.

    Li, C., Li, F., Kao, C.Y., Xu, C.: Image segmentation with simultaneous illumination and reflectance estimation: an energy minimization approach. In: 2009 IEEE 12th International Conference on Computer Vision (ICCV), Kyoto, Japan, pp. 702–708 (2009)

  16. 16.

    Li, C., Xu, C., Gui, C., Fox, M.D.: Distance regularized level set evolution and its application to image segmentation. IEEE Trans. Image Process. 19(12), 3243–3254 (2010)

    MathSciNet  MATH  Article  Google Scholar 

  17. 17.

    Li, C.M., Huang, R., Ding, Z.H., Gatenby, J.C., Metaxas, D.N., Gore, J.C.: A level set method for image segmentation in the presence of intensity inhomogeneities with application to MRI. IEEE Trans. Image Process. 20(7), 2007–2016 (2011)

    MathSciNet  MATH  Article  Google Scholar 

  18. 18.

    Li, Y., Shen, L.: Skin lesion analysis towards melanoma detection using deep learning network. Sensors 18(2), 322–329 (2018)

    Article  Google Scholar 

  19. 19.

    Min, H., Jia, W., Zhao, Y., Zuo, W.M., Ling, H.B., Luo, Y.T.: LATE: a level-set method based on local approximation of Taylor expansion for segmenting intensity inhomogeneous images. IEEE Trans. Image Process. 27(10), 5016–5031 (2018)

    MathSciNet  MATH  Article  Google Scholar 

  20. 20.

    Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math. 42(5), 577–685 (1989)

    MathSciNet  MATH  Article  Google Scholar 

  21. 21.

    Paulano, F., Jimenez, J.J., Pulido, R.: 3d Segmentation and labeling of fractured bone from ct images. Visual Comput. 30(6–8), 939–948 (2014)

    Article  Google Scholar 

  22. 22.

    Shattuck, D.W., Sandor-Leahy, S.R., Schaper, K.A., Rottenberg, D.A., Leahy, R.M.: Magnetic resonance image tissue classification using a partial volume model. Neuroimage 13(5), 856–876 (2001)

    Article  Google Scholar 

  23. 23.

    Song, L.: Image segmentation based on supervised discriminative learning. Int. J. Pattern Recognit. Artif. Intell. 32(10), 1854027 (2018)

    Article  Google Scholar 

  24. 24.

    Wang, L., Li, C., Sun, Q., Xia, D., Kao, C.Y.: Active contours driven by local and global intensity fitting energy with application to brain MR image segmentation. J. Comput. Med. Imaging Graph. 33(7), 520–531 (2009)

    Article  Google Scholar 

  25. 25.

    Wang, Y.L., Yang, J.F., Yin, W.T., Zhang, Y.: A new alternating minimization algorithm for total variation image reconstruction. SIAM J. Imaging Sci. 1(3), 248–272 (2008)

    MathSciNet  MATH  Article  Google Scholar 

  26. 26.

    Xian, M., Zhang, Y.T., Cheng, H.D., Xu, F., Zhang, B.Y., Ding, J.R.: Automatic breast ultrasound image segmentation: a survey. Pattern Recognit. 79, 340–355 (2018)

    Article  Google Scholar 

  27. 27.

    Xiao, C.X., Gan, J.J., Hu, X.Y.: Fast level set image and video segmentation using new evolution indicator operators. Visual Comput. 29(1), 27–39 (2013)

    Article  Google Scholar 

  28. 28.

    Xing, F.Y., Xie, Y.P., Yang, L.: An automatic learning-based framework for robust nucleus segmentation. IEEE Trans. Med. Imaging 35(2), 550–566 (2016)

    Article  Google Scholar 

  29. 29.

    Xu, C., Prince, J.L.: Snakes, shapes, and gradient vector flow. IEEE Trans. Image Process. 7(3), 359–369 (1998)

    MathSciNet  MATH  Article  Google Scholar 

  30. 30.

    Xu, G., Li, X., Lei, B., Lv, K.: Unsupervised color image segmentation with color-alone feature using region growing pulse coupled neural network. Neurocomputing 306, 1–16 (2018)

    Article  Google Scholar 

  31. 31.

    Yang, Y., Boying, W.: Split Bregman method for minimization of improved active contour model combining local and global information dynamically. J. Math. Anal. Appl. 389(1), 351–366 (2012)

    MathSciNet  MATH  Article  Google Scholar 

  32. 32.

    Yang, Y., Li, C., Kao, C.Y., Osher, S.: Split Bregman method for minimization of region-scalable fitting energy for image segmentation. In: International Symposium on Visual Computing (ISVC). Lecture Notes in Computer Science, vol 6454, pp. 117–128. Springer, Berlin (2010)

    Google Scholar 

  33. 33.

    Yang, Y., Wu, B.: A new and fast multiphase image segmentation model for color images. Math. Probl. Eng. 2012, 494761 (2012)

    MathSciNet  MATH  Google Scholar 

  34. 34.

    Yang, Y., Zhao, Y., Wu, B., Wang, H.: A fast multiphase image segmentation model for gray images. Comput. Math. Appl. 67(8), 1559–1581 (2014)

    MathSciNet  MATH  Article  Google Scholar 

  35. 35.

    Zha, Z.Y., Liu, X., Zhang, X.G., Chen, Y., Tang, L., Bai, Y., Wang, Q., Shang, Z.H.: Compressed sensing image reconstruction via adaptive sparse nonlocal regularization. Visual Comput. 34(1), 117–137 (2018)

    Article  Google Scholar 

  36. 36.

    Zhang, H.Z., Xie, X.H.: Divergence of gradient convolution: deformable segmentation with arbitrary initializations. IEEE Trans. Image Process. 24(11), 3902–3914 (2015)

    MathSciNet  MATH  Article  Google Scholar 

  37. 37.

    Zhang, T.: Optimized fuzzy clustering algorithms for brain MRI image segmentation based on local Gaussian probability and anisotropic weight models. Int. J. Pattern Recognit. Artif. Intell. 32(9), 1857005 (2018)

    MathSciNet  Article  Google Scholar 

  38. 38.

    Zhong, F., Qin, X.Y., Peng, Q.S.: Robust image segmentation against complex color distribution. Visual Comput. 27(6–8), 707–716 (2011)

    Article  Google Scholar 

  39. 39.

    Zhou, Y.F., Pan, X., Wang, W.P., Yin, Y.L., Zhang, C.M.: Superpixels by bilateral geodesic distance. IEEE Trans. Circuits Syst. Video 27(11), 2281–2293 (2017)

    Article  Google Scholar 

Download references


This study was funded by Shenzhen Fundamental Research Plan (No. JCYJ20160505175141489).

Author information



Corresponding author

Correspondence to Yunyun Yang.

Ethics declarations

Conflict of interest

We declare that we have no conflict of interest.

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

Verify currency and authenticity via CrossMark

Cite this article

Yang, Y., Jia, W. & Wu, B. Simultaneous segmentation and correction model for color medical and natural images with intensity inhomogeneity. Vis Comput 36, 717–731 (2020).

Download citation


  • Level set method
  • Intensity inhomogeneity
  • Split Bregman method
  • Image segmentation
  • Correction
  • Color images

Mathematics Subject Classification

  • 90C47
  • 65K10
  • 49M37