Journal of Mathematical Imaging and Vision

, Volume 61, Issue 9, pp 1329–1341 | Cite as

A Novel Total Generalized Variation Model for Image Dehazing

  • Yanan GuEmail author
  • Xiaoping Yang
  • Yiming Gao


In this paper, we propose a new variational model for removing haze from a single input image. The proposed model combines two total generalized variation (TGV) regularizations, which are related to the image intensity and the transmission map, respectively, to build an optimization problem. Actually, TGV functionals are more appropriate for describing a natural color image and its transmission map with slanted plane. By minimizing the energy functional with double-TGV regularizations, we obtain the final haze-free image and the refined transmission map simultaneously instead of the general two-step framework. The existence and uniqueness of solutions to the proposed variational model are further obtained. Moreover, the variational model can be solved in a unified way by realizing a primal–dual method for associated saddle-point problems. A number of experimental results on natural hazy images are presented to demonstrate our superior performance, in comparison with some state-of-the-art methods in terms of the subjective and objective visual quality assessments. Compared with the total variation-based models, the proposed model can generate a haze-free image with less staircasing artifacts in the slanted plane and more details in the remote scene of an input image.


Dehaze Atmospheric scatting model TGV Dark channel prior 



The funding was provided by National Natural Science Foundation of China (Grant Nos. 11531005, 91330101).


  1. 1.
    Nayar, S.K., Narasimhan, S.G.: Vision in bad weather. Proc. IEEE Conf. Comput. Vis. 2, 820–827 (1999)Google Scholar
  2. 2.
    Narasimhan, S.G., Nayar, S.K.: Contrast restoration of weather degraded images. IEEE Trans. Pattern Anal. Mach. Learn. 25(6), 713–724 (2003)CrossRefGoogle Scholar
  3. 3.
    Tan, R.T.: Visibility in bad weather from a single image. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–8 (2008)Google Scholar
  4. 4.
    Fattal, R.: Single image dehazing. ACM Trans. Graph. 27(3), 72:1–72:10 (2008)CrossRefGoogle Scholar
  5. 5.
    He, K., Sun, J., Tang, X.: Single image haze removal using dark channel prior. IEEE Trans. Pattern Anal. Mach. Intell. 33(12), 2341–2353 (2011)CrossRefGoogle Scholar
  6. 6.
    Tarel, J.-P., Hautière, N.: Fast visibility restoration from a single color or gray level image. In: Proceedings of IEEE 12th International Conference on Computer Vision, pp. 2201–2208 (2009)Google Scholar
  7. 7.
    Meng, G., Wang, Y., Duan, J., Xiang, S., Pan, C.: Efficient image dehazing with boundary constraint and contextual regularization. In: Proceedings of IEEE International Conference on Computer Vision, pp. 617–624 (2013)Google Scholar
  8. 8.
    Zhu, Q., Mai, J., Shao, L.: A fast single image haze removal algorithm using color attenuation prior. IEEE Trans. Image Process. 24(11), 3522–3533 (2015)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Fang, F., Li, F., Zeng, T.: Single image dehazing and denoising: a fast variational approach. SIAM J. Imaging Sci. 7(2), 969–996 (2014)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Chen, C., Do, Minh N., Wang, J.: Robust image and video dehazing with visual artifact suppression via gradient residual minimization. ECCV 9906, 576–591 (2016)Google Scholar
  11. 11.
    Cai, B., Xu, X., Jia, K., Qing, C., Tao, D.: DehazeNet: an end-to-end system for single image haze removal. IEEE Trans. Image Process. 25(11), 5187–5198 (2016)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Ren, W., Liu, S., Zhang, H., Pan, J., Cao, X., Yang, M.: Single image dehazing via multi-scale convolutional neural networks. Comput. Vision ECCV 9906, 154–169 (2016)Google Scholar
  13. 13.
    Bredies, K.: Recovering piecewise smooth multichannel images by minimization of convex functionals with total generalized variation penalty. Lecture Notes Comput. Sci. 8293, 44–77 (2014)CrossRefGoogle Scholar
  14. 14.
    Berman, D., Avidan, S., Treibitz, T.: Non-local image dehazing. In: CVPR, pp. 1674–1682 (2016)Google Scholar
  15. 15.
    Li, B., Peng, X., Wang, Z., Xu, J., Feng, D.: An all-in-one network for dehazing and beyond. In: ICCV (2017)Google Scholar
  16. 16.
    Zhang, H., Patel, V.M.: Densely connected pyramid dehazing network. In: CVPR (2018)Google Scholar
  17. 17.
    Xu, Y., Wen, J., Fei, L., Zhang, Z.: Review of video and image defogging algorithms and related studies on image restoration and enhancement. IEEE Access 4, 165–188 (2017)CrossRefGoogle Scholar
  18. 18.
    Yu, X., Xiao, C., Deng, M., Peng, L.: A classification algorithm to distinguish image as haze or non-haze. In: Proceedings of IEEE International Conference on Image Graphics, pp. 286–289 (2011)Google Scholar
  19. 19.
    Jobson, D.J., Rahman, Z.-U., Woodell, G.A., Hines, G.D.: A comparison of visual statistics for the image enhancement of FORESITE aerial images with those of major image classes. In: Proceedings of SPIE, pp. 624601-1–624601-8 (2006)Google Scholar
  20. 20.
    Ma, Z., Jie, W.: Single-scale retinex sea fog removal algorithm fused the edge information. J. Comput. Aided Des. Comput. Graph. 27(2), 217–225 (2015)Google Scholar
  21. 21.
    Tripathi, A.K., Mukhopadhyay, S.: Removal of fog from images: a review. IETE Tech. Rev. 29(2), 148–156 (2012)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of ScienceNanjing University of Science and TechnologyNanjingPeople’s Republic of China
  2. 2.Department of MathematicsNanjing UniversityNanjingPeople’s Republic of China

Personalised recommendations