Journal of Mathematical Imaging and Vision

, Volume 52, Issue 3, pp 345–355 | Cite as

Retinex by Higher Order Total Variation \(L^{1}\) Decomposition

  • Jingwei Liang
  • Xiaoqun Zhang


In this paper, we propose a reflectance and illumination decomposition model for the Retinex problem via high-order total variation and \(L^{1}\) decomposition. Based on the observation that illumination varies smoother than reflectance, we propose a convex variational model which can effectively decompose the gradient field of images into salient edges and relatively smoother illumination field through the first- and second-order total variation regularizations. The proposed model can be efficiently solved by a primal–dual splitting method. Numerical experiments on both grayscale and color images show the strength of the proposed model with applications to Retinex illusions, medical image bias field removal, and color image shadow correction.


Retinex Image decomposition High-order total variation Shadow correction 



We would like to thank the authors of [18] and [22] for sharing their source codes, and the reviewers of this manuscript for their helpful comments and suggestions. The work of X. Zhang was supported by NSFC11101277, NSFC91330102 and 973 program (#2015CB856000).


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.GREYC, CNRS UMR 6072, ENSICAEN, Université de CaenCaenFrance
  2. 2.Department of Mathematics, MOE-LSC, and Institute of Natural SciencesShanghai Jiao Tong UniversityShanghaiChina

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