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

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Abstract

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.

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  1. http://web.mit.edu/persci/people/adelson/checkershadow_illusion.html

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Acknowledgments

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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Authors and Affiliations

  1. GREYC, CNRS UMR 6072, ENSICAEN, Université de Caen, Caen, France

    Jingwei Liang

  2. Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China

    Xiaoqun Zhang

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  1. Jingwei Liang
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Correspondence to Xiaoqun Zhang.

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Liang, J., Zhang, X. Retinex by Higher Order Total Variation \(L^{1}\) Decomposition. J Math Imaging Vis 52, 345–355 (2015). https://doi.org/10.1007/s10851-015-0568-x

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