The Visual Computer

, Volume 33, Issue 3, pp 355–369 | Cite as

Intrinsic image estimation using near-\(L_0\) sparse optimization

  • Shouhong Ding
  • Bin Sheng
  • Zhifeng Xie
  • Lizhuang MaEmail author
Original Article


The objective of intrinsic images estimation is to decompose an input image into its intrinsic shading and reflectance components. This is a well-known under-constrained problem that has long been an open challenge. This paper proposes a novel approach for automatic intrinsic images decomposition that uses a new reflectance sparsity prior. On the basis of the observation that the reflectance of natural objects is commonly piecewise constant, we formalize this constraint on the entire reflectance image using the \(L_0\) sparse loss function that enforces the variation in reflectance images to be of high-frequency and sparse. This new sparsity constraint significantly improves the quality of Retinex intrinsic images estimation. It also functions effectively by combining a class of global sparsity priors on reflectance. Experimental results on MIT benchmark dataset as well as various real-world images and synthetic images demonstrate the effectiveness and versatility of our approach.


Intrinsic image decomposition Reflectance Shading \(L_0\) sparsity 



The work is supported by the National Natural Science Foundation of China (Nos. 61133009, 61472245, 61572316 and 61303093), National High-tech R&D Program of China (863 Program) (Grant No. 2015AA011604). The authors would also like to thank the reviewers for their helpful suggestions.

Supplementary material

371_2015_1205_MOESM1_ESM.pdf (86 mb)
Supplementary material 1 (pdf 88093 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Shouhong Ding
    • 1
  • Bin Sheng
    • 1
  • Zhifeng Xie
    • 2
  • Lizhuang Ma
    • 1
    Email author
  1. 1.Department of Computer Science and Engineering (CSE)Shanghai Jiao Tong UniversityShanghaiChina
  2. 2.Department of Film and Television EngineeringShanghai UniversityShanghaiChina

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