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International Journal of Computer Vision

, Volume 83, Issue 1, pp 101–119 | Cite as

Issues About Retinex Theory and Contrast Enhancement

  • Marcelo Bertalmío
  • Vicent Caselles
  • Edoardo Provenzi
Article
First Online:
Received:
Accepted:

Abstract

We present an interpretation of Land’s Retinex theory that we show to be consistent with the original formulation. The proposed model relies on the computation of the expectation value of a suitable random variable weighted with a kernel function, thus the name Kernel-Based Retinex (KBR) for the corresponding algorithm. KBR shares the same intrinsic characteristics of the original Retinex: it can reduce the effect of a color cast and enhance details in low-key images but, since it can only increase pixel intensities, it is not able to enhance over-exposed pictures. Comparing the analytical structure of KBR with that of a recent variational model of color image enhancement, we are able to perform an analysis of the action of KBR on contrast, showing the need to anti-symmetrize its equation in order to produce a two-sided contrast modification, able to enhance both under and over-exposed pictures. The anti-symmetrized KBR equations show clear correspondences with other existing color correction models, in particular ACE, whose relationship with Retinex has always been difficult to clarify. Finally, from an image processing point of view, we mention that both KBR and its antisymmetric version are free from the chromatic noise due to the use of paths in the original Retinex implementation and that they can be suitably approximated in order to reduce their computational complexity from \(\mathcal{O}(N^{2})\) to \(\mathcal{O}(N\log N)\) , being N the number of input pixels.

Keywords

Retinex Contrast enhancement Variational methods Color image processing 
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References

  1. Ambrosio, L., Gigli, N., & Savaré, G. (2005). Gradient flows in metric spaces and in the space of probability measures. In Lectures in mathematics, Basel: Birkhäuser. Google Scholar
  2. Barash, D. (2002). A fundamental relationship between bilateral filtering, adaptive smoothing, and the nonlinear diffusion equation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24, 844–847. CrossRefGoogle Scholar
  3. Bertalmío, M., & Cowan, J. (2009). Implementing the Retinex algorithm with Wilson-Cowan equations, Journal of Physiology, Paris (to appear). Google Scholar
  4. Bertalmío, M., Caselles, V., Provenzi, E., & Rizzi, A. (2007). Perceptual color correction through variational techniques. IEEE Transactions on Image Processing, 16, 1058–1072. CrossRefMathSciNetGoogle Scholar
  5. Blake, A. (1985). Boundary conditions of lightness computation in Mondrian world. Computer Vision, Graphics and Image Processing, 32, 314–327. CrossRefGoogle Scholar
  6. Bressloff, P., Cowan, J., Golubitsky, M., Thomas, P., & Wiener, M. (2002). What geometric visual hallucinations tell us about the visual cortex. Neural Computation, 14(3), 473–491. MATHCrossRefGoogle Scholar
  7. Cooper, T. J., & Baqai, F. A. (2004). Analysis and extensions of the Frankle-McCann Retinex algorithm. Journal of Electronic Imaging, 13, 85–92. CrossRefGoogle Scholar
  8. Frankle, J., & McCann, J. J. (1983). Method and apparatus for lightness imaging. U.S. Patent, 4, 348,336, 1983. Google Scholar
  9. Funt, B., Ciurea, F., & McCann, J. J. (2004). Retinex in MATLAB. Journal of Electronic Imaging, 13(1), 48–57. CrossRefGoogle Scholar
  10. Glasser, L., McKinney, A., Reilly, C., & Schnelle, P. (1958). Cube-root color coordinate system. Journal of the Optical Society of America, 48, 736–740. CrossRefGoogle Scholar
  11. Horn, B. (1974). Determining lightness from an image. Computer Graphics and Image Processing, 3, 277–299. CrossRefGoogle Scholar
  12. Hurlbert, A. (1986). Formal connections between lightness algorithms. Journal of the Optical Society of America A, 3, 1684–1693. CrossRefGoogle Scholar
  13. Jobson, D., Rahman, Z., & Woodell, G. (1997a). A multiscale Retinex for bridging the gap between color images and the human observation of scenes. IEEE Transactions on Image Processing, 6(7), 965–976. CrossRefGoogle Scholar
  14. Jobson, D., Rahman, Z., & Woodell, G. (1997b). Properties and performance of a center/surround Retinex. IEEE Transactions on Image Processing, 6(3), 451–462. CrossRefGoogle Scholar
  15. Kimmel, R., Elad, M., Shaked, D., Keshet, R., & Sobel, I. (2003). A variational framework for Retinex. International Journal of Computer Vision, 52, 7–23. MATHCrossRefGoogle Scholar
  16. Land, E. (1977). The Retinex theory of color vision. Scientific American, 237, 108–128. MathSciNetCrossRefGoogle Scholar
  17. Land, E. (1983). Recent advances in Retinex theory and some implications for cortical computations: Color vision and the natural image. Proceedings of the National Academy Science of the United State of America, 80, 5163–5169. CrossRefGoogle Scholar
  18. Land, E. (1986). An alternative technique for the computation of the designator in the Retinex theory of color vision. Proceedings of the National Academy Science of the United State of America, 83, 3078–3080. CrossRefGoogle Scholar
  19. Land, E., McCann, J. (1971). Lightness and Retinex theory. Journal of the Optical Society of America, 61(1), 1–11. CrossRefGoogle Scholar
  20. Marini, D., & Rizzi, A. (2000). A computational approach to color adaptation effects. Image and Vision Computing, 18, 1005–1014. CrossRefGoogle Scholar
  21. Marr, D. (1974). The computation of lightness by the primate retina. Vision Research, 14(12), 1377–1388. CrossRefGoogle Scholar
  22. McCann, J., McKee, S., & Taylor, T. (1976). Quantitative studies in Retinex theory: a comparison between theoretical predictions and observer responses to the ‘color mondrian’ experiments. Journal of Vision Research, 16, 445–458. CrossRefGoogle Scholar
  23. McCann, J. J. (2004). Capturing a black cat in shade: past and present of Retinex color appearance models. Journal of Electronic Imaging, 13(1), 36–47. CrossRefGoogle Scholar
  24. Palma-Amestoy, R., Provenzi, E., Caselles, V., & Bertalmío, M. (2009). A perceptually inspired variational framework for color enhancement. IEEE Transactions on Pattern Analysis and Machine Intelligence 31(3), 458–474. CrossRefGoogle Scholar
  25. Provenzi, E., De Carli, L., Rizzi, A., & Marini, D. (2005). Mathematical definition and analysis of the Retinex algorithm. Journal of the Optical Society of America A, 22(12), 2613–2621. CrossRefMathSciNetGoogle Scholar
  26. Provenzi, E., Fierro, M., Rizzi, A., De Carli, L., Gadia, D., Marini, D. (2007). Random spray Retinex: a new Retinex implementation to investigate the local properties of the model. IEEE Transactions on Image Processing, 16, 162–171. CrossRefMathSciNetGoogle Scholar
  27. Provenzi, E., Gatta, C., Fierro, M., & Rizzi, A. (2008). A spatially variant white patch and gray world method for color image enhancement driven by local contrast. IEEE Transactions on Pattern Analysis and Machine Intelligence 30(10), 1757–1770. CrossRefGoogle Scholar
  28. Rizzi, A., Gatta, C., & Marini, D. (2003). A new algorithm for unsupervised global and local color correction. Pattern Recognition Letters, 24, 1663–1677. CrossRefGoogle Scholar
  29. Rizzi, A., Gatta, C., & Marini, D. (2004). From Retinex to automatic color equalization: issues in developing a new algorithm for unsupervised color equalization. Journal of Electronic Imaging, 13(1), 75–84. CrossRefGoogle Scholar
  30. Tomasi, C., & Manduchi, R. (1998). Bilateral filtering for gray and color images. In ICCV ’98: Proceedings of the sixth international conference on computer vision, Washington, DC, USA, 1998 (pp. 839–846). IEEE Computer Society, Los Alamitos. Google Scholar
  31. Wilson, H., & Cowan, J. (1972). Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical Journal, 12, 1–24. CrossRefGoogle Scholar
  32. Wilson, H., & Cowan, J. (1973). A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Biological Cybernetics, 13(2), 55–80. Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Marcelo Bertalmío
    • 1
  • Vicent Caselles
    • 1
  • Edoardo Provenzi
    • 1
  1. 1.Departament de Tecnologies de la Informació i les ComunicacionsUniversitat Pompeu FabraBarcelonaSpain

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