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.
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References
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.
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.
Bertalmío, M., & Cowan, J. (2009). Implementing the Retinex algorithm with Wilson-Cowan equations, Journal of Physiology, Paris (to appear).
Bertalmío, M., Caselles, V., Provenzi, E., & Rizzi, A. (2007). Perceptual color correction through variational techniques. IEEE Transactions on Image Processing, 16, 1058–1072.
Blake, A. (1985). Boundary conditions of lightness computation in Mondrian world. Computer Vision, Graphics and Image Processing, 32, 314–327.
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.
Cooper, T. J., & Baqai, F. A. (2004). Analysis and extensions of the Frankle-McCann Retinex algorithm. Journal of Electronic Imaging, 13, 85–92.
Frankle, J., & McCann, J. J. (1983). Method and apparatus for lightness imaging. U.S. Patent, 4, 348,336, 1983.
Funt, B., Ciurea, F., & McCann, J. J. (2004). Retinex in MATLAB. Journal of Electronic Imaging, 13(1), 48–57.
Glasser, L., McKinney, A., Reilly, C., & Schnelle, P. (1958). Cube-root color coordinate system. Journal of the Optical Society of America, 48, 736–740.
Horn, B. (1974). Determining lightness from an image. Computer Graphics and Image Processing, 3, 277–299.
Hurlbert, A. (1986). Formal connections between lightness algorithms. Journal of the Optical Society of America A, 3, 1684–1693.
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.
Jobson, D., Rahman, Z., & Woodell, G. (1997b). Properties and performance of a center/surround Retinex. IEEE Transactions on Image Processing, 6(3), 451–462.
Kimmel, R., Elad, M., Shaked, D., Keshet, R., & Sobel, I. (2003). A variational framework for Retinex. International Journal of Computer Vision, 52, 7–23.
Land, E. (1977). The Retinex theory of color vision. Scientific American, 237, 108–128.
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.
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.
Land, E., McCann, J. (1971). Lightness and Retinex theory. Journal of the Optical Society of America, 61(1), 1–11.
Marini, D., & Rizzi, A. (2000). A computational approach to color adaptation effects. Image and Vision Computing, 18, 1005–1014.
Marr, D. (1974). The computation of lightness by the primate retina. Vision Research, 14(12), 1377–1388.
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.
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.
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.
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.
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.
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.
Rizzi, A., Gatta, C., & Marini, D. (2003). A new algorithm for unsupervised global and local color correction. Pattern Recognition Letters, 24, 1663–1677.
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.
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.
Wilson, H., & Cowan, J. (1972). Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical Journal, 12, 1–24.
Wilson, H., & Cowan, J. (1973). A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Biological Cybernetics, 13(2), 55–80.
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Bertalmío, M., Caselles, V. & Provenzi, E. Issues About Retinex Theory and Contrast Enhancement. Int J Comput Vis 83, 101–119 (2009). https://doi.org/10.1007/s11263-009-0221-5
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DOI: https://doi.org/10.1007/s11263-009-0221-5