Abstract
Retinex theory addresses the problem of separating the illumination from the reflectance in a given image and thereby compensating for non-uniform lighting. This is in general an ill-posed problem. In this paper we propose a variational model for the Retinex problem that unifies previous methods. Similar to previous algorithms, it assumes spatial smoothness of the illumination field. In addition, knowledge of the limited dynamic range of the reflectance is used as a constraint in the recovery process. A penalty term is also included, exploiting a-priori knowledge of the nature of the reflectance image. The proposed formulation adopts a Bayesian view point of the estimation problem, which leads to an algebraic regularization term, that contributes to better conditioning of the reconstruction problem.
Based on the proposed variational model, we show that the illumination estimation problem can be formulated as a Quadratic Programming optimization problem. An efficient multi-resolution algorithm is proposed. It exploits the spatial correlation in the reflectance and illumination images. Applications of the algorithm to various color images yield promising results.
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References
Barnard, K. and Funt, B. 1998. Investigations into multy-scale Retinex, In Proc. Color Imaging in Multimedia 98, Derby.
Bertsekas, D.P. 1995. Non-Linear Programming. Athena Scientific: Belmont, MA.
Blake, A. 1985. Boundary conditions of lightness computation in mondrian world. Computer Vision Graphics and Image Processing, 32:314–327.
Blake, A. and Zisserman, A. 1987. Visual Reconstruction. The MIT Press: Cambridge, MA.
Bornemann, F. and Deuflhard, P. 1996. The cascadic multigrid method for elliptic problems. Numerische Mathematik, 75:135– 152.
Brainard, D.H. and Wandell, B. 1986. Analysis of the Retinex theory of color vision. J. Opt. Soc. Am. A, 3:1651–1661.
Faugeras, O.D. 1979. Digital image color processing within the framework of a human visual system. IEEE Trans. on ASSP, 27:380–393.
Frankle, J. and McCann, J. 1983. Method and apparatus for lightness imaging, US Patent no. 4, 384,336.
Funt, B.V., Ciurea, F., and McCann, J. 2000. Retinex in Matlab. In Proc. of IS&T/SID Eighth Color Imaging Conference, pp. 112– 121.
Funt, B.V., Drew, M.S., and Brockington, M. 1992. Recovering shading from color images. In Proc. European Conference on Computer Vision (ECCV'92), pp. 124–132.
Geman, S. and Geman, D. 1984. Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images. IEEE Trans. on Pattern Analysis ans Machine, 6:721–741.
Horn, B.K.P. 1974. Determining lightness from an image. Computer Graphics and Image Processing, 3:277–299.
Jobson, D.J., Rahman, Z., and Woodell, G.A. 1997a. Properties and performance of the center/surround Retinex. IEEE Trans. on Image Proc., 6:451–462.
Jobson, D.J., Rahman, Z., and Woodell, G.A. 1997b. A multiscale Retinex for bridging the gap between color images and the human observation of scenes. IEEE Trans. on Image Proc., 6.
Kimmel, R., Elad, M., Shaked, D., Keshet, R., and Sobel, I. 1999. A variational framework for Retinex. Hewlett Packard Laboratories TR no. HPL-1999-151.
Lagendijk, R.L. and Biemond, J. 1991. Iterative Identification and Restoration of Images. Kluwer Academic Publishing: Boston, MA.
Land, E.H. 1977. The Retinex theory of color vision. Sci. Amer., 237:108–128.
Land, E.H. 1983. Recent advances in the Retinex theory and some implications for cortical computations: Color vision and the natural image. Proc. Nat. Acad. Sci. USA, 80:5163–5169.
Land, E.H. 1986. An alternative technique for the computation of the designator in the Retinex theory of color vision. Proc. Nat. Acad. Sci. USA, 83:3078–3080.
Land, E.H. and McCann, J.J. 1971. Lightness and the retinex theory. J. Opt. Soc. Am., 61:1–11.
Luenberger, D.G. 1987. Linear and Non-Linear Programming. 2nd edn. Addison-Wesley: Menlo-Park, CA.
Marroquin, J., Mitter, J., and Poggio, T. 1987. Probabilistic solution for ill-posed problems in computational vision. J. of the American Statistical Assoc., 82:76–89.
McCann, J. 1999. Lessons learned from mondrians applied to real images and color gamuts. In Proc. IS&T/SID 7th Color Imaging Conference, pp. 1–8.
Oppenheim, A.V. and Schafer, R.W. 1975. Digital Signal Processing. Prentice Hall: NJ.
Papoulis, A. 1991. Probability, Random Variables, and Stochastic Processes. 3rd edn. McGraw-Hill: New York, pp. 345–346.
Stockham Jr., T.G. 1972. Image processing in the context of a visual model. Proc. of the IEEE, 60:828–842.
Terzopoulos, D. 1986. Image analysis using multigrid relaxation methods. IEEE Trans. on PAMI, 8:129–139.
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Kimmel, R., Elad, M., Shaked, D. et al. A Variational Framework for Retinex. International Journal of Computer Vision 52, 7–23 (2003). https://doi.org/10.1023/A:1022314423998
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DOI: https://doi.org/10.1023/A:1022314423998