Abstract

We present a detailed mathematical analysis of the original Retinex algorithm due to Land and McCann [J. Opt. Soc. Am. 61, 1 (1071) ]. To this end, we propose an analytic formula that describes the algorithm behavior. More than one Retinex version (e.g., with and without threshold) is examined. The behavior of Retinex varying the number of paths is predicted, and its recursive iterations are mathematically analyzed using the formula. The mathematical setting presented serves as a common ground for the various Retinex implementations. Its validity is confirmed by the tests on images that we have performed.

© 2005 Optical Society of America

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  1. E. Land, J. J. McCann, “Lightness and Retinex theory,” J. Opt. Soc. Am. 61, 1–11 (1971).
    [CrossRef] [PubMed]
  2. J. J. McCann, S. P. McKee, T. H. Taylor, “Quantitative studies in Retinex theory. A comparison between theoretical predictions and observer responses to the ‘color mondrian’ experiments,” Vision Res. 16, 445–458 (1976).
    [CrossRef]
  3. D. H. Brainard, B. A. Wandell, “Analysis of the Retinex theory of color vision,” J. Opt. Soc. Am. A 3, 1651–1661 (1986).
    [CrossRef] [PubMed]
  4. R. A. Young, “Color vision and the Retinex theory,” Science 238, 1731–1732 (1987).
    [CrossRef] [PubMed]
  5. A. Moore, J. Allman, R. Goodman, “A real-time neural system for color constancy,” IEEE Trans. Neural Netw. 2, 237–247 (1991).
    [CrossRef] [PubMed]
  6. D. J. Jobson, Z. Rahman, G. A. Woodell, “A multiscale Retinex for bridging the gap between color images and the human observation of scenes,” IEEE Trans. Image Process. 6, 965–976 (1997).
    [CrossRef] [PubMed]
  7. D. J. Jobson, Z. Rahman, G. A. Woodell, “Properties and performance of a center/surround retinex,” IEEE Trans. Image Process. 6, 451–462 (1997).
    [CrossRef] [PubMed]
  8. K. Barnard, B. Funt, “Investigations into multi-scale Retinex,” Vision and Technology (Wiley, 1999), pp. 9–17.
  9. S. O. Huck, C. L. Fales, R. E. Davis, R. Alter-Gartenberg, “Visual communication with Retinex coding,” Appl. Opt. 39, 1711–1730 (2000).
    [CrossRef]
  10. D. Marini, A. Rizzi, “A computational approach to color adaptation effects,” Image Vis. Comput. 18, 1005–1014 (2000).
    [CrossRef]
  11. J. D. Cowan, P. C. Bressloff, “Visual cortex and the Retinex algorithm,” in Human Vision and Electronic Imaging VIIB. E. Rogowitz and N. T. Pappas, eds., Proc. SPIE4662, 278–285 (2002).
  12. G. D. Finlayson, S. D. Hordley, M. S. Drew, “Removing shadows from images using retinex,” in Proceedings of the IS&T/SID Tenth Color Image Conference: Color Science and Engineering System Technology (Society for Information Display, 2002), pp. 73–79.
  13. A. C. Hurlbert, C. J. Wolf, “Contribution of local and global cone-contrasts to color appearance: a Retinex-like model,” in Human Vision and Electronic Imaging VII, B. E. Rogowitz and N. T. Pappas, eds., Proc. SPIE4662, 286–297 (2002).
  14. M. Pilu, S. Pollard, “A light-weight text image processing method for handheld embedded cameras,” in Proceedings of the British Machine Vision Conference, (British Machine Vision Association, http://www.cmp.uea.uk/research/bmvc/; School of Information Systems, University of East Anglia, Norwich, UK, 2002), pp. 547–556.
  15. A. Rizzi, D. Marini, L. De Carli, “LUT and multilevel Brownian Retinex colour correction,” Mach. Graphics Vision 11(2/3), 153–168 (2002).
  16. R. Kimmel, M. Elad, “A variational frame - work for Retinex,” Int. J. Comput. Vis. 52, 7–23 (2003).
    [CrossRef]
  17. G. Ramponi, L. Tenze, S. Carrato, S. Marsi, “Nonlinear contrast enhancement based on the Retinex approach,” in Image Processing: Algorithms and Systems II, E. Dougherty, J. T. Astola, and K. O. Egiazarian, eds., Proc. SPIE5014, 169–177 (2003).
  18. F. Ciurea, B. Funt, “Tuning Retinex parameters,” J. Electron. Imaging 13, 58–64 (2004).
    [CrossRef]
  19. T. J. Cooper, F. A. Baqai, “Analysis and extensions of the Frankle–McCann Retinex algorithm,” J. Electron. Imaging 13, 85–92 (2004).
    [CrossRef]
  20. B. Funt, F. Ciurea, J. J. McCann, “Retinex in Matlab,” J. Electron. Imaging 13, 48–57 (2004).
    [CrossRef]
  21. J. J. McCann, “Capturing a black cat in shade: past and present of Retinex color appearance models,” J. Electron. Imaging 13, 36–47 (2004).
    [CrossRef]
  22. L. Meylan, S. E. Süsstrunk, “Bio-inspired image enhancement for natural color images,” in Human Vision and Electronic Imaging IX, B. E. Roqowritz and T. N. Pappas, eds., Proc. SPIE5292, 46–56 (2004).
  23. N. Moroney, I. Tastl, “Comparison of Retinex and iCAM for scene rendering,” J. Electron. Imaging 13, 139–145 (2004).
    [CrossRef]
  24. Z. Rahman, D. J. Jobson, G. A. Woodell, “Retinex processing for automatic image enhancement,” J. Electron. Imaging 13, 100–110 (2004).
    [CrossRef]
  25. H. K. Rising, “Analysis and generalization of Retinex by recasting the algorithm in wavelets,” J. Electron. Imaging 13, 93–99 (2004).
    [CrossRef]
  26. A. Rizzi, C. Gatta, B. Piacentini, M. Fierro, D. Marini, “Human-visual-system-inspired tone mapping algorithm for HDR images,” in Human Vision Electronic Imaging IX, B. E. Rogowitz and T. N. Pappas, eds., Proc. SPIE5292, 57–68 (2004).
  27. A. Rizzi, C. Gatta, D. Marini, “From Retinex to automatic color equalization: issues in developing a new algorithm for unsupervised color equalization,” J. Electron. Imaging 13, 75–84 (2004).
    [CrossRef]
  28. R. Sobol, “Improving the Retinex algorithm for rendering wide dynamic range photographs,” J. Electron. Imaging 13, 65–74 (2004).
    [CrossRef]
  29. E. Land, “The Retinex theory of color vision,” Sci. Am. March 1977, pp. 2–17.
  30. E. Land, “Recent advances in retinex theory and some implications for cortical computations: color vision and the natural image,” Proc. Natl. Acad. Sci. U.S.A. 80, 5163–5169 (1983).
    [CrossRef] [PubMed]
  31. J. Frankle, J. J. McCann, “Method and apparatus for lightness imaging,” U.S. Patent 4,348,336 May 17, 1983.
  32. E. Land, “An alternative technique for the computation of the designator in the retinex theory of color vision,” Proc. Natl. Acad. Sci. U.S.A. 83, 3078–3080 (1986).
    [CrossRef] [PubMed]
  33. J. J. McCann and 25 other authors, “Special session on Retinex at 40,” J. Electron. Imaging 13, 6–145 (2004).
    [CrossRef]

2004 (10)

F. Ciurea, B. Funt, “Tuning Retinex parameters,” J. Electron. Imaging 13, 58–64 (2004).
[CrossRef]

T. J. Cooper, F. A. Baqai, “Analysis and extensions of the Frankle–McCann Retinex algorithm,” J. Electron. Imaging 13, 85–92 (2004).
[CrossRef]

B. Funt, F. Ciurea, J. J. McCann, “Retinex in Matlab,” J. Electron. Imaging 13, 48–57 (2004).
[CrossRef]

J. J. McCann, “Capturing a black cat in shade: past and present of Retinex color appearance models,” J. Electron. Imaging 13, 36–47 (2004).
[CrossRef]

N. Moroney, I. Tastl, “Comparison of Retinex and iCAM for scene rendering,” J. Electron. Imaging 13, 139–145 (2004).
[CrossRef]

Z. Rahman, D. J. Jobson, G. A. Woodell, “Retinex processing for automatic image enhancement,” J. Electron. Imaging 13, 100–110 (2004).
[CrossRef]

H. K. Rising, “Analysis and generalization of Retinex by recasting the algorithm in wavelets,” J. Electron. Imaging 13, 93–99 (2004).
[CrossRef]

A. Rizzi, C. Gatta, D. Marini, “From Retinex to automatic color equalization: issues in developing a new algorithm for unsupervised color equalization,” J. Electron. Imaging 13, 75–84 (2004).
[CrossRef]

R. Sobol, “Improving the Retinex algorithm for rendering wide dynamic range photographs,” J. Electron. Imaging 13, 65–74 (2004).
[CrossRef]

J. J. McCann and 25 other authors, “Special session on Retinex at 40,” J. Electron. Imaging 13, 6–145 (2004).
[CrossRef]

2003 (1)

R. Kimmel, M. Elad, “A variational frame - work for Retinex,” Int. J. Comput. Vis. 52, 7–23 (2003).
[CrossRef]

2002 (1)

A. Rizzi, D. Marini, L. De Carli, “LUT and multilevel Brownian Retinex colour correction,” Mach. Graphics Vision 11(2/3), 153–168 (2002).

2000 (2)

S. O. Huck, C. L. Fales, R. E. Davis, R. Alter-Gartenberg, “Visual communication with Retinex coding,” Appl. Opt. 39, 1711–1730 (2000).
[CrossRef]

D. Marini, A. Rizzi, “A computational approach to color adaptation effects,” Image Vis. Comput. 18, 1005–1014 (2000).
[CrossRef]

1997 (2)

D. J. Jobson, Z. Rahman, G. A. Woodell, “A multiscale Retinex for bridging the gap between color images and the human observation of scenes,” IEEE Trans. Image Process. 6, 965–976 (1997).
[CrossRef] [PubMed]

D. J. Jobson, Z. Rahman, G. A. Woodell, “Properties and performance of a center/surround retinex,” IEEE Trans. Image Process. 6, 451–462 (1997).
[CrossRef] [PubMed]

1991 (1)

A. Moore, J. Allman, R. Goodman, “A real-time neural system for color constancy,” IEEE Trans. Neural Netw. 2, 237–247 (1991).
[CrossRef] [PubMed]

1987 (1)

R. A. Young, “Color vision and the Retinex theory,” Science 238, 1731–1732 (1987).
[CrossRef] [PubMed]

1986 (2)

D. H. Brainard, B. A. Wandell, “Analysis of the Retinex theory of color vision,” J. Opt. Soc. Am. A 3, 1651–1661 (1986).
[CrossRef] [PubMed]

E. Land, “An alternative technique for the computation of the designator in the retinex theory of color vision,” Proc. Natl. Acad. Sci. U.S.A. 83, 3078–3080 (1986).
[CrossRef] [PubMed]

1983 (1)

E. Land, “Recent advances in retinex theory and some implications for cortical computations: color vision and the natural image,” Proc. Natl. Acad. Sci. U.S.A. 80, 5163–5169 (1983).
[CrossRef] [PubMed]

1976 (1)

J. J. McCann, S. P. McKee, T. H. Taylor, “Quantitative studies in Retinex theory. A comparison between theoretical predictions and observer responses to the ‘color mondrian’ experiments,” Vision Res. 16, 445–458 (1976).
[CrossRef]

1971 (1)

Allman, J.

A. Moore, J. Allman, R. Goodman, “A real-time neural system for color constancy,” IEEE Trans. Neural Netw. 2, 237–247 (1991).
[CrossRef] [PubMed]

Alter-Gartenberg, R.

Baqai, F. A.

T. J. Cooper, F. A. Baqai, “Analysis and extensions of the Frankle–McCann Retinex algorithm,” J. Electron. Imaging 13, 85–92 (2004).
[CrossRef]

Barnard, K.

K. Barnard, B. Funt, “Investigations into multi-scale Retinex,” Vision and Technology (Wiley, 1999), pp. 9–17.

Brainard, D. H.

Bressloff, P. C.

J. D. Cowan, P. C. Bressloff, “Visual cortex and the Retinex algorithm,” in Human Vision and Electronic Imaging VIIB. E. Rogowitz and N. T. Pappas, eds., Proc. SPIE4662, 278–285 (2002).

Carrato, S.

G. Ramponi, L. Tenze, S. Carrato, S. Marsi, “Nonlinear contrast enhancement based on the Retinex approach,” in Image Processing: Algorithms and Systems II, E. Dougherty, J. T. Astola, and K. O. Egiazarian, eds., Proc. SPIE5014, 169–177 (2003).

Ciurea, F.

F. Ciurea, B. Funt, “Tuning Retinex parameters,” J. Electron. Imaging 13, 58–64 (2004).
[CrossRef]

B. Funt, F. Ciurea, J. J. McCann, “Retinex in Matlab,” J. Electron. Imaging 13, 48–57 (2004).
[CrossRef]

Cooper, T. J.

T. J. Cooper, F. A. Baqai, “Analysis and extensions of the Frankle–McCann Retinex algorithm,” J. Electron. Imaging 13, 85–92 (2004).
[CrossRef]

Cowan, J. D.

J. D. Cowan, P. C. Bressloff, “Visual cortex and the Retinex algorithm,” in Human Vision and Electronic Imaging VIIB. E. Rogowitz and N. T. Pappas, eds., Proc. SPIE4662, 278–285 (2002).

Davis, R. E.

De Carli, L.

A. Rizzi, D. Marini, L. De Carli, “LUT and multilevel Brownian Retinex colour correction,” Mach. Graphics Vision 11(2/3), 153–168 (2002).

Drew, M. S.

G. D. Finlayson, S. D. Hordley, M. S. Drew, “Removing shadows from images using retinex,” in Proceedings of the IS&T/SID Tenth Color Image Conference: Color Science and Engineering System Technology (Society for Information Display, 2002), pp. 73–79.

Elad, M.

R. Kimmel, M. Elad, “A variational frame - work for Retinex,” Int. J. Comput. Vis. 52, 7–23 (2003).
[CrossRef]

Fales, C. L.

Fierro, M.

A. Rizzi, C. Gatta, B. Piacentini, M. Fierro, D. Marini, “Human-visual-system-inspired tone mapping algorithm for HDR images,” in Human Vision Electronic Imaging IX, B. E. Rogowitz and T. N. Pappas, eds., Proc. SPIE5292, 57–68 (2004).

Finlayson, G. D.

G. D. Finlayson, S. D. Hordley, M. S. Drew, “Removing shadows from images using retinex,” in Proceedings of the IS&T/SID Tenth Color Image Conference: Color Science and Engineering System Technology (Society for Information Display, 2002), pp. 73–79.

Frankle, J.

J. Frankle, J. J. McCann, “Method and apparatus for lightness imaging,” U.S. Patent 4,348,336 May 17, 1983.

Funt, B.

F. Ciurea, B. Funt, “Tuning Retinex parameters,” J. Electron. Imaging 13, 58–64 (2004).
[CrossRef]

B. Funt, F. Ciurea, J. J. McCann, “Retinex in Matlab,” J. Electron. Imaging 13, 48–57 (2004).
[CrossRef]

K. Barnard, B. Funt, “Investigations into multi-scale Retinex,” Vision and Technology (Wiley, 1999), pp. 9–17.

Gatta, C.

A. Rizzi, C. Gatta, D. Marini, “From Retinex to automatic color equalization: issues in developing a new algorithm for unsupervised color equalization,” J. Electron. Imaging 13, 75–84 (2004).
[CrossRef]

A. Rizzi, C. Gatta, B. Piacentini, M. Fierro, D. Marini, “Human-visual-system-inspired tone mapping algorithm for HDR images,” in Human Vision Electronic Imaging IX, B. E. Rogowitz and T. N. Pappas, eds., Proc. SPIE5292, 57–68 (2004).

Goodman, R.

A. Moore, J. Allman, R. Goodman, “A real-time neural system for color constancy,” IEEE Trans. Neural Netw. 2, 237–247 (1991).
[CrossRef] [PubMed]

Hordley, S. D.

G. D. Finlayson, S. D. Hordley, M. S. Drew, “Removing shadows from images using retinex,” in Proceedings of the IS&T/SID Tenth Color Image Conference: Color Science and Engineering System Technology (Society for Information Display, 2002), pp. 73–79.

Huck, S. O.

Hurlbert, A. C.

A. C. Hurlbert, C. J. Wolf, “Contribution of local and global cone-contrasts to color appearance: a Retinex-like model,” in Human Vision and Electronic Imaging VII, B. E. Rogowitz and N. T. Pappas, eds., Proc. SPIE4662, 286–297 (2002).

Jobson, D. J.

Z. Rahman, D. J. Jobson, G. A. Woodell, “Retinex processing for automatic image enhancement,” J. Electron. Imaging 13, 100–110 (2004).
[CrossRef]

D. J. Jobson, Z. Rahman, G. A. Woodell, “Properties and performance of a center/surround retinex,” IEEE Trans. Image Process. 6, 451–462 (1997).
[CrossRef] [PubMed]

D. J. Jobson, Z. Rahman, G. A. Woodell, “A multiscale Retinex for bridging the gap between color images and the human observation of scenes,” IEEE Trans. Image Process. 6, 965–976 (1997).
[CrossRef] [PubMed]

Kimmel, R.

R. Kimmel, M. Elad, “A variational frame - work for Retinex,” Int. J. Comput. Vis. 52, 7–23 (2003).
[CrossRef]

Land, E.

E. Land, “An alternative technique for the computation of the designator in the retinex theory of color vision,” Proc. Natl. Acad. Sci. U.S.A. 83, 3078–3080 (1986).
[CrossRef] [PubMed]

E. Land, “Recent advances in retinex theory and some implications for cortical computations: color vision and the natural image,” Proc. Natl. Acad. Sci. U.S.A. 80, 5163–5169 (1983).
[CrossRef] [PubMed]

E. Land, J. J. McCann, “Lightness and Retinex theory,” J. Opt. Soc. Am. 61, 1–11 (1971).
[CrossRef] [PubMed]

E. Land, “The Retinex theory of color vision,” Sci. Am. March 1977, pp. 2–17.

Marini, D.

A. Rizzi, C. Gatta, D. Marini, “From Retinex to automatic color equalization: issues in developing a new algorithm for unsupervised color equalization,” J. Electron. Imaging 13, 75–84 (2004).
[CrossRef]

A. Rizzi, D. Marini, L. De Carli, “LUT and multilevel Brownian Retinex colour correction,” Mach. Graphics Vision 11(2/3), 153–168 (2002).

D. Marini, A. Rizzi, “A computational approach to color adaptation effects,” Image Vis. Comput. 18, 1005–1014 (2000).
[CrossRef]

A. Rizzi, C. Gatta, B. Piacentini, M. Fierro, D. Marini, “Human-visual-system-inspired tone mapping algorithm for HDR images,” in Human Vision Electronic Imaging IX, B. E. Rogowitz and T. N. Pappas, eds., Proc. SPIE5292, 57–68 (2004).

Marsi, S.

G. Ramponi, L. Tenze, S. Carrato, S. Marsi, “Nonlinear contrast enhancement based on the Retinex approach,” in Image Processing: Algorithms and Systems II, E. Dougherty, J. T. Astola, and K. O. Egiazarian, eds., Proc. SPIE5014, 169–177 (2003).

McCann, J. J.

J. J. McCann and 25 other authors, “Special session on Retinex at 40,” J. Electron. Imaging 13, 6–145 (2004).
[CrossRef]

B. Funt, F. Ciurea, J. J. McCann, “Retinex in Matlab,” J. Electron. Imaging 13, 48–57 (2004).
[CrossRef]

J. J. McCann, “Capturing a black cat in shade: past and present of Retinex color appearance models,” J. Electron. Imaging 13, 36–47 (2004).
[CrossRef]

J. J. McCann, S. P. McKee, T. H. Taylor, “Quantitative studies in Retinex theory. A comparison between theoretical predictions and observer responses to the ‘color mondrian’ experiments,” Vision Res. 16, 445–458 (1976).
[CrossRef]

E. Land, J. J. McCann, “Lightness and Retinex theory,” J. Opt. Soc. Am. 61, 1–11 (1971).
[CrossRef] [PubMed]

J. Frankle, J. J. McCann, “Method and apparatus for lightness imaging,” U.S. Patent 4,348,336 May 17, 1983.

McKee, S. P.

J. J. McCann, S. P. McKee, T. H. Taylor, “Quantitative studies in Retinex theory. A comparison between theoretical predictions and observer responses to the ‘color mondrian’ experiments,” Vision Res. 16, 445–458 (1976).
[CrossRef]

Meylan, L.

L. Meylan, S. E. Süsstrunk, “Bio-inspired image enhancement for natural color images,” in Human Vision and Electronic Imaging IX, B. E. Roqowritz and T. N. Pappas, eds., Proc. SPIE5292, 46–56 (2004).

Moore, A.

A. Moore, J. Allman, R. Goodman, “A real-time neural system for color constancy,” IEEE Trans. Neural Netw. 2, 237–247 (1991).
[CrossRef] [PubMed]

Moroney, N.

N. Moroney, I. Tastl, “Comparison of Retinex and iCAM for scene rendering,” J. Electron. Imaging 13, 139–145 (2004).
[CrossRef]

Piacentini, B.

A. Rizzi, C. Gatta, B. Piacentini, M. Fierro, D. Marini, “Human-visual-system-inspired tone mapping algorithm for HDR images,” in Human Vision Electronic Imaging IX, B. E. Rogowitz and T. N. Pappas, eds., Proc. SPIE5292, 57–68 (2004).

Pilu, M.

M. Pilu, S. Pollard, “A light-weight text image processing method for handheld embedded cameras,” in Proceedings of the British Machine Vision Conference, (British Machine Vision Association, http://www.cmp.uea.uk/research/bmvc/; School of Information Systems, University of East Anglia, Norwich, UK, 2002), pp. 547–556.

Pollard, S.

M. Pilu, S. Pollard, “A light-weight text image processing method for handheld embedded cameras,” in Proceedings of the British Machine Vision Conference, (British Machine Vision Association, http://www.cmp.uea.uk/research/bmvc/; School of Information Systems, University of East Anglia, Norwich, UK, 2002), pp. 547–556.

Rahman, Z.

Z. Rahman, D. J. Jobson, G. A. Woodell, “Retinex processing for automatic image enhancement,” J. Electron. Imaging 13, 100–110 (2004).
[CrossRef]

D. J. Jobson, Z. Rahman, G. A. Woodell, “Properties and performance of a center/surround retinex,” IEEE Trans. Image Process. 6, 451–462 (1997).
[CrossRef] [PubMed]

D. J. Jobson, Z. Rahman, G. A. Woodell, “A multiscale Retinex for bridging the gap between color images and the human observation of scenes,” IEEE Trans. Image Process. 6, 965–976 (1997).
[CrossRef] [PubMed]

Ramponi, G.

G. Ramponi, L. Tenze, S. Carrato, S. Marsi, “Nonlinear contrast enhancement based on the Retinex approach,” in Image Processing: Algorithms and Systems II, E. Dougherty, J. T. Astola, and K. O. Egiazarian, eds., Proc. SPIE5014, 169–177 (2003).

Rising, H. K.

H. K. Rising, “Analysis and generalization of Retinex by recasting the algorithm in wavelets,” J. Electron. Imaging 13, 93–99 (2004).
[CrossRef]

Rizzi, A.

A. Rizzi, C. Gatta, D. Marini, “From Retinex to automatic color equalization: issues in developing a new algorithm for unsupervised color equalization,” J. Electron. Imaging 13, 75–84 (2004).
[CrossRef]

A. Rizzi, D. Marini, L. De Carli, “LUT and multilevel Brownian Retinex colour correction,” Mach. Graphics Vision 11(2/3), 153–168 (2002).

D. Marini, A. Rizzi, “A computational approach to color adaptation effects,” Image Vis. Comput. 18, 1005–1014 (2000).
[CrossRef]

A. Rizzi, C. Gatta, B. Piacentini, M. Fierro, D. Marini, “Human-visual-system-inspired tone mapping algorithm for HDR images,” in Human Vision Electronic Imaging IX, B. E. Rogowitz and T. N. Pappas, eds., Proc. SPIE5292, 57–68 (2004).

Sobol, R.

R. Sobol, “Improving the Retinex algorithm for rendering wide dynamic range photographs,” J. Electron. Imaging 13, 65–74 (2004).
[CrossRef]

Süsstrunk, S. E.

L. Meylan, S. E. Süsstrunk, “Bio-inspired image enhancement for natural color images,” in Human Vision and Electronic Imaging IX, B. E. Roqowritz and T. N. Pappas, eds., Proc. SPIE5292, 46–56 (2004).

Tastl, I.

N. Moroney, I. Tastl, “Comparison of Retinex and iCAM for scene rendering,” J. Electron. Imaging 13, 139–145 (2004).
[CrossRef]

Taylor, T. H.

J. J. McCann, S. P. McKee, T. H. Taylor, “Quantitative studies in Retinex theory. A comparison between theoretical predictions and observer responses to the ‘color mondrian’ experiments,” Vision Res. 16, 445–458 (1976).
[CrossRef]

Tenze, L.

G. Ramponi, L. Tenze, S. Carrato, S. Marsi, “Nonlinear contrast enhancement based on the Retinex approach,” in Image Processing: Algorithms and Systems II, E. Dougherty, J. T. Astola, and K. O. Egiazarian, eds., Proc. SPIE5014, 169–177 (2003).

Wandell, B. A.

Wolf, C. J.

A. C. Hurlbert, C. J. Wolf, “Contribution of local and global cone-contrasts to color appearance: a Retinex-like model,” in Human Vision and Electronic Imaging VII, B. E. Rogowitz and N. T. Pappas, eds., Proc. SPIE4662, 286–297 (2002).

Woodell, G. A.

Z. Rahman, D. J. Jobson, G. A. Woodell, “Retinex processing for automatic image enhancement,” J. Electron. Imaging 13, 100–110 (2004).
[CrossRef]

D. J. Jobson, Z. Rahman, G. A. Woodell, “Properties and performance of a center/surround retinex,” IEEE Trans. Image Process. 6, 451–462 (1997).
[CrossRef] [PubMed]

D. J. Jobson, Z. Rahman, G. A. Woodell, “A multiscale Retinex for bridging the gap between color images and the human observation of scenes,” IEEE Trans. Image Process. 6, 965–976 (1997).
[CrossRef] [PubMed]

Young, R. A.

R. A. Young, “Color vision and the Retinex theory,” Science 238, 1731–1732 (1987).
[CrossRef] [PubMed]

Appl. Opt. (1)

IEEE Trans. Image Process. (2)

D. J. Jobson, Z. Rahman, G. A. Woodell, “A multiscale Retinex for bridging the gap between color images and the human observation of scenes,” IEEE Trans. Image Process. 6, 965–976 (1997).
[CrossRef] [PubMed]

D. J. Jobson, Z. Rahman, G. A. Woodell, “Properties and performance of a center/surround retinex,” IEEE Trans. Image Process. 6, 451–462 (1997).
[CrossRef] [PubMed]

IEEE Trans. Neural Netw. (1)

A. Moore, J. Allman, R. Goodman, “A real-time neural system for color constancy,” IEEE Trans. Neural Netw. 2, 237–247 (1991).
[CrossRef] [PubMed]

Image Vis. Comput. (1)

D. Marini, A. Rizzi, “A computational approach to color adaptation effects,” Image Vis. Comput. 18, 1005–1014 (2000).
[CrossRef]

Int. J. Comput. Vis. (1)

R. Kimmel, M. Elad, “A variational frame - work for Retinex,” Int. J. Comput. Vis. 52, 7–23 (2003).
[CrossRef]

J. Electron. Imaging (10)

A. Rizzi, C. Gatta, D. Marini, “From Retinex to automatic color equalization: issues in developing a new algorithm for unsupervised color equalization,” J. Electron. Imaging 13, 75–84 (2004).
[CrossRef]

R. Sobol, “Improving the Retinex algorithm for rendering wide dynamic range photographs,” J. Electron. Imaging 13, 65–74 (2004).
[CrossRef]

N. Moroney, I. Tastl, “Comparison of Retinex and iCAM for scene rendering,” J. Electron. Imaging 13, 139–145 (2004).
[CrossRef]

Z. Rahman, D. J. Jobson, G. A. Woodell, “Retinex processing for automatic image enhancement,” J. Electron. Imaging 13, 100–110 (2004).
[CrossRef]

H. K. Rising, “Analysis and generalization of Retinex by recasting the algorithm in wavelets,” J. Electron. Imaging 13, 93–99 (2004).
[CrossRef]

J. J. McCann and 25 other authors, “Special session on Retinex at 40,” J. Electron. Imaging 13, 6–145 (2004).
[CrossRef]

F. Ciurea, B. Funt, “Tuning Retinex parameters,” J. Electron. Imaging 13, 58–64 (2004).
[CrossRef]

T. J. Cooper, F. A. Baqai, “Analysis and extensions of the Frankle–McCann Retinex algorithm,” J. Electron. Imaging 13, 85–92 (2004).
[CrossRef]

B. Funt, F. Ciurea, J. J. McCann, “Retinex in Matlab,” J. Electron. Imaging 13, 48–57 (2004).
[CrossRef]

J. J. McCann, “Capturing a black cat in shade: past and present of Retinex color appearance models,” J. Electron. Imaging 13, 36–47 (2004).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Mach. Graphics Vision (1)

A. Rizzi, D. Marini, L. De Carli, “LUT and multilevel Brownian Retinex colour correction,” Mach. Graphics Vision 11(2/3), 153–168 (2002).

Proc. Natl. Acad. Sci. U.S.A. (2)

E. Land, “An alternative technique for the computation of the designator in the retinex theory of color vision,” Proc. Natl. Acad. Sci. U.S.A. 83, 3078–3080 (1986).
[CrossRef] [PubMed]

E. Land, “Recent advances in retinex theory and some implications for cortical computations: color vision and the natural image,” Proc. Natl. Acad. Sci. U.S.A. 80, 5163–5169 (1983).
[CrossRef] [PubMed]

Science (1)

R. A. Young, “Color vision and the Retinex theory,” Science 238, 1731–1732 (1987).
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Vision Res. (1)

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[CrossRef]

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J. D. Cowan, P. C. Bressloff, “Visual cortex and the Retinex algorithm,” in Human Vision and Electronic Imaging VIIB. E. Rogowitz and N. T. Pappas, eds., Proc. SPIE4662, 278–285 (2002).

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A. C. Hurlbert, C. J. Wolf, “Contribution of local and global cone-contrasts to color appearance: a Retinex-like model,” in Human Vision and Electronic Imaging VII, B. E. Rogowitz and N. T. Pappas, eds., Proc. SPIE4662, 286–297 (2002).

M. Pilu, S. Pollard, “A light-weight text image processing method for handheld embedded cameras,” in Proceedings of the British Machine Vision Conference, (British Machine Vision Association, http://www.cmp.uea.uk/research/bmvc/; School of Information Systems, University of East Anglia, Norwich, UK, 2002), pp. 547–556.

K. Barnard, B. Funt, “Investigations into multi-scale Retinex,” Vision and Technology (Wiley, 1999), pp. 9–17.

L. Meylan, S. E. Süsstrunk, “Bio-inspired image enhancement for natural color images,” in Human Vision and Electronic Imaging IX, B. E. Roqowritz and T. N. Pappas, eds., Proc. SPIE5292, 46–56 (2004).

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A. Rizzi, C. Gatta, B. Piacentini, M. Fierro, D. Marini, “Human-visual-system-inspired tone mapping algorithm for HDR images,” in Human Vision Electronic Imaging IX, B. E. Rogowitz and T. N. Pappas, eds., Proc. SPIE5292, 57–68 (2004).

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Figures (4)

Fig. 1
Fig. 1

(a) Gradient of gray levels between 50 and 150. (b) gradient filtered by Retinex without threshold.

Fig. 2
Fig. 2

(Color online) (a) Gallery original image. (b) Book original image.

Fig. 3
Fig. 3

(a) Gallery iteratively filtered. (b) Book iteratively filtered.

Fig. 4
Fig. 4

(Color online) (a) Gallery image of convergence. (b) Book image of convergence. (c) Gallery filtered using paths with 2 4 nodes. (d) Gallery filtered using paths with 2 10 nodes.

Tables (2)

Tables Icon

Table 1 First Step in the Proof by Induction

Tables Icon

Table 2 Last Step in the Proof by Induction

Equations (26)

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L ( i ) = k l i , j k N , l i , j k = x path δ log I x + 1 I x ,
δ = { 1 if log I x + 1 I x > threshold 0 otherwise } .
L ( i ) = 1 N k = 1 N t k = 1 n k 1 δ k ( R t k ) ,
δ k ( R t k ) = { R t k if 0 < R t k 1 ϵ 1 if 1 ϵ < R t k < 1 + ϵ R t k if 1 + ϵ R t k 1 + ϵ m k = 0 t k 1 δ k ( R m k ) 1 m k = 0 t k 1 δ k ( R m k ) if R t k > 1 + ϵ m k = 0 t k 1 δ k ( R m k ) } ,
L ( i ) = 1 N k = 1 N L k ( i ) .
L ( i ) = 1 N k = 1 N [ ( exp log ) ( L k ( i ) ) ] = 1 N k = 1 N ( exp log ) ( t k = 1 n k 1 δ k ( R t k ) ) .
L ( i ) = 1 N k = 1 N exp ( t k = 1 n k 1 log [ δ k ( R t k ) ] ) .
δ ̃ k ( R ̃ t k ) = { R ̃ t k if < R ̃ t k ϵ ̃ 0 if ϵ ̃ < R ̃ t k < ϵ ̃ R ̃ t k if ϵ ̃ R ̃ t k ϵ ̃ m k = 0 t k 1 δ ̃ k ( R ̃ m k ) m k = 0 t k 1 δ ̃ k ( R ̃ m k ) if R ̃ t k > ϵ ̃ m k = 0 t k 1 δ ̃ k ( R ̃ m k ) } ,
L ( i ) = 1 N k = 1 N exp ( t k = 1 n k 1 δ ̃ k ( R ̃ t k ) ) .
δ k ( R t k ) = { R t k if 0 < R t k m k = 0 t k 1 δ k ( R m k ) 1 1 m k = 0 t k 1 δ k ( R m k ) if R t k m k = 0 t k 1 δ k ( R m k ) > 1 } ;
δ ( I ( x 2 ) I ( j ) ) δ ( I ( x H ) I ( x H 1 ) ) δ ( I ( x H + 1 ) I ( x H ) ) δ ( I ( i ) I ( x n 1 ) ) ,
I ( x 2 ) I ( j ) I ( x 3 ) I ( x 2 ) δ ( I ( x H ) I ( x H 1 ) ) δ ( I ( x H + 1 ) I ( x H ) ) δ ( I ( i ) I ( x n 1 ) ) ,
I ( x H 1 ) I ( j ) δ ( I ( x H ) I ( x H 1 ) ) δ ( I ( x H + 1 ) I ( x H ) ) δ ( I ( i ) I ( x n 1 ) ) .
I ( x H 1 ) I ( j ) I ( x H ) I ( x H 1 ) = I ( x H ) I ( j ) ,
δ ( I ( x H + 1 ) I ( x H ) ) δ ( I ( i ) I ( x n 1 ) ) .
I ( x H + 1 ) I ( x H ) I ( x H + 2 ) I ( x H + 1 ) I ( x K ) I ( x K 1 ) I ( x K + 1 ) I ( x K ) = I ( x K + 1 ) I ( x H ) < 1 .
L k ( i ) = I ( i ) I ( x H k ) ,
L ( i ) = 1 N k = 1 N I ( i ) I ( x H k ) ,
L ( i ) = 1 N k = 1 N exp ( I ̃ ( i ) I ̃ ( x H k ) )
L ( i ) = I ( i ) 1 N k = 1 N 1 I ( x H k ) ,
L 2 ( i ) = ( L L ) ( i ) = 1 N k = 1 N L ( i ) L ( x H k ) ,
L 2 ( i ) L ( i ) = 1 N k = 1 N 1 L ( x H k ) .
L m ( i ) L m 1 ( i ) = 1 N k = 1 N 1 L m 1 ( x H k m 1 ) ,
L ( i ) = I ( i ) lim N 1 N k = 1 N 1 I ( x H k ) .
L ( i ) = I ( i ) lim N 1 N ( 1 I ( x H 1 ) + 1 I ( x H 2 ) + + 1 I ( x H N 0 1 ) + N N 0 I ( x ¯ ) ) .
L ( i ) = I ( i ) I ( x ¯ ) .

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