Abstract

Sensations of color show a strong correlation with reflectance, even though the amount of visible light reaching the eye depends on the product of reflectance and illumination. The visual system must achieve this remarkable result by a scheme that does not measure flux. Such a scheme is described as the basis of retinex theory. This theory assumes that there are three independent cone systems, each starting with a set of receptors peaking, respectively, in the long-, middle-, and short-wavelength regions of the visible spectrum. Each system forms a separate image of the world in terms of lightness that shows a strong correlation with reflectance within its particular band of wavelengths. These images are not mixed, but rather are compared to generate color sensations. The problem then becomes how the lightness of areas in these separate images can be independent of flux. This article describes the mathematics of a lightness scheme that generates lightness numbers, the biologic correlate of reflectance, independent of the flux from objects

© 1971 Optical Society of America

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  1. Although sensations of lightness show a strong correlation with reflectances in most real-life situations, there are many important departures from this strong correlation. The color-contrast experiments of Chevreul2 and Mach bands3 are examples of such departures. In addition, in complex images, there are small but systematic changes of lightness when the over-all level of illumination changes (Jameson and Hurvich4; Bartleson and Breneman5). And, of course, any general theory must, as well, explain the simple situations in which surround comprises the entire environment (Hess and Pretori6; Wallach7; Stevens and Galanter8).
  2. M. E. Chevreul, De la Loi du Contraste Simultane des Couleurs (Pitois-Levrault, Paris, 1839).
  3. E. Mach, Sitzber. Math. Naturw. Kl. Kais. Akad. Wiss. 52/2, 302 (1865).
  4. D. Jameson and L. M. Hurvich, Science 133, 174 (1961).
  5. C. J. Bartleson and E. J. Breneman, J. Opt. Soc. Am. 57, 953 (1967).
  6. C. Hess and H. Pretori, Arch. Ophthalmol. 40, 1 (1884).
  7. H. Wallach, J. Exptl. Psychol. 38, 310 (1948).
  8. S. S. Stevens and E. H. Galanter, J. Exptl. Psychol. 54, 377 (1957).
  9. We avoided the use of a pattern of squares because previous experience had taught us the hazard of the superposition of afterimages as the eye moves10. Our completed display uses rectangles in an array the format of which reminded us of a painting by Piet Mondrian in the Tate Gallery in London. Thus we call our display the Mondrian.
  10. N. Daw, Nature 196, 1143 (1962).
  11. E. H. Land, Am. Scientist 52, 247 (1964).
  12. S. Hecht and Y. Hsia, J. Opt. Soc. Am. 35, 261 (1945).
  13. E. H. Land, Proc. Natl. Acad. Sci. U. S. 45, 115 (1959).
  14. E. H. Land, Proc. Natl. Acad. Sci. U. S. 45, 636 (1959).
  15. E. H. Land, Sci. Am. 201, 16 (May 1959).
  16. E. H. Land, Proc. Roy. Soc. (London) 39, 1 (1962).
  17. J. J. McCann and J. Benton, J. Opt. Soc. Am. 59, 103 (1969).
  18. Y. LeGrand, Light, Colour and Vision, 2nd ed. (Chapman and Hall, London, 1968), p. 225.
  19. Committee on Colorimetry, Optical Society of America, The Science of Color (Crowell, New York, 1953), p. 52 (available from Optical Society, Washington, D. C.).
  20. R. M. Evans, An Introduction to Color (Wiley, New York, 1948), p. 119.
  21. Reference 20, p. 159.
  22. Figure 6 was made as a transparency so that the photograph would be the best possible reproduction of the original experiment. The range of luminances of the original display was about 500 to 1. The reproduction must have a range of transmittances that approaches that range of luminances. In addition, the photograph must not alter the relative luminances of any areas by non-linearities of the film response. It is very difficult to obtain both these properties in reflection prints, whereas the greater intrinsic dynamic range of a transparency allowed us to satisfy both conditions. In addition, the optical densities of each area across the horizontal midline of Fig. 6 are the same as those in Fig. 4.
  23. We are deeply indebted to L. Feranni and S. Kagan for developing the electronic representation of the system for finding the sequential product. The work on this display helped us to clarify our analysis.
  24. F. Ratliff, Mach Bands: Quantitative Studies on Neural Networks in the Retina (Holden-Day, San Francisco, 1965), p. 110.
  25. J. J. McCann, E. H. Land, and S. M. Tatnall, Am. J. Optom. Arch. Acad. Optom. 47, 845 (1970).
  26. P. K. Brown and G. Wald, Science 144, 45 (1964).
  27. W. B. Marks, W. H. Dobelle, and E. F. MacNichol, Science 143, 1181 (1964).
  28. H. J. A. Dartnall, Bull. Brit. Med. Council 9, 24 (1953).

Bartleson, C. J.

C. J. Bartleson and E. J. Breneman, J. Opt. Soc. Am. 57, 953 (1967).

Benton, J.

J. J. McCann and J. Benton, J. Opt. Soc. Am. 59, 103 (1969).

Breneman, E. J.

C. J. Bartleson and E. J. Breneman, J. Opt. Soc. Am. 57, 953 (1967).

Brown, P. K.

P. K. Brown and G. Wald, Science 144, 45 (1964).

Chevreul, M. E.

M. E. Chevreul, De la Loi du Contraste Simultane des Couleurs (Pitois-Levrault, Paris, 1839).

Dartnall, H. J. A.

H. J. A. Dartnall, Bull. Brit. Med. Council 9, 24 (1953).

Daw, N.

N. Daw, Nature 196, 1143 (1962).

Dobelle, W. H.

W. B. Marks, W. H. Dobelle, and E. F. MacNichol, Science 143, 1181 (1964).

Evans, R. M.

R. M. Evans, An Introduction to Color (Wiley, New York, 1948), p. 119.

Feranni, L.

We are deeply indebted to L. Feranni and S. Kagan for developing the electronic representation of the system for finding the sequential product. The work on this display helped us to clarify our analysis.

Galanter, E. H.

S. S. Stevens and E. H. Galanter, J. Exptl. Psychol. 54, 377 (1957).

Hecht, S.

S. Hecht and Y. Hsia, J. Opt. Soc. Am. 35, 261 (1945).

Hess, C.

C. Hess and H. Pretori, Arch. Ophthalmol. 40, 1 (1884).

Hsia, Y.

S. Hecht and Y. Hsia, J. Opt. Soc. Am. 35, 261 (1945).

Hurvich, L. M.

D. Jameson and L. M. Hurvich, Science 133, 174 (1961).

Jameson, D.

D. Jameson and L. M. Hurvich, Science 133, 174 (1961).

Kagan, S.

We are deeply indebted to L. Feranni and S. Kagan for developing the electronic representation of the system for finding the sequential product. The work on this display helped us to clarify our analysis.

Land, E. H.

J. J. McCann, E. H. Land, and S. M. Tatnall, Am. J. Optom. Arch. Acad. Optom. 47, 845 (1970).

E. H. Land, Proc. Natl. Acad. Sci. U. S. 45, 115 (1959).

E. H. Land, Proc. Natl. Acad. Sci. U. S. 45, 636 (1959).

E. H. Land, Sci. Am. 201, 16 (May 1959).

E. H. Land, Proc. Roy. Soc. (London) 39, 1 (1962).

E. H. Land, Am. Scientist 52, 247 (1964).

LeGrand, Y.

Y. LeGrand, Light, Colour and Vision, 2nd ed. (Chapman and Hall, London, 1968), p. 225.

Mach, E.

E. Mach, Sitzber. Math. Naturw. Kl. Kais. Akad. Wiss. 52/2, 302 (1865).

MacNichol, E. F.

W. B. Marks, W. H. Dobelle, and E. F. MacNichol, Science 143, 1181 (1964).

Marks, W. B.

W. B. Marks, W. H. Dobelle, and E. F. MacNichol, Science 143, 1181 (1964).

McCann, J. J.

J. J. McCann, E. H. Land, and S. M. Tatnall, Am. J. Optom. Arch. Acad. Optom. 47, 845 (1970).

J. J. McCann and J. Benton, J. Opt. Soc. Am. 59, 103 (1969).

Pretori, H.

C. Hess and H. Pretori, Arch. Ophthalmol. 40, 1 (1884).

Ratliff, F.

F. Ratliff, Mach Bands: Quantitative Studies on Neural Networks in the Retina (Holden-Day, San Francisco, 1965), p. 110.

Stevens, S. S.

S. S. Stevens and E. H. Galanter, J. Exptl. Psychol. 54, 377 (1957).

Tatnall, S. M.

J. J. McCann, E. H. Land, and S. M. Tatnall, Am. J. Optom. Arch. Acad. Optom. 47, 845 (1970).

Wald, G.

P. K. Brown and G. Wald, Science 144, 45 (1964).

Wallach, H.

H. Wallach, J. Exptl. Psychol. 38, 310 (1948).

Other (28)

Although sensations of lightness show a strong correlation with reflectances in most real-life situations, there are many important departures from this strong correlation. The color-contrast experiments of Chevreul2 and Mach bands3 are examples of such departures. In addition, in complex images, there are small but systematic changes of lightness when the over-all level of illumination changes (Jameson and Hurvich4; Bartleson and Breneman5). And, of course, any general theory must, as well, explain the simple situations in which surround comprises the entire environment (Hess and Pretori6; Wallach7; Stevens and Galanter8).

M. E. Chevreul, De la Loi du Contraste Simultane des Couleurs (Pitois-Levrault, Paris, 1839).

E. Mach, Sitzber. Math. Naturw. Kl. Kais. Akad. Wiss. 52/2, 302 (1865).

D. Jameson and L. M. Hurvich, Science 133, 174 (1961).

C. J. Bartleson and E. J. Breneman, J. Opt. Soc. Am. 57, 953 (1967).

C. Hess and H. Pretori, Arch. Ophthalmol. 40, 1 (1884).

H. Wallach, J. Exptl. Psychol. 38, 310 (1948).

S. S. Stevens and E. H. Galanter, J. Exptl. Psychol. 54, 377 (1957).

We avoided the use of a pattern of squares because previous experience had taught us the hazard of the superposition of afterimages as the eye moves10. Our completed display uses rectangles in an array the format of which reminded us of a painting by Piet Mondrian in the Tate Gallery in London. Thus we call our display the Mondrian.

N. Daw, Nature 196, 1143 (1962).

E. H. Land, Am. Scientist 52, 247 (1964).

S. Hecht and Y. Hsia, J. Opt. Soc. Am. 35, 261 (1945).

E. H. Land, Proc. Natl. Acad. Sci. U. S. 45, 115 (1959).

E. H. Land, Proc. Natl. Acad. Sci. U. S. 45, 636 (1959).

E. H. Land, Sci. Am. 201, 16 (May 1959).

E. H. Land, Proc. Roy. Soc. (London) 39, 1 (1962).

J. J. McCann and J. Benton, J. Opt. Soc. Am. 59, 103 (1969).

Y. LeGrand, Light, Colour and Vision, 2nd ed. (Chapman and Hall, London, 1968), p. 225.

Committee on Colorimetry, Optical Society of America, The Science of Color (Crowell, New York, 1953), p. 52 (available from Optical Society, Washington, D. C.).

R. M. Evans, An Introduction to Color (Wiley, New York, 1948), p. 119.

Reference 20, p. 159.

Figure 6 was made as a transparency so that the photograph would be the best possible reproduction of the original experiment. The range of luminances of the original display was about 500 to 1. The reproduction must have a range of transmittances that approaches that range of luminances. In addition, the photograph must not alter the relative luminances of any areas by non-linearities of the film response. It is very difficult to obtain both these properties in reflection prints, whereas the greater intrinsic dynamic range of a transparency allowed us to satisfy both conditions. In addition, the optical densities of each area across the horizontal midline of Fig. 6 are the same as those in Fig. 4.

We are deeply indebted to L. Feranni and S. Kagan for developing the electronic representation of the system for finding the sequential product. The work on this display helped us to clarify our analysis.

F. Ratliff, Mach Bands: Quantitative Studies on Neural Networks in the Retina (Holden-Day, San Francisco, 1965), p. 110.

J. J. McCann, E. H. Land, and S. M. Tatnall, Am. J. Optom. Arch. Acad. Optom. 47, 845 (1970).

P. K. Brown and G. Wald, Science 144, 45 (1964).

W. B. Marks, W. H. Dobelle, and E. F. MacNichol, Science 143, 1181 (1964).

H. J. A. Dartnall, Bull. Brit. Med. Council 9, 24 (1953).

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