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).
    [Crossref] [PubMed]
  5. C. J. Bartleson and E. J. Breneman, J. Opt. Soc. Am. 57, 953 (1967).
    [Crossref] [PubMed]
  6. C. Hess and H. Pretori, Arch. Ophthalmol. 40, 1 (1884).
  7. H. Wallach, J. Exptl. Psychol. 38, 310 (1948).
    [Crossref]
  8. S. S. Stevens and E. H. Galanter, J. Exptl. Psychol. 54, 377 (1957).
    [Crossref]
  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 moves.10 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).
    [Crossref] [PubMed]
  11. E. H. Land, Am. Scientist 52, 247 (1964).
  12. S. Hecht and Y. Hsia, J. Opt. Soc. Am. 35, 261 (1945).
    [Crossref]
  13. E. H. Land, Proc. Natl. Acad. Sci. U. S. 45, 115 (1959).
    [Crossref]
  14. E. H. Land, Proc. Natl. Acad. Sci. U. S. 45, 636 (1959).
    [Crossref]
  15. E. H. Land, Sci. Am. 201, 16 (May1959).
  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).
    [Crossref] [PubMed]
  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).
    [Crossref]
  26. P. K. Brown and G. Wald, Science 144, 45 (1964).
    [Crossref] [PubMed]
  27. W. B. Marks, W. H. Dobelle, and E. F. MacNichol, Science 143, 1181 (1964).
    [Crossref] [PubMed]
  28. H. J. A. Dartnall, Bull. Brit. Med. Council 9, 24 (1953).

1970 (1)

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

1969 (1)

1967 (1)

1964 (3)

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

P. K. Brown and G. Wald, Science 144, 45 (1964).
[Crossref] [PubMed]

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

1962 (2)

N. Daw, Nature 196, 1143 (1962).
[Crossref] [PubMed]

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

1961 (1)

D. Jameson and L. M. Hurvich, Science 133, 174 (1961).
[Crossref] [PubMed]

1959 (3)

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

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

E. H. Land, Sci. Am. 201, 16 (May1959).

1957 (1)

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

1953 (1)

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

1948 (1)

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

1945 (1)

1884 (1)

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

1865 (1)

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

Bartleson, C. J.

Benton, J.

Breneman, E. J.

Brown, P. K.

P. K. Brown and G. Wald, Science 144, 45 (1964).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Dobelle, W. H.

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

Evans, R. M.

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

Galanter, E. H.

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

Hecht, S.

Hess, C.

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

Hsia, Y.

Hurvich, L. M.

D. Jameson and L. M. Hurvich, Science 133, 174 (1961).
[Crossref] [PubMed]

Jameson, D.

D. Jameson and L. M. Hurvich, Science 133, 174 (1961).
[Crossref] [PubMed]

Land, E. H.

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

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

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

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

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

E. H. Land, Sci. Am. 201, 16 (May1959).

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).
[Crossref] [PubMed]

Marks, W. B.

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

McCann, J. J.

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

J. J. McCann and J. Benton, J. Opt. Soc. Am. 59, 103 (1969).
[Crossref] [PubMed]

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).
[Crossref]

Tatnall, S. M.

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

Wald, G.

P. K. Brown and G. Wald, Science 144, 45 (1964).
[Crossref] [PubMed]

Wallach, H.

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

Am. J. Optom. Arch. Acad. Optom. (1)

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

Am. Scientist (1)

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

Arch. Ophthalmol. (1)

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

Bull. Brit. Med. Council (1)

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

J. Exptl. Psychol. (2)

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

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

J. Opt. Soc. Am. (3)

Nature (1)

N. Daw, Nature 196, 1143 (1962).
[Crossref] [PubMed]

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

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

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

Proc. Roy. Soc. (London) (1)

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

Sci. Am. (1)

E. H. Land, Sci. Am. 201, 16 (May1959).

Science (3)

P. K. Brown and G. Wald, Science 144, 45 (1964).
[Crossref] [PubMed]

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

D. Jameson and L. M. Hurvich, Science 133, 174 (1961).
[Crossref] [PubMed]

Sitzber. Math. Naturw. Kl. Kais. Akad. Wiss. (1)

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

Other (10)

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).

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 moves.10 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.

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.

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Figures (10)

F. 1
F. 1

Spectral transmittances of bandpass interference filters.

F. 2
F. 2

Luminance vs position for two-squares-and-a-happening experiment.

F. 3
F. 3

Picture of two-squares-and-a-happening experiment. Place a pencil over the boundary between the two gray areas.

F. 5
F. 5

Reflectance along one path between the top and bottom of a black-and-white Mondrian. The numbers at the bottom indicate the ratios of reflectances at adjacent edges along the path.

F. 7
F. 7

Luminances of Mondrian (illuminated from below) at particular points along the path from top to bottom. The numbers at the bottom indicate the ratios of luminances at adjacent edges along the path.

F. 8
F. 8

Specific example of how the machine operates. The numbers at the left are the luminances of various areas in a display. Pairs of receptors that straddle the boundaries between adjacent areas generate the ratios of reflectances shown in the center column of figures. These ratios are multiplied to form sequential products that are reset if larger than 1.0 and read off the fiber, to form the output of the system.

F. 9
F. 9

A variety of equivalent sequential-products models. In (a), two opposed logarithmic receptors (A,B) first sum with, each other (C) and then sum with the continued product (D at E). This total quantity is both the readout of the system (F) and the new continued product (D′) that is combined with the next receptor pair output. In (b), each photocell is the leading photocell for one bridge pair and the trailing photocell for the next bridge pair. In (c), a third variation is perhaps more biologically oriented. The receptor K transmits its signal to its synapses I and E. Synapse I is an inhibitory synapse and adds to the sum of J and the sequential product N. The new sequential product is formed at L and is tapped off the chain between the two synapses I and E. Synapse E is excitatory and combines with this new sequential product N′ for the computation of the next sequential product.

F. 10
F. 10

Photograph of retinex machine reproducing the white, gray, and black wheel. The spotlight on the far left illuminates the wheel on the back wall and the camera on the center left forms an inverted image of it. The photocell pairs in the camera send the ratios of luminances to the electronics on the right which computes the sequential product and transmits it to the display below. The machine gives the same outputs regardless of the position of the spotlight.

F. 11
F. 11

Schematic diagram for one receptor pair of the electronic embodiment of the system. The output of the photocell A is logarithmically amplified and opposed to the logarithmically amplified output of the photocell B. The opposed signals are summed at C and then summed with the continued product D at E. In the machine, as contrasted with the scheme in Fig. 9(a), the signal is amplified to drive bulb F and to isolate the continued product output D′ which is passed on to the next receptor pair. The bulb F in the schematic diagram is in the display panel. Because the bulbs were chosen so that, under the particular condition of their use, they have an antilogarithmic response, there is no separate antilog amplifier. The flux from the bulb corresponds with the lightness value computed by the sequential product up to that point on the chain.

F. 12
F. 12

Absorption curves of visual pigments. These curves we calculated using the Dartnall nomogram28 and the maximum wavelengths 570, 535, and 445 nm.