Abstract

We develop a model of how the visual system finds the colors of objects that have unknown shapes and positions. The model relies on mechanisms of light adaptation, coupled with eye movements, to recover three descriptors of surface reflectance that are represented in the signals of an achromatic mechanism and two color-opponent mechanisms. These descriptors are transformed to yield estimates of hue, the dimension of surface color that is independent of object shape and viewing geometry.

© 1986 Optical Society of America

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Corrections

M. D’Zmura and P. Lennie, "Mechanisms of color constancy: erratum," J. Opt. Soc. Am. A 3, 2121_1-2121 (1986)
https://www.osapublishing.org/josaa/abstract.cfm?uri=josaa-3-12-2121_1

References

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  1. D. B. Judd, D. L. MacAdam, G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. 54, 1031–1040 (1964).
    [Crossref]
  2. E. R. Dixon, “Spectral distribution of Australian daylight,” J. Opt. Soc. Am. 68, 437–450 (1978).
    [Crossref]
  3. J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychon. Sci. 1, 369–370 (1964).
  4. L. T. Maloney, “Computational approaches to color constancy,” Applied Psychology Lab. Tech. Rep. 1985-01 (Stanford University, Stanford, Calif., 1985).
  5. P. Sällström, “Colour and physics: some remarks concerning the physical aspects of human colour vision,” Institute of Physics Rep. 73-09 (University of Stockholm, Sweden, 1973).
  6. M. H. Brill, “A device performing illuminant-invariant assessment of chromatic relations,” J. Theor. Biol. 71, 473–478 (1978).
    [Crossref] [PubMed]
  7. M. H. Brill, “Further features of the illuminant-invariant trichromatic photosensor,” J. Theor. Biol. 78, 305–308 (1979).
    [Crossref] [PubMed]
  8. G. Buchsbaum, “A spatial processor model for object colour perception,” J. Franklin Inst. 310, 1–26 (1980).
    [Crossref]
  9. L. T. Maloney, B. A. Wandell, “Color constancy: a method for recovering surface spectral reflectance,” J. Opt. Soc. Am. A 3, 29–33 (1986).
    [Crossref] [PubMed]
  10. H. Yilmaz, “Color vision and a new approach to general perception,” in Biological Prototypes and Synthetic Systems, E. E. Bernard, M. R. Kare, eds. (Plenum, New York, 1962).
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  13. T. S. Trowbridge, K. P. Reitz, “Average irregularity representation of a rough surface for ray reflection,” J. Opt. Soc. Am. 65, 531–536 (1975).
    [Crossref]
  14. B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975).
    [Crossref]
  15. J. N. Lythgoe, The Ecology of Vision (Clarendon, Oxford, 1979).
  16. K. Nassau, The Physics and Chemistry of Color; The Fifteen Causes of Color (Wiley, New York, 1983).
  17. S. A. Shafer, “Using color to separate reflection components,” Department of Computer Sciences Tech. Rep. 136 (University of Rochester, New York, 1984).
  18. V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
    [Crossref] [PubMed]
  19. E. H. Land, J. J. McCann, “Lightness and retinex theory,” J. Opt. Soc. Am. 61, 1–11 (1971).
    [Crossref] [PubMed]
  20. 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]
  21. H. Helson, “Fundamental problems in color vision. I. The principle governing changes in hue, saturation and lightness of non-selective samples in chromatic illumination,” J. Exp. Psychol. 23, 439–476 (1938).
    [Crossref]
  22. D. B. Judd, “Hue saturation and lightness of surface colors with chromatic illumination,” J. Opt. Soc. Am. 30, 2–32 (1940).
    [Crossref]
  23. H. Helson, D. B. Judd, M. H. Warren, “Object-color changes from daylight to incandescent filament illumination,” Illum. Eng. 47, 221–232 (1952).
  24. E. H. Land, “The retinex theory of color vision,” Sci. Am. 237, 108–128 (1977).
    [Crossref] [PubMed]
  25. E. H. Land, “Recent advances in retinex theory and some implications for cortical computations: color vision and the natural image,” Proc. Natl. Acad. Sci. USA 80, 5163–5169 (1983).
  26. E. H. Land, “Recent advances in retinex theory,” Vision Res. 26, 7–21 (1986).
    [Crossref] [PubMed]
  27. W. S. Stiles, “Increment thresholds and the mechanisms of colour vision,” Doc. Ophthalm. 3, 138–163 (1949).
    [Crossref]
  28. W. S. Stiles, Mechanisms of Colour Vision (Academic, New York, 1978).
  29. J. M. Valeton, D. van Norren, “Light adaptation of primate cones: an analysis based on extracellular data,” Vision Res. 23, 1539–1547 (1983).
    [Crossref] [PubMed]
  30. H. von Helmholtz, Treatise on Physiological Optics, J. P. C. Southall, ed. (Dover, New York, 1962), Vol. II.
  31. D. Jameson, L. M. Hurvich, “Color adaptation: sensitivity, contrast, after-images,” in Handbook of Sensory Physiology, D. Jameson, L. M. Hurvich, eds. (Springer-Verlag, New York, 1972), Vol. VII/4.
    [Crossref]
  32. J. D. Mollon, P. G. Polden, “An anomaly in the response of the eye to light of short wavelengths,” Phil. Trans. R. Soc. London Ser. B 278, 207–240 (1977).
    [Crossref]
  33. E. J. Augenstein, E. N. Pugh, “The dynamics of the Π1colour mechanism: further evidence for two sites of adaptation,” J. Physiol. 272, 247–281 (1977).
  34. E. N. Pugh, J. D. Mollon, “A theory of the Π1and Π3colour mechanisms of Stiles,” Vision Res. 19, 293–312 (1979).
    [Crossref]
  35. J. M. Loomis, “Transient tritanopia: failure of time-intensity reciprocity in adaptation to long-wavelength light,” Vision Res. 20, 837–846 (1980).
    [Crossref]
  36. B. A. Wandell, E. N. Pugh, “A field-additive pathway detects brief-duration, long-wavelength incremental flashes,” Vision Res. 20, 613–624 (1980).
    [Crossref] [PubMed]
  37. B. A. Wandell, E. N. Pugh, “Detection of long-duration incremental flashes by a chromatically coded pathway,” Vision Res. 20, 625–635 (1980).
    [Crossref]
  38. J. M. Valeton, D. van Norren, “Transient tritanopia at the level of the erg b-wave,” Vision Res. 19, 689–693 (1979).
    [Crossref] [PubMed]
  39. R. L. DeValois, I. Abramov, G. H. Jacobs, “Analysis of response patterns of LGN cells,” J. Opt. Soc. Am. 56, 966–977 (1966).
    [Crossref]
  40. T. N. Wiesel, D. H. Hubel, “Spatial and chromatic interactions in the lateral geniculate body of the rhesus monkey,” J. Neurophysiol. 29, 1115–1156 (1966).
    [PubMed]
  41. F. M. DeMonasterio, P. Gouras, “Functional properties of ganglion cells of the rhesus monkey retina,” J. Physiol. 251, 167–195 (1975).
  42. F. M. DeMonasterio, P. Gouras, D. J. Tolhurst, “Concealed colour opponency in ganglion cells of the rhesus monkey retina,” J. Physiol. 251, 217–229 (1975).
  43. B. H. Crawford, “Visual adaptation in relation to brief conditioning stimuli,” Proc. R. Soc. London Ser. B 134, 283–302 (1947).
    [Crossref]
  44. M. M. Hayhoe, N. Benimoff, D. C. Hood, “The time course of multiplicative and subtractive adaptation processes,” Vision Res. (to be published).
  45. A. L. Yarbus, Eye Movements and Vision, B. Haigh, translator, L. A. Riggs, ed. (Plenum, New York, 1967).
  46. C. C. A. M. Gielen, J. A. M. Van Gisbergen, A. J. H. Vendrik, “Reconstruction of responses of colour-opponent neurones in monkey lateral geniculate nucleus,” Biol. Cybern. 44, 211–221 (1982).
    [Crossref]
  47. A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. 357, 241–265 (1984).
  48. B. O’Neill, Elementary Differential Geometry (Academic, New York, 1966).
  49. C. R. Ingling, E. Martinez-Uriegas, “The relationship between spectral sensitivity and spatial sensitivity for the primate r, g x-channel,” Vision Res. 23, 1495–1500 (1983).
    [Crossref]

1986 (2)

1984 (1)

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. 357, 241–265 (1984).

1983 (3)

C. R. Ingling, E. Martinez-Uriegas, “The relationship between spectral sensitivity and spatial sensitivity for the primate r, g x-channel,” Vision Res. 23, 1495–1500 (1983).
[Crossref]

J. M. Valeton, D. van Norren, “Light adaptation of primate cones: an analysis based on extracellular data,” Vision Res. 23, 1539–1547 (1983).
[Crossref] [PubMed]

E. H. Land, “Recent advances in retinex theory and some implications for cortical computations: color vision and the natural image,” Proc. Natl. Acad. Sci. USA 80, 5163–5169 (1983).

1982 (1)

C. C. A. M. Gielen, J. A. M. Van Gisbergen, A. J. H. Vendrik, “Reconstruction of responses of colour-opponent neurones in monkey lateral geniculate nucleus,” Biol. Cybern. 44, 211–221 (1982).
[Crossref]

1980 (4)

J. M. Loomis, “Transient tritanopia: failure of time-intensity reciprocity in adaptation to long-wavelength light,” Vision Res. 20, 837–846 (1980).
[Crossref]

B. A. Wandell, E. N. Pugh, “A field-additive pathway detects brief-duration, long-wavelength incremental flashes,” Vision Res. 20, 613–624 (1980).
[Crossref] [PubMed]

B. A. Wandell, E. N. Pugh, “Detection of long-duration incremental flashes by a chromatically coded pathway,” Vision Res. 20, 625–635 (1980).
[Crossref]

G. Buchsbaum, “A spatial processor model for object colour perception,” J. Franklin Inst. 310, 1–26 (1980).
[Crossref]

1979 (3)

M. H. Brill, “Further features of the illuminant-invariant trichromatic photosensor,” J. Theor. Biol. 78, 305–308 (1979).
[Crossref] [PubMed]

J. M. Valeton, D. van Norren, “Transient tritanopia at the level of the erg b-wave,” Vision Res. 19, 689–693 (1979).
[Crossref] [PubMed]

E. N. Pugh, J. D. Mollon, “A theory of the Π1and Π3colour mechanisms of Stiles,” Vision Res. 19, 293–312 (1979).
[Crossref]

1978 (2)

E. R. Dixon, “Spectral distribution of Australian daylight,” J. Opt. Soc. Am. 68, 437–450 (1978).
[Crossref]

M. H. Brill, “A device performing illuminant-invariant assessment of chromatic relations,” J. Theor. Biol. 71, 473–478 (1978).
[Crossref] [PubMed]

1977 (3)

J. D. Mollon, P. G. Polden, “An anomaly in the response of the eye to light of short wavelengths,” Phil. Trans. R. Soc. London Ser. B 278, 207–240 (1977).
[Crossref]

E. J. Augenstein, E. N. Pugh, “The dynamics of the Π1colour mechanism: further evidence for two sites of adaptation,” J. Physiol. 272, 247–281 (1977).

E. H. Land, “The retinex theory of color vision,” Sci. Am. 237, 108–128 (1977).
[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]

1975 (5)

T. S. Trowbridge, K. P. Reitz, “Average irregularity representation of a rough surface for ray reflection,” J. Opt. Soc. Am. 65, 531–536 (1975).
[Crossref]

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975).
[Crossref]

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[Crossref] [PubMed]

F. M. DeMonasterio, P. Gouras, “Functional properties of ganglion cells of the rhesus monkey retina,” J. Physiol. 251, 167–195 (1975).

F. M. DeMonasterio, P. Gouras, D. J. Tolhurst, “Concealed colour opponency in ganglion cells of the rhesus monkey retina,” J. Physiol. 251, 217–229 (1975).

1971 (1)

1967 (1)

1966 (2)

R. L. DeValois, I. Abramov, G. H. Jacobs, “Analysis of response patterns of LGN cells,” J. Opt. Soc. Am. 56, 966–977 (1966).
[Crossref]

T. N. Wiesel, D. H. Hubel, “Spatial and chromatic interactions in the lateral geniculate body of the rhesus monkey,” J. Neurophysiol. 29, 1115–1156 (1966).
[PubMed]

1964 (2)

D. B. Judd, D. L. MacAdam, G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. 54, 1031–1040 (1964).
[Crossref]

J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychon. Sci. 1, 369–370 (1964).

1952 (1)

H. Helson, D. B. Judd, M. H. Warren, “Object-color changes from daylight to incandescent filament illumination,” Illum. Eng. 47, 221–232 (1952).

1949 (1)

W. S. Stiles, “Increment thresholds and the mechanisms of colour vision,” Doc. Ophthalm. 3, 138–163 (1949).
[Crossref]

1947 (1)

B. H. Crawford, “Visual adaptation in relation to brief conditioning stimuli,” Proc. R. Soc. London Ser. B 134, 283–302 (1947).
[Crossref]

1940 (1)

1938 (1)

H. Helson, “Fundamental problems in color vision. I. The principle governing changes in hue, saturation and lightness of non-selective samples in chromatic illumination,” J. Exp. Psychol. 23, 439–476 (1938).
[Crossref]

Abramov, I.

Augenstein, E. J.

E. J. Augenstein, E. N. Pugh, “The dynamics of the Π1colour mechanism: further evidence for two sites of adaptation,” J. Physiol. 272, 247–281 (1977).

Benimoff, N.

M. M. Hayhoe, N. Benimoff, D. C. Hood, “The time course of multiplicative and subtractive adaptation processes,” Vision Res. (to be published).

Brill, M. H.

M. H. Brill, “Further features of the illuminant-invariant trichromatic photosensor,” J. Theor. Biol. 78, 305–308 (1979).
[Crossref] [PubMed]

M. H. Brill, “A device performing illuminant-invariant assessment of chromatic relations,” J. Theor. Biol. 71, 473–478 (1978).
[Crossref] [PubMed]

Buchsbaum, G.

G. Buchsbaum, “A spatial processor model for object colour perception,” J. Franklin Inst. 310, 1–26 (1980).
[Crossref]

Cohen, J.

J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychon. Sci. 1, 369–370 (1964).

Crawford, B. H.

B. H. Crawford, “Visual adaptation in relation to brief conditioning stimuli,” Proc. R. Soc. London Ser. B 134, 283–302 (1947).
[Crossref]

DeMonasterio, F. M.

F. M. DeMonasterio, P. Gouras, D. J. Tolhurst, “Concealed colour opponency in ganglion cells of the rhesus monkey retina,” J. Physiol. 251, 217–229 (1975).

F. M. DeMonasterio, P. Gouras, “Functional properties of ganglion cells of the rhesus monkey retina,” J. Physiol. 251, 167–195 (1975).

Derrington, A. M.

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. 357, 241–265 (1984).

DeValois, R. L.

Dixon, E. R.

Gielen, C. C. A. M.

C. C. A. M. Gielen, J. A. M. Van Gisbergen, A. J. H. Vendrik, “Reconstruction of responses of colour-opponent neurones in monkey lateral geniculate nucleus,” Biol. Cybern. 44, 211–221 (1982).
[Crossref]

Gouras, P.

F. M. DeMonasterio, P. Gouras, D. J. Tolhurst, “Concealed colour opponency in ganglion cells of the rhesus monkey retina,” J. Physiol. 251, 217–229 (1975).

F. M. DeMonasterio, P. Gouras, “Functional properties of ganglion cells of the rhesus monkey retina,” J. Physiol. 251, 167–195 (1975).

Hayhoe, M. M.

M. M. Hayhoe, N. Benimoff, D. C. Hood, “The time course of multiplicative and subtractive adaptation processes,” Vision Res. (to be published).

Helson, H.

H. Helson, D. B. Judd, M. H. Warren, “Object-color changes from daylight to incandescent filament illumination,” Illum. Eng. 47, 221–232 (1952).

H. Helson, “Fundamental problems in color vision. I. The principle governing changes in hue, saturation and lightness of non-selective samples in chromatic illumination,” J. Exp. Psychol. 23, 439–476 (1938).
[Crossref]

Hood, D. C.

M. M. Hayhoe, N. Benimoff, D. C. Hood, “The time course of multiplicative and subtractive adaptation processes,” Vision Res. (to be published).

Hubel, D. H.

T. N. Wiesel, D. H. Hubel, “Spatial and chromatic interactions in the lateral geniculate body of the rhesus monkey,” J. Neurophysiol. 29, 1115–1156 (1966).
[PubMed]

Hurvich, L. M.

D. Jameson, L. M. Hurvich, “Color adaptation: sensitivity, contrast, after-images,” in Handbook of Sensory Physiology, D. Jameson, L. M. Hurvich, eds. (Springer-Verlag, New York, 1972), Vol. VII/4.
[Crossref]

Ingling, C. R.

C. R. Ingling, E. Martinez-Uriegas, “The relationship between spectral sensitivity and spatial sensitivity for the primate r, g x-channel,” Vision Res. 23, 1495–1500 (1983).
[Crossref]

Jacobs, G. H.

Jameson, D.

D. Jameson, L. M. Hurvich, “Color adaptation: sensitivity, contrast, after-images,” in Handbook of Sensory Physiology, D. Jameson, L. M. Hurvich, eds. (Springer-Verlag, New York, 1972), Vol. VII/4.
[Crossref]

Judd, D. B.

Krauskopf, J.

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. 357, 241–265 (1984).

Land, E. H.

E. H. Land, “Recent advances in retinex theory,” Vision Res. 26, 7–21 (1986).
[Crossref] [PubMed]

E. H. Land, “Recent advances in retinex theory and some implications for cortical computations: color vision and the natural image,” Proc. Natl. Acad. Sci. USA 80, 5163–5169 (1983).

E. H. Land, “The retinex theory of color vision,” Sci. Am. 237, 108–128 (1977).
[Crossref] [PubMed]

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

Lennie, P.

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. 357, 241–265 (1984).

Loomis, J. M.

J. M. Loomis, “Transient tritanopia: failure of time-intensity reciprocity in adaptation to long-wavelength light,” Vision Res. 20, 837–846 (1980).
[Crossref]

Lythgoe, J. N.

J. N. Lythgoe, The Ecology of Vision (Clarendon, Oxford, 1979).

MacAdam, D. L.

Maloney, L. T.

L. T. Maloney, B. A. Wandell, “Color constancy: a method for recovering surface spectral reflectance,” J. Opt. Soc. Am. A 3, 29–33 (1986).
[Crossref] [PubMed]

L. T. Maloney, “Computational approaches to color constancy,” Applied Psychology Lab. Tech. Rep. 1985-01 (Stanford University, Stanford, Calif., 1985).

Martinez-Uriegas, E.

C. R. Ingling, E. Martinez-Uriegas, “The relationship between spectral sensitivity and spatial sensitivity for the primate r, g x-channel,” Vision Res. 23, 1495–1500 (1983).
[Crossref]

McCann, J. J.

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. H. Land, J. J. McCann, “Lightness and retinex theory,” J. Opt. Soc. Am. 61, 1–11 (1971).
[Crossref] [PubMed]

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]

Mollon, J. D.

E. N. Pugh, J. D. Mollon, “A theory of the Π1and Π3colour mechanisms of Stiles,” Vision Res. 19, 293–312 (1979).
[Crossref]

J. D. Mollon, P. G. Polden, “An anomaly in the response of the eye to light of short wavelengths,” Phil. Trans. R. Soc. London Ser. B 278, 207–240 (1977).
[Crossref]

Nassau, K.

K. Nassau, The Physics and Chemistry of Color; The Fifteen Causes of Color (Wiley, New York, 1983).

O’Neill, B.

B. O’Neill, Elementary Differential Geometry (Academic, New York, 1966).

Phong, B. T.

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975).
[Crossref]

Pokorny, J.

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[Crossref] [PubMed]

Polden, P. G.

J. D. Mollon, P. G. Polden, “An anomaly in the response of the eye to light of short wavelengths,” Phil. Trans. R. Soc. London Ser. B 278, 207–240 (1977).
[Crossref]

Pugh, E. N.

B. A. Wandell, E. N. Pugh, “A field-additive pathway detects brief-duration, long-wavelength incremental flashes,” Vision Res. 20, 613–624 (1980).
[Crossref] [PubMed]

B. A. Wandell, E. N. Pugh, “Detection of long-duration incremental flashes by a chromatically coded pathway,” Vision Res. 20, 625–635 (1980).
[Crossref]

E. N. Pugh, J. D. Mollon, “A theory of the Π1and Π3colour mechanisms of Stiles,” Vision Res. 19, 293–312 (1979).
[Crossref]

E. J. Augenstein, E. N. Pugh, “The dynamics of the Π1colour mechanism: further evidence for two sites of adaptation,” J. Physiol. 272, 247–281 (1977).

Reitz, K. P.

Sällström, P.

P. Sällström, “Colour and physics: some remarks concerning the physical aspects of human colour vision,” Institute of Physics Rep. 73-09 (University of Stockholm, Sweden, 1973).

Shafer, S. A.

S. A. Shafer, “Using color to separate reflection components,” Department of Computer Sciences Tech. Rep. 136 (University of Rochester, New York, 1984).

Smith, V. C.

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[Crossref] [PubMed]

Sparrow, E. M.

Stiles, W. S.

W. S. Stiles, “Increment thresholds and the mechanisms of colour vision,” Doc. Ophthalm. 3, 138–163 (1949).
[Crossref]

W. S. Stiles, Mechanisms of Colour Vision (Academic, New York, 1978).

G. Wyszecki, W. S. Stiles, Color Science. Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982).

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]

Tolhurst, D. J.

F. M. DeMonasterio, P. Gouras, D. J. Tolhurst, “Concealed colour opponency in ganglion cells of the rhesus monkey retina,” J. Physiol. 251, 217–229 (1975).

Torrance, K. E.

Trowbridge, T. S.

Valeton, J. M.

J. M. Valeton, D. van Norren, “Light adaptation of primate cones: an analysis based on extracellular data,” Vision Res. 23, 1539–1547 (1983).
[Crossref] [PubMed]

J. M. Valeton, D. van Norren, “Transient tritanopia at the level of the erg b-wave,” Vision Res. 19, 689–693 (1979).
[Crossref] [PubMed]

Van Gisbergen, J. A. M.

C. C. A. M. Gielen, J. A. M. Van Gisbergen, A. J. H. Vendrik, “Reconstruction of responses of colour-opponent neurones in monkey lateral geniculate nucleus,” Biol. Cybern. 44, 211–221 (1982).
[Crossref]

van Norren, D.

J. M. Valeton, D. van Norren, “Light adaptation of primate cones: an analysis based on extracellular data,” Vision Res. 23, 1539–1547 (1983).
[Crossref] [PubMed]

J. M. Valeton, D. van Norren, “Transient tritanopia at the level of the erg b-wave,” Vision Res. 19, 689–693 (1979).
[Crossref] [PubMed]

Vendrik, A. J. H.

C. C. A. M. Gielen, J. A. M. Van Gisbergen, A. J. H. Vendrik, “Reconstruction of responses of colour-opponent neurones in monkey lateral geniculate nucleus,” Biol. Cybern. 44, 211–221 (1982).
[Crossref]

von Helmholtz, H.

H. von Helmholtz, Treatise on Physiological Optics, J. P. C. Southall, ed. (Dover, New York, 1962), Vol. II.

Wandell, B. A.

L. T. Maloney, B. A. Wandell, “Color constancy: a method for recovering surface spectral reflectance,” J. Opt. Soc. Am. A 3, 29–33 (1986).
[Crossref] [PubMed]

B. A. Wandell, E. N. Pugh, “Detection of long-duration incremental flashes by a chromatically coded pathway,” Vision Res. 20, 625–635 (1980).
[Crossref]

B. A. Wandell, E. N. Pugh, “A field-additive pathway detects brief-duration, long-wavelength incremental flashes,” Vision Res. 20, 613–624 (1980).
[Crossref] [PubMed]

Warren, M. H.

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Figures (8)

Fig. 1
Fig. 1

A, Three basis functions S1(λ), S2(λ), and S3(λ) used to model surface reflectance functions. The absolute values of reflectance (R) for S1, S2, and S3 are not indicated; their contributions to a given surface reflectance are set by scalars in the model. B, The basis function S0(λ), identical to S1(λ), that describes the spectral properties of the specular component of reflectance. Part A of this figure may be reinterpreted as a description of the spectral properties of the diffuse component.

Fig. 2
Fig. 2

Color circle showing variation in contributions of S1, S2, and S3 to surface reflectance functions. The basis functions are summed in appropriate ways to generate the surface reflectance functions shown here. The ratio of contributions to reflectance made by S3 and S2 determines the azimuth θ, which represents hue.

Fig. 3
Fig. 3

A, A three-dimensional space of photoreceptor quantum catches (R, G, B) in which lies the locus L of responses to lights from different points on a single, uniformly colored object; both specular and diffuse components of reflectance vary across the surface of the object. L lies within a single plane determined by the response to the specular component, which has the chromaticity of the illuminant and varies along the axis labeled I, and the response to the diffuse component, which varies along the axis labeled D. A chromaticity plane CP is centered on and perpendicular to the axis I. Variations in L perpendicular to CP represent changes in lightness. B, Projection of L onto CP, showing that saturation may also change across a single uniformly colored surface. The azimuth θ that represents hue is a geometrically stable color descriptor.

Fig. 4
Fig. 4

A, Representation in the (R, G, B) space of responses L and L to two objects, lit by the same illuminant I, that have different diffuse components of reflectance (D and D). The two planes described by L and L intersect along the axis I, which describes the chromaticity of the illuminant, because the specular component of reflectance is common to both objects. The responses from two or more objects that define distinct planes can thus be used to find the axis I that describes the chromaticity of the illuminant. B, Projection of L and L onto the chromaticity plane CP. The lines described by the responses intersect at the point I marking the chromaticity of the illuminant.

Fig. 5
Fig. 5

The effect of scaling cone signals on the variations fL in the “light–dark” component S1, shown for two dimensions of response. Illuminants I and I determine axes in the (R, G) space of quantum catches that describe variations in the contribution of S1 to reflectance. If the average light bears the relative SPD of the illuminant, then the average light from the scene is some amount a of the function S1 multiplied by either I or I. These average lights produce average quantum catch levels of (WRWG) and (WRWG), respectively; scaling cone quantum catches by these averages produces a space of scaled cone signals (r, g), in which the axis that describes variations in S1 is independent of the chromaticity of the illuminant. The average reflectance value a comes to lie in a fixed position in (r, g) space: without knowledge of a only relative values of reflectance may be recovered from scaled cone signals.

Fig. 6
Fig. 6

Inability of simple scaling of cone signals to produce color constancy. Variations in the contributions of S1, S2, and S3 to surface reflectance in a scene lit by illuminants I or I are shown in the (R, G, B) space of quantum catches (left) and in the (r, g, b) space of scaled cone signals (right). Although scaling by average quantum catches can make the axes IS1 and IS1 coincide along axis S1 in (r, g, b) space, scaling will not make coincident the axes that describe the contributions of S2 and S3 to reflectance.

Fig. 7
Fig. 7

Color space in which can be represented the chromatic sensitivity of a cell adapted to some steady light represented by the “white point” W. The sensitivity of a cell that combines cone signals linearly may be represented by a vector G, its response gradient. The vector G represents the most effective choice of chromatic contrasts to use in stimulating the cell. The preferred hue θG of the cell may be found by projecting G onto the chromaticity plane.

Fig. 8
Fig. 8

Gradient representation of successive stages in the analysis of chromatic signals. The most effective stimuli for chromatically opponent units in the retina and parvocellular layers of the LGN (bottom row) are represented in the color space of Fig. 7. Arrows show that the best stimuli become increasingly achromatic as spatial frequency is increased. Opposing tendencies to respond to achromatic stimuli are canceled by addition of signals from appropriate pairs of units. The result (middle row) is mechanisms that at all spatial frequencies respond best to purely chromatic modulations about W. Linear combinations of signals from these units, in turn, result in mechanisms that respond maximally to any desired hue (top row).

Equations (16)

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S ( λ ) i = 1 3 n i S i ( λ ) .
S ( x , λ ) f s ( x ) S 0 ( λ ) + f d ( x ) [ i = 1 3 n i S i ( λ ) ] = specular + diffuse .
f L ( x ) = f s ( x ) + f d ( x ) n 1 .
S ( x , λ ) f L ( x ) S 1 ( λ ) + f d ( x ) n 2 S 2 ( λ ) + f d ( x ) n 3 S 3 ( λ ) = lightness + red green + yellow blue .
I ( λ ) i = 1 3 m i I i ( λ ) .
L ( x ) f L ( x ) ( i = 1 3 m i I i S 1 ) + f d ( x ) n 2 ( i = 1 3 m i I i S 2 ) + f d ( x ) n 3 ( i = 1 3 m i I i S 3 ) .
q k = L , Q k = 400 700 L ( λ ) Q k ( λ ) d λ .
q k ( x ) f L ( x ) i = 1 3 m i I i S 1 , Q k + f d ( x ) n 2 i = 1 3 m i I i S 2 , Q k + f d ( x ) n 3 i = 1 3 m i I i S 3 , Q k , for 1 k 3.
[ q 1 ( x ) q 2 ( x ) q 3 ( x ) ] [ I ( m ) S 1 , Q 1 I ( m ) S 2 , Q 1 I ( m ) S 3 , Q 1 I ( m ) S 1 , Q 2 I ( m ) S 2 , Q 2 I ( m ) S 3 , Q 2 I ( m ) S 1 , Q 3 I ( m ) S 2 , Q 3 I ( m ) S 3 , Q 3 ] [ f L ( x ) f d ( x ) n 2 f d ( x ) n 3 ] .
q ( x ) G ( m ) p ( x ) ,
H ( m ) = G ( m ) 1 ,
H ( m ) p ( x ) .
D ( m ) [ 1 / a I ( m ) S 1 , Q 1 0 0 0 1 / a I ( m ) S 1 , Q 2 0 0 0 1 / a I ( m ) S 1 , Q 3 ]
D ( m ) q ( x ) D ( m ) G ( m ) p ( x ) .
E ( m ) = [ D ( m ) G ( m ) ] 1 ,
E ( m ) D ( m ) q ( x ) p ( x ) .

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