Abstract

Viewing the lights reflected by a set of three or more surfaces, a trichromatic visual system can recover three color-constant descriptors of reflectance per surface if the color of the surfaces’ illuminant changes. This holds true for a broad range of models that relate photoreceptor, surface, and illuminant spectral properties. Changing illumination, which creates the problem of color constancy, affords its solution.

© 1992 Optical Society of America

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References

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  1. 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).
    [CrossRef] [PubMed]
  2. E. H. Land, “Recent advances in retinex theory,” Vision Res. 26, 7–21 (1986).
    [CrossRef] [PubMed]
  3. P. Sällström, “Colour and physics: some remarks concerning the physical aspects of human colour vision,” Univ. Stockholm Inst. Phys. Rep. 73-09 (1973).
  4. M. H. Brill, “A device performing illuminant-invariant assessment of chromatic relations,”J. Theor. Biol. 71, 473–478 (1978).
    [CrossRef] [PubMed]
  5. G. Buchsbaum, “A spatial processor model for object colour perception,”J. Franklin Inst. 310, 1–26 (1980).
    [CrossRef]
  6. 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]
  7. M. D’Zmura, P. Lennie, “Mechanisms of color constancy,” J. Opt. Soc. Am. A 3, 1662–1672 (1986).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  11. 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]
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    [CrossRef]
  13. G. Wyszecki, W. S. Stiles, Color Science. Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  20. S. Tominaga, B. A. Wandell, “Standard surface-reflectance model and illuminant estimation,” J. Opt. Soc. Am. A 6, 576–584 (1989).
    [CrossRef]
  21. P. Lennie, M. D’Zmura, “Mechanisms of color vision,” Crit. Rev. Neurobiol. 3, 333–400 (1988).
    [PubMed]
  22. D. Brainard, B. A. Wandell, “A bilinear model of the illuminant’s effect on color appearance,” in Computational Models of Visual Processing, M. Landy, J. A. Movshon, eds. (Massachusetts Institute of Technology, Cambridge, Mass., 1991), pp. 171–186.
  23. D. H. Marimont, B. A. Wandell, A. B. Poirson, “Predicting receptor responses from low-dimensional descriptions of surface and illuminant spectra,” in Society for Information Display 1991 Digest of Technical Papers (Society for Information Display, Playa del Rey, Calif., 1991).
  24. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C. The Art of Scientific Computing (Cambridge U. Press, New York, 1988).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  29. S. Ullman, The Interpretation of Visual Motion (Massachusetts Institute of Technology, Cambridge, Mass., 1979).

1991 (1)

B. V. Funt, M. S. Drew, J. Ho, “Color constancy from mutual reflection,” Int. J. Comp. Vis. 6, 5–24 (1991).
[CrossRef]

1989 (2)

1988 (1)

P. Lennie, M. D’Zmura, “Mechanisms of color vision,” Crit. Rev. Neurobiol. 3, 333–400 (1988).
[PubMed]

1987 (1)

B. A. Wandell, “The synthesis and analysis of color images,”IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 105–116 (1987).
[CrossRef]

1986 (6)

1983 (1)

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).
[CrossRef] [PubMed]

1980 (1)

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

1975 (1)

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]

1973 (1)

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

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).

1955 (1)

1953 (1)

E. L. Krinov, “Spectral reflectance properties of natural formations,”NRC Tech. Transl. TT-439 (1953).

Brainard, D.

D. Brainard, B. A. Wandell, “A bilinear model of the illuminant’s effect on color appearance,” in Computational Models of Visual Processing, M. Landy, J. A. Movshon, eds. (Massachusetts Institute of Technology, Cambridge, Mass., 1991), pp. 171–186.

Brill, M. H.

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).

D’Zmura, M.

P. Lennie, M. D’Zmura, “Mechanisms of color vision,” Crit. Rev. Neurobiol. 3, 333–400 (1988).
[PubMed]

M. D’Zmura, P. Lennie, “Mechanisms of color constancy,” J. Opt. Soc. Am. A 3, 1662–1672 (1986).
[CrossRef]

Dixon, E. R.

Drew, M. S.

B. V. Funt, M. S. Drew, J. Ho, “Color constancy from mutual reflection,” Int. J. Comp. Vis. 6, 5–24 (1991).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C. The Art of Scientific Computing (Cambridge U. Press, New York, 1988).

Funt, B. V.

B. V. Funt, M. S. Drew, J. Ho, “Color constancy from mutual reflection,” Int. J. Comp. Vis. 6, 5–24 (1991).
[CrossRef]

Hallikainen, J.

Ho, J.

B. V. Funt, M. S. Drew, J. Ho, “Color constancy from mutual reflection,” Int. J. Comp. Vis. 6, 5–24 (1991).
[CrossRef]

Hunter, R. S.

R. S. Hunter, The Measurement of Appearance (Wiley, New York, 1975).

Hurlbert, A.

Hurvich, L. M.

Jaaskelainen, T.

Jameson, D.

Judd, D. B.

Krinov, E. L.

E. L. Krinov, “Spectral reflectance properties of natural formations,”NRC Tech. Transl. TT-439 (1953).

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).
[CrossRef] [PubMed]

Lee, H.-C.

Lennie, P.

P. Lennie, M. D’Zmura, “Mechanisms of color vision,” Crit. Rev. Neurobiol. 3, 333–400 (1988).
[PubMed]

M. D’Zmura, P. Lennie, “Mechanisms of color constancy,” J. Opt. Soc. Am. A 3, 1662–1672 (1986).
[CrossRef]

MacAdam, D. L.

Maloney, L. T.

Marimont, D. H.

D. H. Marimont, B. A. Wandell, A. B. Poirson, “Predicting receptor responses from low-dimensional descriptions of surface and illuminant spectra,” in Society for Information Display 1991 Digest of Technical Papers (Society for Information Display, Playa del Rey, Calif., 1991).

Parkkinen, J. P. S.

Poirson, A. B.

D. H. Marimont, B. A. Wandell, A. B. Poirson, “Predicting receptor responses from low-dimensional descriptions of surface and illuminant spectra,” in Society for Information Display 1991 Digest of Technical Papers (Society for Information Display, Playa del Rey, Calif., 1991).

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]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C. The Art of Scientific Computing (Cambridge U. Press, New York, 1988).

Sällström, P.

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

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]

Stiles, W. S.

G. Wyszecki, W. S. Stiles, Color Science. Concepts and Methods, Quantitatiue Data and Formulas (Wiley, New York, 1967).

G. Wyszecki, W. S. Stiles, Color Science. Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982).

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C. The Art of Scientific Computing (Cambridge U. Press, New York, 1988).

Tominaga, S.

Ullman, S.

S. Ullman, The Interpretation of Visual Motion (Massachusetts Institute of Technology, Cambridge, Mass., 1979).

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C. The Art of Scientific Computing (Cambridge U. Press, New York, 1988).

Wandell, B. A.

S. Tominaga, B. A. Wandell, “Standard surface-reflectance model and illuminant estimation,” J. Opt. Soc. Am. A 6, 576–584 (1989).
[CrossRef]

B. A. Wandell, “The synthesis and analysis of color images,”IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 105–116 (1987).
[CrossRef]

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]

D. H. Marimont, B. A. Wandell, A. B. Poirson, “Predicting receptor responses from low-dimensional descriptions of surface and illuminant spectra,” in Society for Information Display 1991 Digest of Technical Papers (Society for Information Display, Playa del Rey, Calif., 1991).

D. Brainard, B. A. Wandell, “A bilinear model of the illuminant’s effect on color appearance,” in Computational Models of Visual Processing, M. Landy, J. A. Movshon, eds. (Massachusetts Institute of Technology, Cambridge, Mass., 1991), pp. 171–186.

Wyszecki, G.

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]

G. Wyszecki, W. S. Stiles, Color Science. Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982).

G. Wyszecki, W. S. Stiles, Color Science. Concepts and Methods, Quantitatiue Data and Formulas (Wiley, New York, 1967).

Yellott, J. I.

J. I. Yellott, University of California, Irvine, Irvine, Calif. 92717 (personal communication, 1991).

Crit. Rev. Neurobiol. (1)

P. Lennie, M. D’Zmura, “Mechanisms of color vision,” Crit. Rev. Neurobiol. 3, 333–400 (1988).
[PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

B. A. Wandell, “The synthesis and analysis of color images,”IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 105–116 (1987).
[CrossRef]

Int. J. Comp. Vis. (1)

B. V. Funt, M. S. Drew, J. Ho, “Color constancy from mutual reflection,” Int. J. Comp. Vis. 6, 5–24 (1991).
[CrossRef]

J. Franklin Inst. (1)

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

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (7)

J. Theor. Biol. (1)

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

NRC Tech. Transl. (1)

E. L. Krinov, “Spectral reflectance properties of natural formations,”NRC Tech. Transl. TT-439 (1953).

Proc. Natl. Acad. Sci. USA (1)

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).
[CrossRef] [PubMed]

Psychon. Sci. (1)

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

Univ. Stockholm Inst. Phys. Rep. (1)

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

Vision Res. (2)

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

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]

Other (8)

J. I. Yellott, University of California, Irvine, Irvine, Calif. 92717 (personal communication, 1991).

G. Wyszecki, W. S. Stiles, Color Science. Concepts and Methods, Quantitatiue Data and Formulas (Wiley, New York, 1967).

S. Ullman, The Interpretation of Visual Motion (Massachusetts Institute of Technology, Cambridge, Mass., 1979).

D. Brainard, B. A. Wandell, “A bilinear model of the illuminant’s effect on color appearance,” in Computational Models of Visual Processing, M. Landy, J. A. Movshon, eds. (Massachusetts Institute of Technology, Cambridge, Mass., 1991), pp. 171–186.

D. H. Marimont, B. A. Wandell, A. B. Poirson, “Predicting receptor responses from low-dimensional descriptions of surface and illuminant spectra,” in Society for Information Display 1991 Digest of Technical Papers (Society for Information Display, Playa del Rey, Calif., 1991).

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C. The Art of Scientific Computing (Cambridge U. Press, New York, 1988).

G. Wyszecki, W. S. Stiles, Color Science. Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982).

R. S. Hunter, The Measurement of Appearance (Wiley, New York, 1975).

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Tables (1)

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Table 1 Tested Components

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

R ( λ ) = j = 1 n r j R j ( λ ) .
A ( λ ) = i = 1 m a i A i ( λ ) .
L ( λ ) = A ( λ ) R ( λ ) = i = 1 m j = 1 n a i r j A i ( λ ) R j ( λ ) .
q k = 400 nm 700 nm Q k ( λ ) L ( λ ) d λ = 400 nm 700 nm Q k ( λ ) [ i = 1 m j = 1 n a i r j A i ( λ ) R j ( λ ) ] d λ .
b j k i = 400 nm 700 nm Q k ( λ ) A i ( λ ) R j ( λ ) d λ .
q k = j = 1 n i = 1 m r j b j k i a i .
d = j = 1 n r j C j a .
d t = j = 1 n r t j C j a .
t = 1 s ρ j t d t = C j a .
E j ρ j = a ,             j = 1 , , n .
F ρ = 0 .

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