Abstract

Human and machine visual sensing is enhanced when surface properties of objects in scenes, including color, can be reliably estimated despite changes in the ambient lighting conditions. We describe a computational method for estimating surface spectral reflectance when the spectral power distribution of the ambient light is not known.

© 1986 Optical Society of America

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References

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  1. See P. Sällström, “Colour and physics: some remarks concerning the physical aspects of human colour vision,” (University of Stockholm, Stockholm, 1973).
  2. The computational method that we develop requires only that the ambient light be approximately constant over small local patches of the image. The method is easier to explain if we restrict attention to a region of the image across which the ambient light does not change.
  3. In general the surface reflectance function may depend on the geometry of the scene, the angle of incidence of the light on the surface, and the angle between the surface and the line of sight. We are concerned here with the analysis of a single image drawn from a scene with fixed geometric relations among objects, light sources, and the visual sensor array. Sx(λ) refers to the proportion of light returned from the object toward the sensor array within that fixed geometrical framework.
  4. D. B. Judd, “Hue saturation and lightness of surface colors with chromatic illumination,” J. Opt. Soc. Am. 30, 2 (1940); 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 (1938).
    [CrossRef]
  5. E. H. Land, J. J. McCann, “Lightness and retinex theory,”J. Opt. Soc. Am. 61, 1 (1971); E. H. Land, “Recent advances in retinex theory and some implications for cortical computations: color vision and the natural image,” Proc. Nat. Acad. Sci. U.S. 80, 5163 (1983); E. H. Land, D. H. Hubel, M. Livingston, S. Perry, M. Burns, “Colour-generating interactions across the corpus callosum,” Nature 303, 616 (1983).
    [CrossRef] [PubMed]
  6. D. Brainard, B. Wandell, “An analysis of the retinex theory of color vision,” (Stanford University, Stanford, Calif., 1985).
  7. G. Buchsbaum, “A spatial processor model for object colour perception,”J. Franklin Inst. 310, 1 (1980).
    [CrossRef]
  8. It is not possible to recover E(λ) better than to within a multiplicative constant given only the sensor quantum catches. If, for example, the intensity of the light is doubled to 2E but all reflectances are halved to ½Sx(λ), it is easy to verify that the sensor quantum catches in Eq. (1) are unchanged. When we speak of recovering the ambient light and surface reflectances, we mean recovery up to this unknown mutiplicative constant.
  9. M. H. Brill, “A device performing illuminant-invariant assessment of chromatic relations,”J. Theor. Biol. 71, 473 (1978).
    [CrossRef] [PubMed]
  10. W. S. Stiles, G. Wyszecki, N. Ohta, “Counting metameric object-color stimuli using frequency-limited spectral reflectance functions,”J. Opt. Soc. Am. 67, 779 (1977).
    [CrossRef]
  11. For a discussion of band-limited functions, see R. Bracewell, The Fourier Transform and Its Application, 2nd ed. (McGraw-Hill, New York, 1978), Chap. 10.
  12. G. Buchsbaum, A. Gottschalk, “Chromaticity coordinates of frequency-limited functions,” J. Opt. Soc. Am. A 1, 885 (1984).
    [CrossRef] [PubMed]
  13. J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychonomic Sci. 1, 369 (1964).
  14. See K. V. Mardia, J. T. Kent, J. M. Bibby, Multivariate Analysis (Academic, London, 1979), Chap. 8, for a discussion of characteristic vector analysis (also known as principal-components analysis or the Karhunen–Loève decomposition).
  15. E. Krinov, Spectral Reflectance Properties of Natural Formations, Technical translation TT-439 (National Research Council of Canada, Ottawa, 1947); details of the fit of Cohen’s characteristic vectors to the Munsell surface reflectances are given in L. Maloney, “Computational approaches to color constancy,” (Stanford University, Stanford, Calif., 1985).
  16. 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 (1964).
    [CrossRef]
  17. E. R. Dixon, “Spectral distribution of Australian daylight,”J. Opt. Soc. Am. 68, 437 (1978); G. T. Winch, M. C. Boshoff, C. J. Kok, A. G. du Toit, “Spectroradiometric and calorimetric characteristics of daylight in the southern hemisphere: Pretoria, South Africa,”J. Opt. Soc. Am. 56, 456 (1966); S. R. Das, V. D. P. Sastri, “Spectral distribution and color of tropical daylight,”J. Opt. Soc. Am. 55, 319 (1965); V. D. P. Sastri, S. R. Das, “Spectral distribution and color of north sky at Delhi,”J. Opt. Soc. Am. 56, 829 (1966); “Typical spectral distributions and color for tropical daylight,”J. Opt. Soc. Am. 58, 391 (1968).
    [CrossRef]
  18. L. Maloney, “Computational approaches to color constancy,” (Stanford University, Stanford, Calif., 1985).
  19. See Ref. 18, Chap. 4, for details.
  20. R. B. MacLeod, “An experimental investigation of brightness constancy,” Arch. Psychol. 135, 1 (1932), reports that human brightness constancy does.
  21. E. N. Willmer, W. D. Wright, “Colour sensitivity of the fovea centralis,” Nature 156, 119 (1945); D. R. Williams, D. I. A. MacLeod, M. Hayhoe, “Punctate sensitivity of the blue-sensitive mechanism,” Vision Res. 21, 1357 (1981); F. M. de Monasterio, S. J. Schein, E. P. McCrane, “Staining of blue-sensitive cones of the macaque retina by a fluorescent dye,” Science 213, 1278 (1981).
    [CrossRef] [PubMed]

1984 (1)

1980 (1)

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

1978 (2)

1977 (1)

1971 (1)

1964 (2)

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

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 (1964).
[CrossRef]

1945 (1)

E. N. Willmer, W. D. Wright, “Colour sensitivity of the fovea centralis,” Nature 156, 119 (1945); D. R. Williams, D. I. A. MacLeod, M. Hayhoe, “Punctate sensitivity of the blue-sensitive mechanism,” Vision Res. 21, 1357 (1981); F. M. de Monasterio, S. J. Schein, E. P. McCrane, “Staining of blue-sensitive cones of the macaque retina by a fluorescent dye,” Science 213, 1278 (1981).
[CrossRef] [PubMed]

1940 (1)

1932 (1)

R. B. MacLeod, “An experimental investigation of brightness constancy,” Arch. Psychol. 135, 1 (1932), reports that human brightness constancy does.

Bibby, J. M.

See K. V. Mardia, J. T. Kent, J. M. Bibby, Multivariate Analysis (Academic, London, 1979), Chap. 8, for a discussion of characteristic vector analysis (also known as principal-components analysis or the Karhunen–Loève decomposition).

Bracewell, R.

For a discussion of band-limited functions, see R. Bracewell, The Fourier Transform and Its Application, 2nd ed. (McGraw-Hill, New York, 1978), Chap. 10.

Brainard, D.

D. Brainard, B. Wandell, “An analysis of the retinex theory of color vision,” (Stanford University, Stanford, Calif., 1985).

Brill, M. H.

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

Buchsbaum, G.

G. Buchsbaum, A. Gottschalk, “Chromaticity coordinates of frequency-limited functions,” J. Opt. Soc. Am. A 1, 885 (1984).
[CrossRef] [PubMed]

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

Cohen, J.

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

Dixon, E. R.

Gottschalk, A.

Judd, D. B.

Kent, J. T.

See K. V. Mardia, J. T. Kent, J. M. Bibby, Multivariate Analysis (Academic, London, 1979), Chap. 8, for a discussion of characteristic vector analysis (also known as principal-components analysis or the Karhunen–Loève decomposition).

Krinov, E.

E. Krinov, Spectral Reflectance Properties of Natural Formations, Technical translation TT-439 (National Research Council of Canada, Ottawa, 1947); details of the fit of Cohen’s characteristic vectors to the Munsell surface reflectances are given in L. Maloney, “Computational approaches to color constancy,” (Stanford University, Stanford, Calif., 1985).

Land, E. H.

MacAdam, D. L.

MacLeod, R. B.

R. B. MacLeod, “An experimental investigation of brightness constancy,” Arch. Psychol. 135, 1 (1932), reports that human brightness constancy does.

Maloney, L.

L. Maloney, “Computational approaches to color constancy,” (Stanford University, Stanford, Calif., 1985).

Mardia, K. V.

See K. V. Mardia, J. T. Kent, J. M. Bibby, Multivariate Analysis (Academic, London, 1979), Chap. 8, for a discussion of characteristic vector analysis (also known as principal-components analysis or the Karhunen–Loève decomposition).

McCann, J. J.

Ohta, N.

Sällström, P.

See P. Sällström, “Colour and physics: some remarks concerning the physical aspects of human colour vision,” (University of Stockholm, Stockholm, 1973).

Stiles, W. S.

Wandell, B.

D. Brainard, B. Wandell, “An analysis of the retinex theory of color vision,” (Stanford University, Stanford, Calif., 1985).

Willmer, E. N.

E. N. Willmer, W. D. Wright, “Colour sensitivity of the fovea centralis,” Nature 156, 119 (1945); D. R. Williams, D. I. A. MacLeod, M. Hayhoe, “Punctate sensitivity of the blue-sensitive mechanism,” Vision Res. 21, 1357 (1981); F. M. de Monasterio, S. J. Schein, E. P. McCrane, “Staining of blue-sensitive cones of the macaque retina by a fluorescent dye,” Science 213, 1278 (1981).
[CrossRef] [PubMed]

Wright, W. D.

E. N. Willmer, W. D. Wright, “Colour sensitivity of the fovea centralis,” Nature 156, 119 (1945); D. R. Williams, D. I. A. MacLeod, M. Hayhoe, “Punctate sensitivity of the blue-sensitive mechanism,” Vision Res. 21, 1357 (1981); F. M. de Monasterio, S. J. Schein, E. P. McCrane, “Staining of blue-sensitive cones of the macaque retina by a fluorescent dye,” Science 213, 1278 (1981).
[CrossRef] [PubMed]

Wyszecki, G.

Arch. Psychol. (1)

R. B. MacLeod, “An experimental investigation of brightness constancy,” Arch. Psychol. 135, 1 (1932), reports that human brightness constancy does.

J. Franklin Inst. (1)

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

J. Opt. Soc. Am. (5)

D. B. Judd, “Hue saturation and lightness of surface colors with chromatic illumination,” J. Opt. Soc. Am. 30, 2 (1940); 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 (1938).
[CrossRef]

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 (1964).
[CrossRef]

E. H. Land, J. J. McCann, “Lightness and retinex theory,”J. Opt. Soc. Am. 61, 1 (1971); E. H. Land, “Recent advances in retinex theory and some implications for cortical computations: color vision and the natural image,” Proc. Nat. Acad. Sci. U.S. 80, 5163 (1983); E. H. Land, D. H. Hubel, M. Livingston, S. Perry, M. Burns, “Colour-generating interactions across the corpus callosum,” Nature 303, 616 (1983).
[CrossRef] [PubMed]

W. S. Stiles, G. Wyszecki, N. Ohta, “Counting metameric object-color stimuli using frequency-limited spectral reflectance functions,”J. Opt. Soc. Am. 67, 779 (1977).
[CrossRef]

E. R. Dixon, “Spectral distribution of Australian daylight,”J. Opt. Soc. Am. 68, 437 (1978); G. T. Winch, M. C. Boshoff, C. J. Kok, A. G. du Toit, “Spectroradiometric and calorimetric characteristics of daylight in the southern hemisphere: Pretoria, South Africa,”J. Opt. Soc. Am. 56, 456 (1966); S. R. Das, V. D. P. Sastri, “Spectral distribution and color of tropical daylight,”J. Opt. Soc. Am. 55, 319 (1965); V. D. P. Sastri, S. R. Das, “Spectral distribution and color of north sky at Delhi,”J. Opt. Soc. Am. 56, 829 (1966); “Typical spectral distributions and color for tropical daylight,”J. Opt. Soc. Am. 58, 391 (1968).
[CrossRef]

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

J. Theor. Biol. (1)

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

Nature (1)

E. N. Willmer, W. D. Wright, “Colour sensitivity of the fovea centralis,” Nature 156, 119 (1945); D. R. Williams, D. I. A. MacLeod, M. Hayhoe, “Punctate sensitivity of the blue-sensitive mechanism,” Vision Res. 21, 1357 (1981); F. M. de Monasterio, S. J. Schein, E. P. McCrane, “Staining of blue-sensitive cones of the macaque retina by a fluorescent dye,” Science 213, 1278 (1981).
[CrossRef] [PubMed]

Psychonomic Sci. (1)

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

Other (10)

See K. V. Mardia, J. T. Kent, J. M. Bibby, Multivariate Analysis (Academic, London, 1979), Chap. 8, for a discussion of characteristic vector analysis (also known as principal-components analysis or the Karhunen–Loève decomposition).

E. Krinov, Spectral Reflectance Properties of Natural Formations, Technical translation TT-439 (National Research Council of Canada, Ottawa, 1947); details of the fit of Cohen’s characteristic vectors to the Munsell surface reflectances are given in L. Maloney, “Computational approaches to color constancy,” (Stanford University, Stanford, Calif., 1985).

L. Maloney, “Computational approaches to color constancy,” (Stanford University, Stanford, Calif., 1985).

See Ref. 18, Chap. 4, for details.

See P. Sällström, “Colour and physics: some remarks concerning the physical aspects of human colour vision,” (University of Stockholm, Stockholm, 1973).

The computational method that we develop requires only that the ambient light be approximately constant over small local patches of the image. The method is easier to explain if we restrict attention to a region of the image across which the ambient light does not change.

In general the surface reflectance function may depend on the geometry of the scene, the angle of incidence of the light on the surface, and the angle between the surface and the line of sight. We are concerned here with the analysis of a single image drawn from a scene with fixed geometric relations among objects, light sources, and the visual sensor array. Sx(λ) refers to the proportion of light returned from the object toward the sensor array within that fixed geometrical framework.

D. Brainard, B. Wandell, “An analysis of the retinex theory of color vision,” (Stanford University, Stanford, Calif., 1985).

For a discussion of band-limited functions, see R. Bracewell, The Fourier Transform and Its Application, 2nd ed. (McGraw-Hill, New York, 1978), Chap. 10.

It is not possible to recover E(λ) better than to within a multiplicative constant given only the sensor quantum catches. If, for example, the intensity of the light is doubled to 2E but all reflectances are halved to ½Sx(λ), it is easy to verify that the sensor quantum catches in Eq. (1) are unchanged. When we speak of recovering the ambient light and surface reflectances, we mean recovery up to this unknown mutiplicative constant.

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Figures (1)

Fig. 1
Fig. 1

Outline of the solution method in the case when there are three classes of sensors (p = 3) and two degrees of freedom in the model of surface reflectances (n = 2). The sensor quantum catches lie on a plane through the origin in the three-dimensional space of sensor quantum catches below. Knowledge of the plane determines the light and the matrix Λ. The matrix Λ is inverted to recover the surface reflectances σx above.

Equations (4)

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ρ k x = E ( λ ) S x ( λ ) R k ( λ ) d λ ,             k = 1 , 2 , , p ,
S x ( λ ) = j = 1 n σ j x S j ( λ )
E ( λ ) = i = 1 m i E i ( λ ) ,
ρ x = Λ σ x ,

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