Abstract

The properties of constancy models based on the proportionality rule of von Kries are examined in a series of simplified examples. It is found that the breadth of receptor-sensitivity functions causes metamerism, thwarting color constancy. Overlap of these functions limits the accuracy of von Kries adaptation for a more subtle reason: it causes nonzero off-diagonal elements in the transformation matrix relating object reflectance to receptor stimulations. Such off-diagonal elements make von Kries adaptation an inexact color-constancy scheme, even when the illuminant is restricted to prevent metamerism.

© 1986 Optical Society of America

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References

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  1. J. A. Worthey, “Limitations of color constancy,” J. Opt. Soc. Am. A 2, 1014–1026 (1985).
    [CrossRef]
  2. J. J. McCann, S. P. McKee, T. H. Taylor, “Quantitative studies in retinex theory,” Vision Res. 16, 445–458 (1976).
    [CrossRef]
  3. S. L. Guth, R. W. Massof, T. Benzschawel, “Vector model for normal and dichromatic color vision,” J. Opt. Soc. Am. 70, 197–212 (1980).
    [CrossRef] [PubMed]
  4. S. K. Park, F. O. Huck, “Estimation of spectral reflectance curves from multispectral image data,” Appl. Opt. 16, 3107–3114 (1977); M. H. Brill, “Further features of the illuminant-invariant trichromatic photosensor,” J. Theor. Biol. 78, 305–308 (1979); G. Buchsbaum, “A spatial processer model for object colour perception,” J. Franklin Inst. 310, 1–26 (1980); 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]
  5. M. H. Brill, G. West, “Chromatic adaptation and color constancy: a possible dichotomy,” Color Res. Appl. 11, 196–204 (1986).
    [CrossRef]
  6. H. E. Ives, “The relation between the color of the illuminant and the color of the illuminated object,” Trans. Illum. Eng. Soc. 7, 62–72 (1912).
  7. N. Karmarkar, “A new polynomial-time algorithm for linear programming,” Combinatorica 4, 373–395 (1984).
    [CrossRef]
  8. G. West, M. H. Brill, “Necessary and sufficient conditions for von Kries chromatic adaptation to give color constancy,” J. Math. Biol. 15, 249–258 (1982).
    [CrossRef] [PubMed]
  9. E. H. Land, “The retinex theory of color vision,” Sci. Am. 237(6), 108–128 (1977); “The retinex,” Am. Sci. 52(2), 247–264 (1964).
    [CrossRef] [PubMed]
  10. N. D. Nyuberg, P. P. Nikolayev, M. M. Bongard, “Constancy of perception of colour,” Biophysics 16, 1094–1107 (1971).
  11. 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]
  12. J. A. Worthey, M. H. Brill, “Heuristic analysis of von Kries color constancy,” J. Opt. Soc. Am. A 2(13), P13–P14 (1985).

1986 (1)

M. H. Brill, G. West, “Chromatic adaptation and color constancy: a possible dichotomy,” Color Res. Appl. 11, 196–204 (1986).
[CrossRef]

1985 (2)

J. A. Worthey, M. H. Brill, “Heuristic analysis of von Kries color constancy,” J. Opt. Soc. Am. A 2(13), P13–P14 (1985).

J. A. Worthey, “Limitations of color constancy,” J. Opt. Soc. Am. A 2, 1014–1026 (1985).
[CrossRef]

1984 (1)

N. Karmarkar, “A new polynomial-time algorithm for linear programming,” Combinatorica 4, 373–395 (1984).
[CrossRef]

1982 (1)

G. West, M. H. Brill, “Necessary and sufficient conditions for von Kries chromatic adaptation to give color constancy,” J. Math. Biol. 15, 249–258 (1982).
[CrossRef] [PubMed]

1980 (1)

1977 (2)

1976 (1)

J. J. McCann, S. P. McKee, T. H. Taylor, “Quantitative studies in retinex theory,” Vision Res. 16, 445–458 (1976).
[CrossRef]

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]

1971 (1)

N. D. Nyuberg, P. P. Nikolayev, M. M. Bongard, “Constancy of perception of colour,” Biophysics 16, 1094–1107 (1971).

1912 (1)

H. E. Ives, “The relation between the color of the illuminant and the color of the illuminated object,” Trans. Illum. Eng. Soc. 7, 62–72 (1912).

Benzschawel, T.

Bongard, M. M.

N. D. Nyuberg, P. P. Nikolayev, M. M. Bongard, “Constancy of perception of colour,” Biophysics 16, 1094–1107 (1971).

Brill, M. H.

M. H. Brill, G. West, “Chromatic adaptation and color constancy: a possible dichotomy,” Color Res. Appl. 11, 196–204 (1986).
[CrossRef]

J. A. Worthey, M. H. Brill, “Heuristic analysis of von Kries color constancy,” J. Opt. Soc. Am. A 2(13), P13–P14 (1985).

G. West, M. H. Brill, “Necessary and sufficient conditions for von Kries chromatic adaptation to give color constancy,” J. Math. Biol. 15, 249–258 (1982).
[CrossRef] [PubMed]

Guth, S. L.

Huck, F. O.

Ives, H. E.

H. E. Ives, “The relation between the color of the illuminant and the color of the illuminated object,” Trans. Illum. Eng. Soc. 7, 62–72 (1912).

Karmarkar, N.

N. Karmarkar, “A new polynomial-time algorithm for linear programming,” Combinatorica 4, 373–395 (1984).
[CrossRef]

Land, E. H.

E. H. Land, “The retinex theory of color vision,” Sci. Am. 237(6), 108–128 (1977); “The retinex,” Am. Sci. 52(2), 247–264 (1964).
[CrossRef] [PubMed]

Massof, R. W.

McCann, J. J.

J. J. McCann, S. P. McKee, T. H. Taylor, “Quantitative studies in retinex theory,” Vision Res. 16, 445–458 (1976).
[CrossRef]

McKee, S. P.

J. J. McCann, S. P. McKee, T. H. Taylor, “Quantitative studies in retinex theory,” Vision Res. 16, 445–458 (1976).
[CrossRef]

Nikolayev, P. P.

N. D. Nyuberg, P. P. Nikolayev, M. M. Bongard, “Constancy of perception of colour,” Biophysics 16, 1094–1107 (1971).

Nyuberg, N. D.

N. D. Nyuberg, P. P. Nikolayev, M. M. Bongard, “Constancy of perception of colour,” Biophysics 16, 1094–1107 (1971).

Park, S. K.

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]

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]

Taylor, T. H.

J. J. McCann, S. P. McKee, T. H. Taylor, “Quantitative studies in retinex theory,” Vision Res. 16, 445–458 (1976).
[CrossRef]

West, G.

M. H. Brill, G. West, “Chromatic adaptation and color constancy: a possible dichotomy,” Color Res. Appl. 11, 196–204 (1986).
[CrossRef]

G. West, M. H. Brill, “Necessary and sufficient conditions for von Kries chromatic adaptation to give color constancy,” J. Math. Biol. 15, 249–258 (1982).
[CrossRef] [PubMed]

Worthey, J. A.

J. A. Worthey, “Limitations of color constancy,” J. Opt. Soc. Am. A 2, 1014–1026 (1985).
[CrossRef]

J. A. Worthey, M. H. Brill, “Heuristic analysis of von Kries color constancy,” J. Opt. Soc. Am. A 2(13), P13–P14 (1985).

Appl. Opt. (1)

Biophysics (1)

N. D. Nyuberg, P. P. Nikolayev, M. M. Bongard, “Constancy of perception of colour,” Biophysics 16, 1094–1107 (1971).

Color Res. Appl. (1)

M. H. Brill, G. West, “Chromatic adaptation and color constancy: a possible dichotomy,” Color Res. Appl. 11, 196–204 (1986).
[CrossRef]

Combinatorica (1)

N. Karmarkar, “A new polynomial-time algorithm for linear programming,” Combinatorica 4, 373–395 (1984).
[CrossRef]

J. Math. Biol. (1)

G. West, M. H. Brill, “Necessary and sufficient conditions for von Kries chromatic adaptation to give color constancy,” J. Math. Biol. 15, 249–258 (1982).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J. A. Worthey, M. H. Brill, “Heuristic analysis of von Kries color constancy,” J. Opt. Soc. Am. A 2(13), P13–P14 (1985).

J. A. Worthey, “Limitations of color constancy,” J. Opt. Soc. Am. A 2, 1014–1026 (1985).
[CrossRef]

Sci. Am. (1)

E. H. Land, “The retinex theory of color vision,” Sci. Am. 237(6), 108–128 (1977); “The retinex,” Am. Sci. 52(2), 247–264 (1964).
[CrossRef] [PubMed]

Trans. Illum. Eng. Soc. (1)

H. E. Ives, “The relation between the color of the illuminant and the color of the illuminated object,” Trans. Illum. Eng. Soc. 7, 62–72 (1912).

Vision Res. (2)

J. J. McCann, S. P. McKee, T. H. Taylor, “Quantitative studies in retinex theory,” Vision Res. 16, 445–458 (1976).
[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]

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Figures (3)

Fig. 1
Fig. 1

HR1 compared with the normal human retina. The solid curves are the spectral sensitivities of the B, G, and R receptors of normal humans.10 The dashed lines are the spectral sensitivities of the three-narrow-band receptors of HR1. In the discussion of the quantitative retinex experiment later in this paper, the dashed lines are to be reinterpreted as the SPD’s of lights. In all figures, where the dashed lines are shown as nearly zero, they are considered to equal 0.0 but have been separated for clarity.

Fig. 2
Fig. 2

HR2 and the spectral-reflectance factors of three object colors. The solid curve is the spectral sensitivity of HR2; it is in fact the familiar function V(λ), so that HR2 may be thought of as a spot photometer. The dashed lines are the spectral-reflectance factors of hypothetical white, green, and red papers. Where the reflectance are drawn nearly equal, they are considered to be equal.

Fig. 3
Fig. 3

HR3 and three-narrow-band lights. The solid lines are the hypothetical broad, nonoverlapping receptor-sensitivity functions, while the dashed lines are the narrow-band SPD’s.

Equations (8)

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P j = S j / S j 0 .
S j = λ ρ ( λ ) E ( λ ) q j ( λ ) ,
P j i = λ ρ i ( λ ) E ( λ ) q j ( λ ) λ ρ 0 ( λ ) E ( λ ) q j ( λ ) .
( R i G i B i ) = Q ( E ( 630 ) 0 0 0 E ( 530 ) 0 0 0 E ( 450 ) ) ( ρ i ( 630 ) ρ i ( 530 ) ρ i ( 450 ) ) ,
Q = ( r ¯ ( 630 ) r ¯ ( 530 ) r ¯ ( 450 ) g ¯ ( 630 ) g ¯ ( 530 ) g ¯ ( 450 ) b ¯ ( 630 ) b ¯ ( 530 ) b ¯ ( 450 ) ) .
( R 0 G 0 B 0 ) = Q ( ρ 0 ( 630 ) 0 0 0 ρ 0 ( 530 ) 0 0 0 ρ 0 ( 450 ) ) ( E ( 630 ) E ( 530 ) E ( 430 ) ) .
S j i / S j 0 = ρ i ( λ j ) / ρ 0 ( λ j ) ,
Q = ( 0.3800 0.7733 0.0343 0.0583 0.9410 0.0635 0.0001 0.0258 0.9160 ) .

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