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  1. W. Richards and E. A. Parks, J. Opt. Soc. Am. 61, 971 (1971).
    [Crossref] [PubMed]
  2. H. Helson, J. Exptl. Psychol. 23, 439 (1938).
    [Crossref]
  3. E. H. Land, Proc. Natl. Acad. Sci. (U.S.) 45, 115 (1959); Proc. Natl. Acad. Sci. (U.S.) 45, 636 (1959).
    [Crossref]
  4. A more sophisticated model would calculate the effective illuminant for each sample independently, using a weighting function that decreases as the distance from the sample decreases. A simpler and undoubtedly a sufficiently accurate approximation, however, would be to consider only the immediate neighbors of the sample, plus the sample itself.
  5. J. von Kries, Arch. Anat. Physiol. (Leipzig, Physiol. Abt.) 2, 503 (1878).
  6. Note that MacAdam’s nonlinear hypothesis for chromatic adaptation also requires different nonlinearities for each channel [D. L. MacAdam, Vision Res. 1, 9 (1961)]. MacAdam’s model differs from the present one by imposing the nonlinearity upon the tristimulus values, rather than upon the von Kries coefficients directly. If the threshold constant a is omitted from MacAdam’s model, and if the nonlinearity is assumed to be the same for both adaptations, then both models become formally equivalent, except in the method used to calculate the exponents Pi.
    [Crossref]
  7. T. N. Wiesel and D. H. Hubel, J. Neurophysiol. 29, 1115 (1966). (See particularly Figs. 2, 6, 10, and 15.)
    [PubMed]

1971 (1)

1966 (1)

T. N. Wiesel and D. H. Hubel, J. Neurophysiol. 29, 1115 (1966). (See particularly Figs. 2, 6, 10, and 15.)
[PubMed]

1961 (1)

Note that MacAdam’s nonlinear hypothesis for chromatic adaptation also requires different nonlinearities for each channel [D. L. MacAdam, Vision Res. 1, 9 (1961)]. MacAdam’s model differs from the present one by imposing the nonlinearity upon the tristimulus values, rather than upon the von Kries coefficients directly. If the threshold constant a is omitted from MacAdam’s model, and if the nonlinearity is assumed to be the same for both adaptations, then both models become formally equivalent, except in the method used to calculate the exponents Pi.
[Crossref]

1959 (1)

E. H. Land, Proc. Natl. Acad. Sci. (U.S.) 45, 115 (1959); Proc. Natl. Acad. Sci. (U.S.) 45, 636 (1959).
[Crossref]

1938 (1)

H. Helson, J. Exptl. Psychol. 23, 439 (1938).
[Crossref]

1878 (1)

J. von Kries, Arch. Anat. Physiol. (Leipzig, Physiol. Abt.) 2, 503 (1878).

Helson, H.

H. Helson, J. Exptl. Psychol. 23, 439 (1938).
[Crossref]

Hubel, D. H.

T. N. Wiesel and D. H. Hubel, J. Neurophysiol. 29, 1115 (1966). (See particularly Figs. 2, 6, 10, and 15.)
[PubMed]

Land, E. H.

E. H. Land, Proc. Natl. Acad. Sci. (U.S.) 45, 115 (1959); Proc. Natl. Acad. Sci. (U.S.) 45, 636 (1959).
[Crossref]

MacAdam, D. L.

Note that MacAdam’s nonlinear hypothesis for chromatic adaptation also requires different nonlinearities for each channel [D. L. MacAdam, Vision Res. 1, 9 (1961)]. MacAdam’s model differs from the present one by imposing the nonlinearity upon the tristimulus values, rather than upon the von Kries coefficients directly. If the threshold constant a is omitted from MacAdam’s model, and if the nonlinearity is assumed to be the same for both adaptations, then both models become formally equivalent, except in the method used to calculate the exponents Pi.
[Crossref]

Parks, E. A.

Richards, W.

von Kries, J.

J. von Kries, Arch. Anat. Physiol. (Leipzig, Physiol. Abt.) 2, 503 (1878).

Wiesel, T. N.

T. N. Wiesel and D. H. Hubel, J. Neurophysiol. 29, 1115 (1966). (See particularly Figs. 2, 6, 10, and 15.)
[PubMed]

Arch. Anat. Physiol. (Leipzig, Physiol. Abt.) (1)

J. von Kries, Arch. Anat. Physiol. (Leipzig, Physiol. Abt.) 2, 503 (1878).

J. Exptl. Psychol. (1)

H. Helson, J. Exptl. Psychol. 23, 439 (1938).
[Crossref]

J. Neurophysiol. (1)

T. N. Wiesel and D. H. Hubel, J. Neurophysiol. 29, 1115 (1966). (See particularly Figs. 2, 6, 10, and 15.)
[PubMed]

J. Opt. Soc. Am. (1)

Proc. Natl. Acad. Sci. (U.S.) (1)

E. H. Land, Proc. Natl. Acad. Sci. (U.S.) 45, 115 (1959); Proc. Natl. Acad. Sci. (U.S.) 45, 636 (1959).
[Crossref]

Vision Res. (1)

Note that MacAdam’s nonlinear hypothesis for chromatic adaptation also requires different nonlinearities for each channel [D. L. MacAdam, Vision Res. 1, 9 (1961)]. MacAdam’s model differs from the present one by imposing the nonlinearity upon the tristimulus values, rather than upon the von Kries coefficients directly. If the threshold constant a is omitted from MacAdam’s model, and if the nonlinearity is assumed to be the same for both adaptations, then both models become formally equivalent, except in the method used to calculate the exponents Pi.
[Crossref]

Other (1)

A more sophisticated model would calculate the effective illuminant for each sample independently, using a weighting function that decreases as the distance from the sample decreases. A simpler and undoubtedly a sufficiently accurate approximation, however, would be to consider only the immediate neighbors of the sample, plus the sample itself.

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Figures (3)

Fig. 1
Fig. 1

First stage of two-stage model applied to the Land effect. The mean illuminant I of the scene is displaced 70% of the distance toward illuminant C, as shown by the arrow. The transformed chromaticities now lie along the dashed line. The second stage of the original model displaces these transformed chromaticities into positions lying within the tongue-shaped area. The primaries are R, Y, and B.

Fig. 2
Fig. 2

Comparison between original first-stage transformation [f(Ki)] and the new approximation [g(Ki)], for a wide range of values of the von Kries coefficient Ki. Note that the ordinate is expanded to run from 0.6 to 1.1.

Fig. 3
Fig. 3

Regions in the CIE diagram having different errors of approximation: open area, error less than 5% for Ki values between 1 2 and 2; double cross-hatched area, error greater than 10% for Ki coefficients between 1 3 and 3. The dot indicates the position of illuminant C.

Equations (6)

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f ( K i ) = K i / ( 0.7 + 0.3 K i ) ,             i = R , Y , B .
g ( K i ) = K i 0.7 .
k i = f ( K i ) P i ,             i = R , Y , B
g ( K i ) P i = K i 0.7 P i .
P i = ( L av / L s ) 1 2
0.7 P i = ( 0.5 L av / L s ) 1 2 .