Abstract

The von Kries coefficient law of chromatic adaptation—that there is linear proportionality between stimulus and response for each of three types of visual receptor—results in systematic discrepancies between prediction and experiment. A hypothesis that the responses of the receptors are nonlinear was fairly successful when applied to three sets of experimental data obtained independently by quite different methods. Analysis of additional data confirms the earlier conclusions that (1) discrepancies of predictions of corresponding colors by the linear hypothesis are significantly large and systematic; (2) the discrepancies are less systematic and are significantly reduced by the nonlinear hypothesis; (3) the most successful forms of the mathematical relations expressing the nonlinearities are systematically dependent on the chromaticities of the adaptations. These forms are substantially the same as those for the three sets of experimental data previously studied.

© 1963 Optical Society of America

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References

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  1. D. L. MacAdam, Farbe 4, 133–143 (1955).
  2. D. L. MacAdam, J. Opt. Soc. Am. 46, 500–513 (1956).
    [Crossref] [PubMed]
  3. D. L. MacAdam, J. Soc. Motion Picture Television Engrs. 65, 455–469 (1956).
  4. D. L. MacAdam, Vision Res. 1, 9–41 (1961).
    [Crossref]
  5. R. W. Burnham, R. M. Evans, and S. M. Newhall, J. Opt. Soc. Am. 47, 35–42 (1957).
    [Crossref]
  6. E. G. T. Wassef, Opt. Acta 5, 101–108 (1958).
    [Crossref]
  7. E. G. T. Wassef, Opt. Acta 6, 378–386 (1959).
    [Crossref]

1961 (1)

D. L. MacAdam, Vision Res. 1, 9–41 (1961).
[Crossref]

1959 (1)

E. G. T. Wassef, Opt. Acta 6, 378–386 (1959).
[Crossref]

1958 (1)

E. G. T. Wassef, Opt. Acta 5, 101–108 (1958).
[Crossref]

1957 (1)

1956 (2)

D. L. MacAdam, J. Opt. Soc. Am. 46, 500–513 (1956).
[Crossref] [PubMed]

D. L. MacAdam, J. Soc. Motion Picture Television Engrs. 65, 455–469 (1956).

1955 (1)

D. L. MacAdam, Farbe 4, 133–143 (1955).

Burnham, R. W.

Evans, R. M.

MacAdam, D. L.

D. L. MacAdam, Vision Res. 1, 9–41 (1961).
[Crossref]

D. L. MacAdam, J. Soc. Motion Picture Television Engrs. 65, 455–469 (1956).

D. L. MacAdam, J. Opt. Soc. Am. 46, 500–513 (1956).
[Crossref] [PubMed]

D. L. MacAdam, Farbe 4, 133–143 (1955).

Newhall, S. M.

Wassef, E. G. T.

E. G. T. Wassef, Opt. Acta 6, 378–386 (1959).
[Crossref]

E. G. T. Wassef, Opt. Acta 5, 101–108 (1958).
[Crossref]

Farbe (1)

D. L. MacAdam, Farbe 4, 133–143 (1955).

J. Opt. Soc. Am. (2)

J. Soc. Motion Picture Television Engrs. (1)

D. L. MacAdam, J. Soc. Motion Picture Television Engrs. 65, 455–469 (1956).

Opt. Acta (2)

E. G. T. Wassef, Opt. Acta 5, 101–108 (1958).
[Crossref]

E. G. T. Wassef, Opt. Acta 6, 378–386 (1959).
[Crossref]

Vision Res. (1)

D. L. MacAdam, Vision Res. 1, 9–41 (1961).
[Crossref]

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Figures (11)

Fig. 1
Fig. 1

Relation between stimulus Y and response V for values of P marked on curves for parameters in the equation relating V to Y such that σV is a minimum for each value of P.

Fig. 2
Fig. 2

Mean relative error of prediction for the linear hypothesis as a function of the location of the green primary.

Fig. 3
Fig. 3

Discrepancy chromaticities and covariance ellipse for one observer and pair of adaptations. The absolute values of ΔS are indicated for each point [two points are coincident at (0.76, 0.24)]. Two points lie outside the diagram and are indicated by arrows.

Fig. 4
Fig. 4

Locations and lengths of major axes of discrepancy ellipses on the basis of linear hypothesis for which axis ratio exceeds 2.00. Numbers refer to tabulated data in original publication.

Fig. 5
Fig. 5

Locations and lengths of major axes of discrepancy ellipses on the basis of nonlinear hypothesis for which axis ratio exceeds 2.00. Numbers refer to tabulated data in original publication.

Fig. 6
Fig. 6

Chromaticity diagram showing contours of equal p for the red response in the power form of the nonlinear hypothesis from MacAdam’s 1956 data. Heads of arrows indicate results from Burnham’s 1956 data.

Fig. 7
Fig. 7

Chromaticity diagram corresponding to Fig. 6 for the green response.

Fig. 8
Fig. 8

Chromaticity diagram corresponding to Fig. 6 for the blue response.

Fig. 9
Fig. 9

Chromaticity diagram showing contours of equal p for the red response in the power form of the nonlinear hypothesis from MacAdam’s 1956 data. Heads of arrows indicate results from Wassef’s 1959 data.

Fig. 10
Fig. 10

Chromaticity diagram corresponding to Fig. 9 for the green response.

Fig. 11
Fig. 11

Chromaticity diagram corresponding to Fig. 9 for the blue response.

Tables (1)

Tables Icon

Table I Root-mean-square errors of prediction of tristimulus sums.

Equations (4)

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

Δ X = X c - X , Δ Y = Y c - Y , Δ Z = Z c - Z , Δ S = Δ X + Δ Y + Δ Z .
ρ = a 1 + b 1 R p 1 , γ = a 2 + b 2 G p 2 , β = a 3 + b 3 B p 3 , ρ = a 4 + b 4 ( R ) p 4 , γ = a 5 + b 5 ( G ) p 5 , β = a 6 + b 6 ( B ) p 6 ,
R = c (     0.32 X + 0.75 Y - 0.07 Z ) , G = c ( - 0.46 X + 1.36 Y + 0.10 Z ) , B = c Z ,
x e = Δ X / Δ S , y e = Δ Y / Δ S .