Abstract

Psychometric scale values for color differences are correlated with physically measured chromaticity differences by use of a formula which postulates that the scale values are proportional to some power, less than unity, of distance in a subjectively isotropic, projective transformation of the CIE chromaticity diagram. Exponents ranging from 0.38 to 0.80 are reported. Eleven to 37% smaller root-mean-square errors of fit to psychometric scale values are obtained with the nonlinear hypothesis than with a linear hypothesis.

© 1963 Optical Society of America

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References

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  1. D. L. MacAdam, J. Opt. Soc. Am. 33, 18–26 (1943).
    [Crossref]

1943 (1)

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Figures (3)

Fig. 1
Fig. 1

Chromaticities (solid circles) and differences (lines) of three sets of tiles used in pair comparisons. Difference numbers shown in circles correspond to numbers in stub of Table I. For differences number 1–12, the luminous reflectance is about 7%; for 13–24, about 32%; for 25–36, about 58%.

Fig. 2
Fig. 2

Ellipses representing equal color differences: A, according to reference 1; B, derived by least-squares nonlinear fitting of data for differences 1 to 12; C, least-squares nonlinear fit for differences 13 to 24; D, least-squares nonlinear fit for differences 25 to 36.

Fig. 3
Fig. 3

Ellipses representing equal color differences at equal increments on psychometric scale for p = 0.37 in nonlinear formula (2). Encircled points represent judged color differences (13 to 24). Adjacent numbers are psychometric scale values of color differences derived from judgments. Arrows indicate largest errors of fit. All other errors are smaller than the radii of the circles.

Tables (2)

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Table I Psychometric scale values and chromaticity differences.

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Table II Rounded coefficients and root-mean-square errors.

Equations (2)

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H ¯ = H 1 [ g 11 ( Δ x ) 2 + 2 g 12 Δ x Δ y + g 22 ( Δ y ) 2 ] 1 2 ,
H ¯ = H 1 D p = H 1 [ g 11 ( Δ x ) 2 + 2 g 12 Δ x Δ y + g 22 ( Δ y ) 2 ] p / 2 ,