Abstract

On the assumption of a color space of constant negative curvature, von Schelling has given simple formulas for the color metric coefficients. An attempt has been made to fit such formulas to newly available color-discrimination data for 12 normal observers. A least-squares analysis indicates that Y should be replaced with the quantity, Y′=Y−0.085X+0.011Z, in the special role assigned to luminance by von Schelling. Corresponding to this change, coordinates x′=X/(X+Y′+Z), y′=Y′/(X+Y′+Z) yield the simplest formulas for the coefficients of the expression for color difference:

Least-squares fitting of the experimental data to von Schelling’s formulas yielded:

These formulas are the best approximations obtainable on the assumption of a color space of constant negative or zero curvature. However, they give such poor approximations to the experimental data that it is concluded that the assumption of a color space inherently more complicated than a space of constant curvature would be required to fit the data to a closeness commensurate with the experimental reproducibility.

© 1957 Optical Society of America

Analytical Approximations for Color Metric Coefficients. II. Friele Approximation

David L. MacAdam
J. Opt. Soc. Am. 54(2) 249-256 (1964)

Analytical Approximations for Color Metric Coefficients. III. Optimization of Parameters in Friele’s Formulas

David L. MacAdam
J. Opt. Soc. Am. 54(9) 1161-1165 (1964)

Analytical Approximations for Color Metric Coefficients. IV. Smoothed Modifications of Friele’s Formulas*

David L. MacAdam
J. Opt. Soc. Am. 55(1) 91-95 (1965)

Friele Approximations for Color Metric Coefficients

L. F. C. Friele
J. Opt. Soc. Am. 56(2) 259_1-260 (1966)

Color Discrimination of Twelve Observers*

W. R. J. Brown
J. Opt. Soc. Am. 47(2) 137-143 (1957)