Abstract

Abrupt changes of trends, characteristic of formulas for color discrimination suggested by Friele, can be smoothed by slight modifications of Friele’s formulas. Except near the places where Friele’s formulas cause these changes, these modifications yield values of metric coefficients asymptotically equal to those derived from Friele’s formulas. Optimum values have been obtained for parameters in the revised formulas and for the primaries. Optimum parameters have also been determined for a set of color metric coefficients derived from old, but widely used, data based on observations by P. G. Nutting, Jr. The mean-square errors of reproduction of the Nutting data, with the smoothed formulas, are 5% less than for the more recent Brown 12-observer data and 21% less than for the somewhat less recent Brown–MacAdam data. The optimum parameters for the Nutting data are intermediate between those for the newer sets of data. Color-mixture curves are shown for direct computation of the required tristimulus values. By use of these, points can be located on the CIE 1959 diagram more easily than by use of the CIE 1931 data.

© 1965 Optical Society of America

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. II. Friele Approximation

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

Smoothed Versions of Friele’s 1965 Approximations for Color Metric Coefficients

David L. MacAdam
J. Opt. Soc. Am. 56(12) 1784_1-1785 (1966)

Friele Approximations for Color Metric Coefficients

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

Optimization of the MacAdam-Modified 1965 Friele Color-Difference Formula

K. D. Chickering
J. Opt. Soc. Am. 57(4) 537-541 (1967)