We have developed a method for determining the parameters of color-difference-perceptibility ellipses for surface colors and have evaluated it by use of new visual data. A new theory was devised, based on the assumption of a normal distribution of color differences in local areas of CIE 1931 chromaticity space. A likelihood function that combines the observer characteristic with the probability of a certain chromaticity point being seen as a match to a color center provides a mathematical description of color-difference perception in <i>x</i>, <i>y</i> space. Best estimates of the color-difference-perception-ellipse parameters and the value of a false-alarm-rate parameter are found by maximizing this likelihood function. Use of this function leads to predicted data that are not significantly different from collected visual data. The unit color-difference-perception ellipse thus calculated describes the locus of chromaticities that have approximately a 60% chance of being seen as matches to the color represented by the center of the ellipse.
Ruth M. Rich, Fred W. Billmeyer, Jr., and William G. Howe, "Method for deriving color-difference-perceptibility ellipses for surface-color samples," J. Opt. Soc. Am. 65, 956-959 (1975)