Method for deriving color-difference-perceptibility ellipses for surface-color samples

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 x, y 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.