Statistics of color-matching experimental data

Abstract

By assuming that color matches are normally distributed in XYZ space, we present a rigorous statistical technique to obtain regions of equally noticeable chromaticity differences. The probability density function of color matches in (x, y, Y) space is calculated according to standard techniques in probability theory. The geometry of the chromaticity thresholds is computed for various confidence levels α. Because of the asymmetry of the probability density function in (x, y, Y) space, the chromaticity thresholds are not symmetrical around the color center. The asymmetries depend on the color center, and they increase when high confidence levels (α < 0.32) are considered. It is our opinion that the technique proposed here can provide a useful tool for checking and evaluating deviations from the elliptic geometry of the chromaticity thresholds. It is formally demonstrated that regions of equally noticeable chromaticity differences are not ellipses when the normality hypothesis is assumed in XYZ space.