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 alpha. 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 (alpha < 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.

We present a discussion about the influence of luminance on the geometry of color-difference thresholds. By assuming that color matchings are normally distributed in XYZ space, we have shown [Appl Opt 38:208 -219 (1999)] that the probability density function of color matches in (x, y, Y) space is not a normal distribution function and it is an asymmetric one. Due to this asymmetry, the curves of equally noticeable chromaticity differences show asymmetries around the color center. The influence of luminance on the shape of these curves is analyzed, and we conclude that the lower the luminance, the larger the asymmetry.

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Presented in this article is a method for the determination of the Weber fraction by analyzing data obtained from color-matching experiments. The method is based on a rigorous analysis of the probability density function derived from discrimination judgments made in the xyY space. Analysis shows the thresholds for luminance increments and decrements are shown to be different and asymmetric and the Weber fraction to depend on the target's level of luminance and chromaticity.

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