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 curt,es is analyzed, and we conclude that the lower the luminance, the larger the asymmetry..