All color difference equations are based, either explicitly or implicitly, on the measurement of the distance between the two colors when plotted in a visually uniform color space. The accuracy of these equations depends upon the approximations assumed in their derivation and the uniformity of the color space chosen. Judd’s Uniform Chromaticity space, Adam’s Chromatic Value space, the Munsell space, and others have been used as the basis of color difference equations.
Instead of explicitly transforming the ICI space into a visually uniform space, its known distortions can be compensated by means of the MacAdam ellipsoids. Color differences may be calculated very simply by a graphical method, assuming any point on the ellipsoid to represent a unit color difference from the center of the ellipsoid. Calculations of this sort have been applied to the Balinkin data on tiles and to data more recently obtained on textile dyeings.
Color differences calculated by this method correlate with visually estimated color differences as closely as do differences calculated by the best of the equations based upon uniform color spaces. This appears to be further confirmation of the validity of the MacAdam ellipsoids and of their usefulness in specification of color tolerances.
H. R. DAVIDSON, "Calculation of Color Differences from Visual Sensitivity Ellipsoids," J. Opt. Soc. Am. 41, 1052-1055 (1951)