CIELAB colour difference is based on the Euclidean distance between two colours represented in the CIE 1976 CIELAB uniform colour space.
A just-noticeable colour difference does not have the same numerical CIELAB colour difference in all regions, and there have been a number of attempts to improve the perceptual uniformity by the use of weighting functions. Some of the common formulas are shown in the spreadsheet ColourDifferenceFormulas.
The effect of the most recent of these, CIEDE2000, is shown in the figure where a constant colour difference of approximately 5 in CIELAB is plotted in CIEDE2000 for all values of a* and b* between +/- 128, and for a constant L* lightness of 50.