The very high complexity of the CIEDE2000 formula [1,2] has shown the inadequateness of the CIELAB system to represent a small-medium color-difference formula. This induced us to carry out an analysis on the OSA-UCS system [3,4,5], where the empirical small-medium color differences are represented by a very high regular ellipsoidal equation [6,7]. Particularly, with regard to the whole set of BFD ellipses  at constant luminance factor, the ellipses have the long axes lying on lines radiating from the achromatic point and both axes have lengths, that are hue independent and linearly chroma dependent. This regularity induces us to perform a logarithmic compression on chroma producing a new space, where the BFD ellipses appear very close to circles with equal radius and the color-difference formula at constant lightness is represented by the equation of a circle. The goodness of this formula, measured by the performance factor PF/3  over the BFD set, is very close, almost equal, to that obtained with the ellipsoidal formula in OSA-UCS space. This means that the quality of the two formulas is nearly identical and that the small-medium color differences at constant lightness are well represented in the chroma logcompressed OSA-UCS space by the equation of a circle.
C. Oleari, R. Huertas, M. Melgosa, "Euclidean Color-Difference Formula in Chroma Compressed OSA-UCS Space" in Proc. IS&T CGIV 2006 3rd European Conf. on Colour in Graphics, Imaging, and Vision, 2006, pp 294 - 297, https://doi.org/10.2352/CGIV.2006.3.1.art00060