The CMC tolerancing method directly addresses our "elliptical" perception of color difference, and therefore is regarded in many industries as a more logical and accurate tolerancing system than CIELAB.
CMC is not a new color space, but a tolerancing system that is based on the L*a*b* color space. The CMC calculation mathematically defines an ellipsoid around a standard color in the color space. This ellipsoid consists of a semi-axis that corresponds to the attributes of hue, chroma, and lightness. It represents the area of acceptance in relation to the standard, the same way the CIELAB "box" defines acceptable difference limits. In CMC, the size of the ellipsoid varies depending on its position in the color space; for example, in the orange region, ellipsoids are narrower, while in the green region, ellipsoids are wider. Also, ellipsoids in high-chroma regions are larger than those in low-chroma regions.
DE2000 was developed to attempt to address one of the major weaknesses of the color tolerance equations,which is using the position of the reference color in CIELAB color space for computing the local distortion of CIELAB color space. When the identifications of the two specimens are reversed (calling the original test specimen the reference and the original reference now the test specimen) the computation results in a different computed color difference. This is contrary to what is observed. Visually, there is no change in the magnitude of the difference between the specimens simply by switching roles. By using the position of the arithmetic average color between the two specimens to compute the local distortions to CIELAB color space, the roles of the two specimens may be switched without changing the magnitude of the computed color difference, in full agreement with the visual assessments.
In DE2000 it is not possible or reasonable to plot groups of colors in terms of the modified space coordinates, L*,a*, b* since the meaning of a* is determined uniquely for each pair of colors. Thus the equation is highly optimized for pairwise comparison of a product standard to a production test specimen but not for statistical process control.