This paper shows a computational technique of how to construct a nearly isometric transformation from a color space with a non-Euclidean color difference formula into an Euclidean space. The resulting transformation is a combination of a one-dimensional color lookup table (CLUT) to transform lightness values and a two-dimensional CLUT to transform chroma and hue coordinates. As an example the CIEDE2000 formula and a new optimized color difference formula for CIECAM02 was used and a transformation into an Euclidean space was calculated. The mean isometric disagreement was far below 3%. Color tolerance ellipsoides were plotted for both investigated color difference formulas and transformed into the new Euclidean space to illustrate the performence of the method. A movie of how the CIEDE2000 system is embedded into an Euclidean space is made available at the website: http://munsell.cis.rit.edu/~pmupci/
Philipp Urban, Roy S. Berns, Mitchell R. Rosen, "Constructing Euclidean Color Spaces based on Color Difference Formulas" in Proc. IS&T 15th Color and Imaging Conf., 2007, pp 77 - 82, https://doi.org/10.2352/CIC.2007.15.1.art00015