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/.
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