In recent years, various color difference formulas were developed for the CIELAB space, such as CMC, CIE94 and CIEDE2000. Although these formulas have achieved greater accuracy in perceptual measurement between colors, many applications cannot take advantage of this greater precision, because the Euclidean distances in CIELAB are not isometric in accordance with these new formulas. Thus, applications such as gamut mapping and color interpolation need a color space that is isometric in relation to the latest color difference formulas. This paper studies the mapping of the CIELAB space, particularly the ab plane of this space according to the metrics of the CIEDE2000 formula, through multidimensional scaling (MDS) techniques, more specifically ISOMAP and an optimization based on Sammon Mapping.