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One of the limitations of CIELAB is that it does not offer a full-fledged chromatic adaptation in that it performs the [[von Kries transform]] method directly in the XYZ color space (often referred to as “wrong von Kries transform”), instead of changing into the [[LMS color space]] first for more precise results. ICC profiles circumvent this shortcoming by using the [[LMS color space#CIECAM97s, LLAB|Bradford transformation matrix]] to the LMS color space (which had first appeared in the [[#LLAB|LLAB color appearance model]]) in conjunction with CIELAB.
Due to the "wrong" transform, CIELAB is known to perform poorly when a non-reference illuminant XYZ value is used, making it a poor CAM. The wrong transform also seems responsible for its irregular blue hue, which bends towards purple as L changes, making it also a non-perfect UCS.
===Nayatani et al. model===
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