CIELAB is a uniform color space (UCS) recommended by CIE in 1976 , and it was later published as a Joint ISO/CIE Standard . A UCS is defined by the CIE International Lighting Vocabulary  as a color space in which equal distances are intended to represent threshold or suprathreshold perceived color differences of equal size. It is one of the most widely used color spaces. The typical applications include color specification and color difference evaluation. The former is to describe a color in perceptual correlates such as lightness, chroma, and hue and to plot samples to understand their relationships. The latter is mainly used for color quality control such as setting color tolerance, color constancy, metamerism, and color rendering.
For the definition equations of the components of CIELAB, see section CIE L*a*b* Formula (CIELAB).
Over the years, color scientists and engineers have been striving to achieve a UCS. To apply UCS, a pair of samples will first be measured by a color measuring instrument to obtain their CIE tristimulus values (XYZ) which will then be transformed to the perceptual correlates such as CIELAB lightness, chroma, and hue angle. The distance between a pair of colors is calculated and reported as color difference (ΔE). This difference will then be judged against a predetermined color tolerance which could be a particular color region and a product. For a particular product, all pairs should be judged as “acceptable,” when the color difference is less than the color tolerance. Otherwise, it will be rejected. A good color difference formula is also called a “single number pass/fail formula,” i.e., to apply a single color tolerance to all color regions.
Over 20 formulae were derived before the recommendation of CIELAB in 1976 . Some of them were derived to fit the spacing of the Munsell color order system. The concept of the Munsell color order system was invented by A. H. Munsell and was based on steps of equal visual perception. Any color can be defined as a point in a three-dimensional Munsell color space. Its associated attributes are Munsell hue (H), Munsell chroma (C), and Munsell value (V) which correspond to the perceived hue, saturation, and lightness, respectively. The spacing of the color samples for each attribute was intensively studied by the members in the Colorimetry Committee of the Optical Society of America (OSA), and the CIE tristimulus values of ideally spaced samples were published in 1943 .
In Eq. 1, the terms of (Vx − Vy) and 0.4(Vy − Vz) correspond to the ANLAB a (redness-greenness) and b (yellowness-blueness) scales, respectively. By adding the third scale 0.23Vy, ANLAB becomes a three-dimensional UCS. It was recommended by the Colour Measurement Committee (CMC) of the Society of Dyers and Colourists (SDC) and became an ISO standard in 1971 for the application in the textile industry. A series of cube root formulae were also derived to simplify the ANLAB formula which involves a cumbersome fifth-order polynomial function. This resulted in CIELAB color difference formula introduced in 1976 . CIELAB units include L*, a*, and b*; the asterisk is used to differentiate the CIELAB system from ANLAB.
In 1976, the CIE recommended two uniform color spaces, CIELAB (or CIE L*a*b*) and CIELUV (or CIE L*u*v*), as it was still not possible to decide which one would correspond better to visual observations.
CIE L*a*b* Formula (CIELAB)
Evaluation of CIELAB Color Space
The results given in Figs. 3 and 4 clearly showed the effect of performance that different experimental results could disagree with each other greatly. The discrepancy between the Luo and Rigg and Munsell datasets is mainly due to the color difference magnitude used in the experimental datasets. CIELAB performs not badly for the large color differences with ΔE* ab about 10 units (see Fig. 3), but predicts very poorly for smaller color differences (ΔE*ab ≤5) (see Fig. 4).
It is desirable to derive a formula based upon a new perceptually uniform color space from a model of color vision theory such as CIECAM02 . A uniform color space is based upon this color appearance model, like CAM02-UCS .
All color difference formulae can only be used in a set of reference viewing conditions defined by the CIE . It will be valuable to derive a parametric color difference formula capable of taking into account different viewing parameters such as illuminant, illuminance level, size of samples, size of color difference, separation, and background. Again, the CIECAM02 model  and its extension, CAM02-UCS , are equipped with these capabilities.
Almost all of the color difference formulae were developed only to predict the color difference between a pair of individual patches. More and more applications require evaluating color differences between a pair of pictorial images. Johnson and Fairchild developed a formula for this purpose .
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