Encyclopedia of Color Science and Technology

2016 Edition
| Editors: Ming Ronnier Luo


Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-8071-7_11



CIELAB is a uniform color space (UCS) recommended by CIE in 1976 [1], and it was later published as a Joint ISO/CIE Standard [2]. A UCS is defined by the CIE International Lighting Vocabulary [3] 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 [4]. 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 [5].

Figure 1 shows the loci for samples having constant Munsell chroma and curves for samples having constant Munsell hue. Since the Munsell samples are based on equal visual steps, for a perfect agreement between the Munsell data and a color space, all loci should be circles with a constant increment between all neighboring chroma steps. As shown in Fig. 1, this is obviously not the case, i.e., one step of chroma in the blue region is at least five times shorter than one step of chroma in the green region. Additionally, all iso-chroma loci are far from being circles, and no iso-hue contours are straight lines. These indicate that there is a very large difference between the Munsell system and the CIE system represented by x,y chromaticity diagram.
CIELAB, Fig. 1

Constant Munsell chroma loci and constant Munsell hue curves at Munsell values of 5 plotted in the CIE chromaticity diagram (From Billmeyer and Saltzman [14])

Some earlier Munsell-based formulae are directly calculated using Munsell H, V, and C values with a weighting factor for each component. In 1944, ANLAB was developed by Adams and Nickerson [6] as given in Eq. 1.
$$ {\Delta \mathrm{E}}_{\mathrm{ANLAB}}=\sqrt{40\ \left\{{\left(0.23{\Delta \mathrm{V}}_{\mathrm{y}}\right)}^2+{\left[\Delta \left({\mathrm{V}}_{\mathrm{x}}-{\mathrm{V}}_{\mathrm{y}}\right)\right]}^2-0.4{\left[\Delta \left({\mathrm{V}}_{\mathrm{y}}-{\mathrm{V}}_{\mathrm{z}}\right)\right]}^2\right\}} $$
$$ \mathrm{I}=1.2219\ {\mathrm{V}}_{\mathrm{I}}-0.23111{{\mathrm{V}}_{\mathrm{I}}}^2+0.23591{{\mathrm{V}}_{\mathrm{I}}}^3-0.021009{{\mathrm{V}}_{\mathrm{I}}}^4+0.00084045{{\mathrm{V}}_{\mathrm{I}}}^5 $$
where I corresponds to X, Y, or Z tristimulus values.

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 [1]. 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)

CIELAB equation is given in Eq. 2.
$$ {L}^{*}=116f\left(Y/{Y}_{\mathrm{n}}\right)-16 $$
$$ {a}^{*}=500\left[ f\left(X/{X}_{\mathrm{n}}\right)-f\left(Y/{Y}_{\mathrm{n}}\right)\right] $$
$$ {b}^{*}=200\left[ f\left(Y/{Y}_{\mathrm{n}}\right)-f\left(Z/{Z}_{\mathrm{n}}\right)\right] $$
$$ f(I) = {I}^{1/3},\ \mathrm{f}\mathrm{o}\mathrm{r}\ I> {\left(\frac{6}{29}\right)}^{ 3} $$
$$ F(I) = \frac{841}{108}I+\frac{16}{116} $$
X, Y, Z and Xn, Yn, Zn are the tristimulus values of the sample and a specific reference white considered. It is common to use the tristimulus values of a CIE standard illuminant as the Xn, Yn, Zn values. Correlates of L*, a*, and b* are lightness, redness-greenness, and yellowness and blueness, respectively.
Correlates of hue and chroma are also defined by converting the rectangular a*, b* axes into polar coordinates (see Eq. 3). The lightness (L*), chroma (Cab*), and hue (hab) correlates correspond to perceived color attributes, which are generally much easier to understand for describing colors.
$$ {h}_{\mathrm{a}\mathrm{b}}={ \tan}^{ -1}\left({b}^{*}/{\mathrm{a}}^{*}\right) $$
$$ {C^{*}}_{\mathrm{ab}}=\sqrt{a^{*2}+{b}^{*2}} $$
Color difference can be calculated using Eq. 4.
$$ \Delta {E^{*}}_{\mathrm{ab}}=\sqrt{\Delta {L^{*}}^2 + \Delta {a^{*}}^2+\Delta {b^{*}}^2} $$
$$ \Delta {E^{*}}_{\mathrm{ab}}=\sqrt{\Delta {L^{*}}^2 + \Delta {C}^{*}{{}_{\mathrm{ab}}}^2+\Delta {H}^{*}{{}_{\mathrm{ab}}}^2} $$
$$ \Delta {H^{*}}_{\mathrm{ab}}=2{\left({C}_{\mathrm{ab}, 1}^{*}\ {C}_{\mathrm{ab}, 2}^{*}\right)}^{1/2} \sin \left[\frac{\left({h}_{\mathrm{ab}, 2}-{h}_{\mathrm{ab}, 1}\right)}{2}\right] $$
and subscripts 1 and 2 represent the samples of the pair considered; the ΔL*, Δa*, Δb*, ΔC*ab, and ΔH*ab are the difference of L*, a*, b*, C*ab, and hue in radiant unit (see Eq. 5) between Samples 1 and 2, respectively.
Figure 2 shows the CIELAB color space. It can be seen that the rectangular coordinates consist of L*, a*, and b*. A positive and negative values of a* represent reddish and greenish colors, respectively. A positive and negative values of b* represent yellowish and bluish colors, respectively. For the polar coordinates, hue angle is ranged from 0° to 360° following a rainbow scale from red, yellow, green, blue, and back to red. The 0°, 90°, 180°, and 270° approximate pure red, yellow, green, and blue colors (or unitary hues). Chroma starts from zero origin of neutral axis having chroma of zero and then increases its chromatic content to become more colorful. The colors located in the cylinder of Fig. 4 have a constant chroma, equally perceived chroma content around the hue circle.
CIELAB, Fig. 2

Illustration of CIELAB color space

Evaluation of CIELAB Color Space

Two sets of data are used here to evaluate the performance of CIELAB space. Figure 3 shows the constant Munsell chroma loci and constant Munsell hue curves at Munsell values of 5 plotted in CIELAB a*b* diagram. It can be seen that the pattern is close to the expectation of a good UCS, i.e., the constant chroma loci are close to circle and constant hue radius are close to a straight line (hue constancy). The uniformity of CIELAB is much better than that of CIE chromaticity diagram (see Fig. 1). However, detailed inspection can be found that the same chroma value in yellow and blue regions could still differ by a factor of almost 2. Also, the constant hue line is very much curved in the areas of orange, blue, and green yellow.
CIELAB, Fig. 3

Constant Munsell chroma loci and constant Munsell hue curves at Munsell values of 5 plotted in the CIELAB a*b* diagram

After the recommendation of the CIELAB formula, some experimental datasets having ΔE*ab ≤5 (representing typical magnitude of industrial color differences) were produced. These sets in general agree with each other. They were later selected to be used to derive different color difference formulae. Figure 4 shows the experimental ellipses obtained from the Luo and Rigg dataset [7]. The dataset includes more color centers and covers a much larger color gamut than the others. A color discrimination ellipse represents the points on the circumference of the ellipse against the center of the ellipse to have the same visual difference. If CIELAB formula agrees perfectly with the experimental results, all ellipses should be constant radius circles. The figure shows the poor performance of CIELAB. For example, all ellipses close to neutral are much smaller than those in the saturated color regions.
CIELAB, Fig. 4

Luo and Rigg experimental color discrimination ellipses plotted in a* b* diagram

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).

Future Directions

Since the recommendation of CIELAB in 1976, many equations were derived by modifying CIELAB such as CMC [8], CIE94 [9], and the more recent CIE recommendation CIEDE2000 [10]. They do fit the datasets (ΔE*ab ≤5) well. However, they do not have an associated color space. The future directions on color difference are given below.
  • 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 [11]. A uniform color space is based upon this color appearance model, like CAM02-UCS [12].

  • All color difference formulae can only be used in a set of reference viewing conditions defined by the CIE [10]. 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 [11] and its extension, CAM02-UCS [12], 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 [13].



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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.State Key Laboratory of Modern Optical InstrumentationZhejiang UniversityHangzhouChina
  2. 2.School of DesignUniversity of LeedsLeedsUK
  3. 3.Graduate Institute of Colour and IlluminationNational Taiwan University of Science and TechnologyTaipeiRepublic of China