Encyclopedia of Color Science and Technology

2016 Edition
| Editors: Ming Ronnier Luo

CIEDE2000, History, Use, and Performance

Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-8071-7_7

Synonyms

Definition

CIEDE2000 [1, 2] is a color-difference formula recommended by the CIE in year 2001. It has also recently been published as an ISO and CIE Joint Standard [3]. It is a modification of CIELAB [4] and gives an overall best performance in predicting experimental datasets. The typical applications are pass/fail decision, color constancy, metamerism, and color rendering.

Overview

Over the years, color scientists and engineers have been striving to achieve a single number pass/fail color-difference equation, i.e., to apply a single pass/fail color difference to all color regions for industrial quality control. In practice, product batches should be visually acceptable against a standard, when a color difference is less than a predetermined color-difference unit (called color tolerance). Reversely, it will be rejected to be returned for re-shading.

In 1976, CIELAB uniform color space was recommended by the CIE. The decision was made based on limited experimental data. It was realized a shortage of reliable experimental data having similar color-difference magnitude as those used in industry (typically with CIELAB color difference (ΔE* ab ) ≤5). Hence, many datasets were produced, in which four datasets were considered to be most comprehensive and robust and were used to derive the new formulae. These datasets are Luo and Rigg [5], RIT-DuPont [6], Witt [7], and Leeds [8]. They have 2776, 156, 418, and 307 pairs of samples and average color differences of 3.0, 1.0, 1.9, and 1.6 ΔE* ab , respectively. All datasets were based on glossy paint samples except that of Luo and Rigg data, which include many subsets based on different materials, and finally all subsets were combined according to the experimental results based on textile samples [5].

Using these data, a series of equations were developed by modifying CIELAB. They all have a generic form as given in Eq. 1:
$$ \Delta E=\sqrt{{\left(\frac{\Delta L*}{k_L{S}_L}\right)}^2+{\left(\frac{\Delta {C}_{ab}*}{k_C{S}_C}\right)}^2+{\left(\frac{\Delta {H}_{ab}*}{k_H{S}_H}\right)}^2+{R}_T\left(\frac{\Delta {C}_{ab}*}{k_C{S}_C}\frac{\Delta {H}_{ab}*}{k_H{S}_H}\right)} $$
(1)
where
$$ \begin{array}{l}\Delta L*={L}_{\mathrm{ab},2} *-{L}_{\mathrm{ab},1}*\\ {}\Delta {C}_{ab}*={C}_{ab,2} *-{C}_{ab,1}*\\ {}\Delta {H}_{ab}*=2\sqrt{C_{ab,2} *{C}_{ab,1}*} \sin \left(\frac{\Delta {h}_{ab}}{2}\right)\\ {}\begin{array}{cc}\hfill \mathrm{where}\hfill & \hfill \Delta {h}_{ab}\hfill \end{array}={h}_{ab,2}-{h}_{ab,1}\end{array} $$
and subscripts 1 and 2 are the two samples in a pair. The R T is an interactive term between ΔCab* and ΔHab*. The S L , S C , and S H are weighting factors for the correlates of L*, Cab*, and hab and are dependent on the positions of the samples in a pair. The k L , k C , and k H are parametric factors to take into account the surface characteristics of the materials in question such as textile, paint, and plastic.

Equation 1 is a form of ellipsoid along the directions of CIELAB lightness, chroma, and hue angle. The ellipsoid can also be rotated in Cab* and hab plane. Four equations were developed after CIELAB in 1976. These were Leeds [8], BFD [9], CIE94 [10] and CMC [11]. The CMC was adopted by the ISO for textile applications in 1992 [11]. The CIE94 was recommended by the CIE for field trials in 1994. Both equations have the first three terms of Eq. 1, and BFD and Leeds include all four terms. All formulae greatly outperform CIELAB to fit the experimental datasets. Industry was confused which equation should be used. Hence, CIE Technical Committee (TC) 1–47 Hue and Lightness-Dependent Correction to Industrial Colour Difference Evaluation was formed in 1998. It was hoped that a generalized and reliable formula could be achieved.

The TC members worked closely together and a formula named CIEDE2000 was recommended [1, 2]. The computation procedure of this formula is given in Eq. 2.

CIEDE2000 (KL:KC:KH) Color-Difference Formula

The input of the equation is two sets of CIELAB values for the samples of the pair in question. The procedure to calculate CIEDE2000 is given below:
  • Step 1. Prepare data to calculatea’, C’, and h’.

  • $$ {L}^{\prime }={L}^{*} $$
  • $$ {a}^{\prime }=\left(1+G\right){a}^{*} $$
  • $$ {b}^{\prime }={b}^{*} $$
  • $$ {C}_{\mathrm{ab}}^{\prime }=\sqrt{{a^{\prime}}^2+{b^{\prime}}^2} $$
  • $$ {h}_{\mathrm{ab}}={ \tan}^{-1}\left(\frac{b^{\prime }}{a^{\prime }}\right) $$
  • where

  • $$ G=0.5\left(1-\sqrt{\frac{{\overline{C_{ab}^{*}}}^7}{{\overline{C_{ab}^{*}}}^7+{25}^7}}\right) $$
  • where \( \overline{C_{ab}^{*}} \) is the arithmetic mean of the C ab * values for a pair of samples.

  • Step 2. Calculate ΔL’, ΔC’,andΔH’.

  • $$ \begin{array}{l}\Delta L^{\prime }={L}_2^{\prime }-{L}_1^{\prime}\\ {}\Delta {C}_{ab}^{\prime }={C}_{ab,2}^{\prime }-{C}_{ab,1}^{\prime}\\ {}\Delta {H}_{ab}^{\prime }=2\sqrt{C_{ab,2}^{\prime }{C}_{ab,1}^{\prime }} \sin \left(\frac{\Delta {h}_{ab}^{\prime }}{2}\right)\\ {}\begin{array}{cc}\hfill \mathrm{where}\hfill & \hfill \Delta {h}_{ab}^{\prime}\hfill \end{array}={h}_{ab,2}^{\prime }-{h}_{ab,1}^{\prime}\end{array} $$
  • Step 3. Calculate CIEDE2000 ΔE 00 .

  • $$ \begin{array}{l}\Delta {E}_{00}=\sqrt{{\left(\frac{\Delta {L}^{\prime }}{k_L{S}_L}\right)}^2+{\left(\frac{\Delta {C}_{ab}^{\prime }}{k_C{S}_C}\right)}^2+{\left(\frac{\Delta {H}_{ab}^{\prime }}{k_H{S}_H}\right)}^2+{R}_T\left(\frac{\Delta {C}_{ab}^{\prime }}{k_C{S}_C}\right)\left(\frac{\Delta {H}_{ab}^{\prime }}{k_H{S}_H}\right)}\\ {}\mathrm{where}\\ {}{S}_L=1+\frac{0.015{\left({\overline{L}}^{\prime }-50\right)}^2}{\sqrt{20+{\left({\overline{L}}^{\prime }-50\right)}^2}}\\ {}\mathrm{and}\\ {}{S}_C=1+0.045\overline{C_{ab}^{\prime }}\\ {}\mathrm{and}\\ {}{S}_H=1+0.015\overline{C_{ab}^{\prime }}T\\ {}\mathrm{where}\\ {}T=1-0.17 \cos \left(\overline{h_{ab}^{\prime }}-{30}^{\mathrm{o}}\right)+0.24 \cos \left(2\overline{h_{ab}^{\prime }}\right)+0.32 \cos \left(3\overline{h_{ab}^{\prime }}+{6}^{\mathrm{o}}\right)-0.20 \cos \left(4\overline{h_{ab}^{\prime }}-{63}^{\mathrm{o}}\right)\\ {}\mathrm{and}\\ {}{R}_T=- \sin \left(2\Delta \theta \right){R}_C\\ {}\mathrm{where}\\ {}\Delta \theta =30 \exp \left\{-{\left[\left(\overline{h_{ab}^{\prime }}-{275}^{\mathrm{o}}\right)/25\right]}^2\right\}\\ {} \mathrm{and}\begin{array}{cc}\hfill \hfill & \hfill {R}_C=2\sqrt{\frac{{{\overline{C}}_{ab}^{\prime}}^7}{{{\overline{C}}_{ab}^{\prime}}^7+{25}^7}}\hfill \end{array}\end{array} $$
    (2)
    Note that \( \overline{L^{\prime }} \), \( \overline{C_{ab}^{\prime }} \), and \( \overline{h_{ab}^{\prime }} \) are the arithmetic means of the L’, C ab , and h ab values for a pair of samples. For calculating the \( \overline{h_{ab}^{\prime }} \) value, caution needs to be taken for neutral colors having hue angles in different quadrants, e.g., Sample 1 and Sample 2 with hue angles of 90° and 300° would have a mean value of 195°, which differs from the correct answer, 15°. This can be obtained by checking the absolute difference between two hue angles. If the difference is less than 180°, the arithmetic mean should be used. Otherwise, 360° should be subtracted from the larger angle, followed by calculating of the arithmetic mean. This gives 300−360° = −60° for the sample and a mean of (90−60°)/2 = 15° in this example.

Three-Term CIEDE2000 Color-Difference Formula

The CIEDE2000 color-difference equation described above includes four terms. In many applications, a three-term equation is required such as for shade sorting and color tolerance specification, indicating direction to a specific difference in recipe prediction. Hence, a three-term CIEDE2000 version was also developed [12] and is Eq. 3:
$$ \Delta {E}_{\mathsf{00}}={\left[{\left(\Delta {L}_{00}\right)}^{\mathsf{2}}+{\left(\Delta {C}_{\mathsf{00}}\right)}^{\mathsf{2}}+{\left(\Delta {H}_{\mathsf{00}}\right)}^{\mathsf{2}}\right]}^{\mathsf{1}/\mathsf{2}} $$
(3)
where
$$ \Delta {L}_{\mathsf{00}}=\frac{\Delta {L}^{\prime }}{k_{\mathsf{L}}{S}_{\mathsf{L}}};\;\Delta {C}_{\mathsf{00}}=\frac{\Delta {C}^{{\prime\prime} }}{S_{\mathsf{C}}^{{\prime\prime} }};\;\Delta {H}_{\mathsf{00}}=\frac{\Delta {H}^{{\prime\prime} }}{S_{\mathsf{H}}^{{\prime\prime} }} $$
and
$$ \Delta {C}^{{\prime\prime} }=\Delta {C}^{\prime } \cos \left(\varphi \right)+\Delta {H}^{\prime } \sin \left(\varphi \right) $$
$$ \Delta {H}^{{\prime\prime} }=\Delta {H}^{\prime } \cos \left(\varphi \right)-\Delta {C}^{\prime } \sin \left(\varphi \right) $$
where \( \tan\;\left(\mathsf{2}\varphi \right)={R}_{\mathsf{T}}\frac{\left({k}_{\mathsf{C}}\;{S}_{\mathsf{C}}\right)\;\left({k}_{\mathsf{H}}\;{S}_{\mathsf{H}}\right)}{{\left({k}_{\mathsf{H}}\;{S}_{\mathsf{H}}\right)}^{\mathsf{2}}-{\left({k}_{\mathsf{C}}\;{S}_{\mathsf{C}}\right)}^{\mathsf{2}}} \)
where φ is taken to be between −90° and 90°. If kHSH = kCSC, then 2φ is equal to 90° and φ is equal to 45°:
$$ {S}_{\mathsf{C}}^{{\prime\prime} }=\left({k}_{\mathsf{C}}\;{S}_{\mathsf{C}}\right)\sqrt{\frac{\mathsf{2}\left({k}_{\mathsf{H}}\;{S}_{\mathsf{H}}\right)}{\mathsf{2}\left({k}_{\mathsf{H}}\;{S}_{\mathsf{H}}\right)+{R}_{\mathsf{T}}\left({k}_{\mathsf{C}}\;{S}_{\mathsf{C}}\right) \tan \left(\varphi \right)}} $$
$$ {S}_{\mathsf{H}}^{{\prime\prime} }=\left({k}_{\mathsf{H}}\;{S}_{\mathsf{H}}\right)\sqrt{\frac{\mathsf{2}\left({k}_{\mathsf{C}}\;{S}_{\mathsf{C}}\right)}{\mathsf{2}\left({k}_{\mathsf{C}}\;{S}_{\mathsf{C}}\right)-{R}_{\mathsf{T}}\left({k}_{\mathsf{H}}\;{S}_{\mathsf{H}}\right) \tan \left(\varphi \right)}} $$
where ΔL′, ΔC′, and ΔH′ and S L , S C , S H , kL, kC, and kH are the same as those in Eq. 2.

The ΔE00 value calculated from Eq. 3 is the same as calculated from Eq. 2.

Evaluation of the CIEDE2000

The typical way to evaluate each formula’s performance is to apply statistical measures. One measure, standardized residual sum of squares (STRESS) index [13], has been widely used as given in Eq. 4. It measures the discrepancy between the calculated color difference (ΔE) and visual difference (ΔV) from an experimental dataset:
$$ \mathrm{STRESS}=100\sqrt{\frac{{\displaystyle \sum {\left(\Delta {E}_i-f\Delta {V}_i\right)}^2}}{f^2{\displaystyle \sum \Delta {V}_i^2}}} $$
(4)
where \( f=\frac{{\displaystyle \sum \Delta {E_i}^2}}{{\displaystyle \sum \Delta {E}_i\Delta {V}_i}} \)
STRESS values are ranged between 0 and 100. For a perfect agreement, STRESS value should be zero. It can be considered as a percentage error prediction. Table 1 gives the performance of the four equations tested using the previous mentioned four datasets together with COM dataset which was combined with a weight for each of the four datasets.
CIEDE2000, History, Use, and Performance, Table 1

Color-difference formula performance in STRESS unit (Copyright of the Society of Dyers and Colourists)

 

COM

BFD

Leeds

RIT-DuPont

Witt

CIELAB

44

42

40

33

52

CIE94

32

34

21

20

32

CIEDE2000

27

30

19

19

30

It can be seen in Table 1 that CIEDE2000 gave an overall best performance. In addition, CIELAB performed the worst. CIEDE2000 performed significantly better than the other formulae except insignificantly better than CIE94 for the Leeds and RIT-DuPont sets.

Another widely used method to evaluate color-difference equations is to use color discrimination ellipses. Figure 1 shows that the experimental ellipses (in black color) obtained from the Luo and Rigg dataset plotted against those (in red color) predicted by CIEDE2000. The color discrimination ellipse is an effective way to represent a number of color-difference pairs in a color center. The color differences between points in the ellipse and the color center represent equal visual color difference. If CIELAB formula agrees perfectly with the experimental results, all ellipses should be constant radius circles. Hence, the pattern shown in Fig. 1 indicates a poor performance of CIELAB, i.e., very small ellipses close to neutral axis; ellipse sizes increase when chroma increases. Comparing the experimental and CIEDE2000 ellipses, both sets fit well, especially in the blue region. (Note that the experimental ellipses for all other color regions generally point toward the neutral except that the blue ellipses point away from the neutral axis. This effect implies that both CMC and CIE94 formulae do fit well to the experimental results in the region.)
CIEDE2000, History, Use, and Performance, Fig. 1

Experimental color discrimination ellipses plotted in a* b* diagram (Copyright of the Society of Dyers and Colourists)

Future Directions

This section showed an outstanding color-difference equation, CIEDE2000, which has been recommended by the CIE. It fits the datasets having magnitude of industrial color differences well. However, it does not have an associated color space. A summary of the future direction on color difference is given below.
  • Almost all of the recent efforts have been spent on the modifications of CIELAB. This has resulted in CIEDE2000 including five corrections of CIELAB to fit the available experimental datasets. It is desirable to derive a formula based upon a new perceptually uniform color space from a particular color vision theory such as CIECAM02 [14].

  • 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, CIECAM02 model and its extension CAM02-UCS [15] are derived to follow this direction.

  • Almost all of the color-difference formulae were developed only to predict the color difference between a pair of large single objects/patches. More and more applications require to predict color differences between a pair of pictorial images. The current formula does not include necessary components to consider spatial variations for evaluating images. Johnson and Fairchild developed a spatial model based on CIEDE2000 [16].

Cross-References

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Copyright information

© Her Majesty the Queen in Right of United Kingdom 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