A simple review of CIE ΔE* (Color Difference) Equations

PHOTO: Techkon SpectroDens 4 all-in-one-color densitometer and spectrophotometer.

If you work in the color industry, either you are a brand owner, merchandise designer, printing professional, paint department staff in Home Depot or Lowe’s, or just a complete color geek like me who likes words like CIE CMC color, you will likely hear the term “ΔE”, pronounced “delta-E”. Since I work in the color industry, I spend most of my time talking to all of the professionals listed above. Not surprisingly, many of them did not start in the printing or color field in their early career. That said, it is important to catch up on some of the most important terminology.

The intent of using ΔE (dE) is to describe the distance between two colors. The barely noticeable difference (JND) of dE is usually 1. In other words, if two colors have a dE less than 1 it is imperceptible and larger than 1 is perceivable. Unfortunately, due to the nature of human color perception (our eyes), the visual perception of colors is different. In general, our eyes are more sensitive to changes in Chroma than lightness. That means, the same dE between two yellows and two greens will very likely look different in our eyes. With that in mind, newer dE equations have been developed over the years and below is a list of 4 major formulas we might encounter in the color reproduction field.

ΔEab (aka. ΔE76, dEab or dE76)
The CIEL*a*b* and ΔEab was introduced by the International Commission on Illumination (CIE) in 1976. Given two colors in the CIEL*a*b* color space, (L₁, a₁, b₁) and (L₂, a₂, b₂), the ΔEab formula is defined as:
dEab equation from http://www.brucelindbloom.com/index.html?ColorDifferenceCalc.html
Where,
L₁– the CIE L* value of reference color
a₁– the CIE a* value of reference color
b₁– the CIE b* value of reference color
L₂– the CIE L* value of sample color
a₂– the CIE a* value of sample color
b₂– the CIE b* value of sample color
The ΔEab has been succeeded by other formulas that are discussed below, while it still bears useful information about the linear distance between two colors.
ΔE_CMC(aka. dE_CMC, CMC l:c)
The CIE is not the only party that defined color differencing equations. The Colour Measurement Committee of the Society of Dyers and Colourists (CMC) defined a new color difference method in 1984, named after the developing committee, CMC l:c.dE_CMC equation from http://www.brucelindbloom.com/index.html?ColorDifferenceCalc.html
This equation takes the complexity of human color sensitivity/perception into consideration based on CIEL*C*h* – notation of colors. There are a few variations in the formula since it allows the user to assign different weights to its lightness (l) and chroma (c) factors. The CMC l:c was developed based on the visual evaluation of textile samples and human vision sensitivity levels in the lightness (l) and the chrome (c), the default ratio of l: c is 2:1, which doubles the tolerance of variation for lightness then that for chroma. The other common ratio of l:c is 1:1. Please consult with your supplier/buyer on which ratio to use if CMC l:c is selected for your production. Different ratios will result in varying sizes of tolerance ellipses, in other words, acceptability of color match.
ΔE₉₄(aka. dE94)
In 1995, the CIE revised the formula by introducing ΔE₉₄ to address the color non-linearity nature under ΔEab. Like CMC l:c method, ΔE₉₄also uses CIEL*C*h* for calculating color differences.

dE₉₄ equation from http://www.brucelindbloom.com/index.html?ColorDifferenceCalc.html
The ΔE₉₄formula provides two coefficients, k and S, which are mostly based on tolerance data from RIT/Dupont from automotive paint research. Most of the time, those two types of coefficients are pre-selected by the software developer based on either textile or graphic arts industry users. While, due to the limitation of the ΔE₉₄that lacking accuracy in the blue-violet region of the color space, which eventually leads to the release of ΔE₂₀₀₀(Martin, 2013)_.
ΔE₂₀₀₀(aka. ΔE₀₀, dE2000, CIEDE2000 or dE00)
The ΔE₂₀₀₀was first proposed by CIE TC1-47 in CIE Publ.142 in 2001 and standardized in 2013. You might find an old ISO white paper or IDEAlliance G7 Specification that still use ΔEab as the dominant color difference formula along with ΔE₂₀₀₀for information purposes only. Since 2013, both ISO and IDEAlliance has adopted ΔE₂₀₀₀ as the new industry standard for calculating color differences.

dE_CMC equation from http://www.brucelindbloom.com/index.html?ColorDifferenceCalc.html

It is obvious that the ΔE₂₀₀₀is much more complex than the ΔEab. In summary, the ΔE₂₀₀₀introduced weight functions: S_L, S_C, S_H, R_T and a’(Neutral), as positional corrections to the lack of uniformity of CIELAB, also parametric factors: K_L, K_C and K_H as corrections accounting for the influence of experimental viewing conditions ( D65, 1000 lx, background gray with L*=50, etc.).There are numerous studies indicating that ΔE₂₀₀₀is superior than other color differencing formulas:“Currently, we have no candidate color space (e.g. DIN99, CAM02, OSAGP , etc.) providing statistically significant improvement upon CIEDE2000.” (CIE TC 1-55, 2016)“From the experiments carried out in the various years it becomes clear that ΔE₂₀₀₀corresponds better with the way human observers perceive small color difference.” (Martin, 2013)“ The CIEDE2000 formula may not be the final word with respect to a colour difference formula for small color differences for industry. The experimental data on which the formula is based are far from perfect. However, at the present time the formula represents the best that can be achieved. In our view, CIEDE2000 is timely because there are two different formulae (CMC and CIE94) being widely used at present. This is clearly unsatisfactory. The new formula offers significant improvements over both.” (M. R. Luo, G. Cui, and B. Rigg, 2002)

Final Verdict

Even though the ΔE₂₀₀₀won’t be the final answer for the best color difference equation for the color field, it is by far the best and most widely used formula in the graphic arts industry backed by ISO and IDEAlliance. But regardless of which color differencing equation you are using, a good color match is what is approved by your customer or whoever pays the bills! That said, please allow me to end this blog using the five rules from Billmeyer (1970/1979):

Select a single method of calculation and use it consistently.
Always specify exactly how the calculations are made.
Never attempt to convert between two color differences calculated by different equations through the use of averaging factors.
Use calculated color differences only as a first approximation in setting tolerance, until they can be confirmed by visual judgments – in other words, verify all calculation visually.
Always remember that nobody accepts or rejects color because of numbers – it’s the way that it looks that counts.

To add some icing on top of the blog, please feel free to download the ΔE calculator we developed. If you have any questions or comments, you are welcome to contact us at service@techkonusa.com.

References
Bruce Lindbloom, varies screenshots of different color differencing formula, April, 2017 (http://www.brucelindbloom.com/index.html?ColorDifferenceCalc.html)
CIE TC 1-55 committee, Recommended Method For Evaluating The Performance of Colour-Difference Formulae, CIE217:2016 (http://www.cie.co.at/publications/recommended-method-evaluating-performance-colour-difference-formulae)
Martin Habekost, Which color differencing equation should be used, International Circular of Graphic Education and Research, No. 6, 2013 (https://www.hdm-stuttgart.de/international_circle/circular/issues/13_01/ICJ_06_2013_02_069.pdf)