# Delta E: The Color Difference

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by Steve Upton

## Contents |

# Delta-E - the color difference

You don't have to spend too long in the color management world before you come across the term Delta-E. As with many things color, it seems simple to understand at first, yet the closer you look, the more elusive it gets.

Delta-E (dE) is a single number that represents the 'distance' between two colors.

The idea is that a dE of 1.0 is the smallest color difference the human eye can see. So any dE less than 1.0 is imperceptible (as in turn the lights off and head to the pub) and it stands to reason that any dE greater than 1.0 is noticeable (as in put the coffee on, we're going to be here a while). Unfortunately - and probably not surprisingly - it's not that simple. Some color differences greater than 1 are perfectly acceptable, maybe even unnoticeable. Also, the same dE color difference between two yellows and two blues may not look like the same difference to the eye and there are other places where it can fall down.

It's perfectly understandable that we would want to have a system to show errors. After all, we've spent the money on the instruments, shouldn't we get numbers from them? Delta-E numbers can be used for:

- how far off is a print or proof from the original
- how much has a device drifted
- how effective is a particular profile for printing or proofing
- removes subjectivity (as much as possible)

## Delta-E 1976

So, a bit of history is probably in order. The L*a*b* colorspace was devised in 1976 (let's just call it Lab for short) and, at the same time delta-E 1976 (dE76) came into being. If you can imagine attaching a string to a color point in 3D Lab space, dE76 describes the sphere that is described by all the possible directions you could pull the string. If you hear people speak of just plain 'delta-E' they are probably referring to dE76. It is also known as dE-Lab and dE-ab (although I'm REALLY not fond of dE-ab as it implies that only the a* and b* color components are calculated and L* is left out)

One problem with dE76 is that Lab itself is not 'perceptually uniform' as its creators had intended. So different amounts of visual color shift in different color areas of Lab might have the same dE76 number. Conversely, the same amount of color shift might result in different dE76 values. Another issue is that the eye is most sensitive to hue differences, then chroma and finally lightness and dE76 does not take this into account (since Lab does not take this into account).

### Difference vs Tolerance

If difference is a number showing how 'far apart' two colors are, tolerance is the meaning of the number. Setting a tolerance level (such as 2.0 dE76) defines what you will accept and what you will reject(reproduction tolerance). The available differencing equations will also produce different shaped 'tolerance regions'.

### Delta-Lab and Delta-LCH

One type of difference calculation that some people use is delta-L, delta-a, delta-b (dLab). By breaking the error into its components you can sometimes get a feel for what might be causing the error. If the tolerance region for dE76 is described as a round sphere, then dLab is a square cube. My favorite variation on this idea is delta-LCH. Remember that LCH is Lightness (the same one as in Lab), Chroma (the distance out from the neutral axis - saturation) and Hue (the angle/direction in the 360 degree range). If d-Lab is a box-shaped region then d-LCH is a wedge - like cutting a piece of a flat round ring or washer. The interesting thing about d-LCH is what it can tell you about inkjet behavior. Different LCH values can refer to different problems, for instance: *larger dL may be a paper difference *larger dC may be paper coating difference *larger dH may be an ink difference

As the eye's sensitivity to hue, chroma, and then lightness differ, the tolerance region around each color that contains acceptable color matches is best represented by an rugby ball-shaped ellipsoid. The more modern color difference formulae use this ellipsoid shape and allow you, the user, to vary several different parameters to tune the numbers to match visual comparisons.

## CMC l:c

In 1984 the CMC (Colour Measurement Committee of the Society of Dyes and Colourists of Great Britain) developed and adopted an equation based on LCH numbers. Intended for the textiles industry, CMC l:c allows the setting of lightness (l) and chroma (c) factors. As the eye is more sensitive to chroma, the default ratio for l:c is 2:1 allowing for 2x the difference in lightness than chroma (numbers). There is also a 'commercial factor' (cf) which allows an overall varying of the size of the tolerance region according to accuracy requirements. A cf=1.0 means that a delta-E CMC value <1.0 is acceptable.

## dE94

A technical committee of the CIE (TC 1-29) published an equation in 1995 called CIE94. The equation is similar to CMC but the weighting functions are largely based on RIT/DuPont tolerance data derived from automotive paint experiments where sample surfaces are smooth. It also has ratios, labeled kL (lightness) and Kc (chroma) and the commercial factor (cf) but these tend to be preset in software and are not often exposed for the user.

## dE2000

Delta-E 2000 is the first major revision of the dE94 equation. Unlike dE94, which assumes that L* correctly reflects the perceived differences in lightness, dE2000 varies the weighting of L* depending on where in the lightness range the color falls. dE2000 is still under consideration and does not seem to be widely supported in graphics arts applications.

## A few important points about delta-E calculations in general

- dE calculations are based on colorimetry which means they are illuminant-dependent. Don't try comparing numbers calculated from colors viewed / measured under different illuminants.
- differing dE due to illuminant is metamerism. If colors are 'adapted' to the same white point then you have a metamerism index.

## Finally, which equation should be chosen and how should it be used?

- for basic / fast calculations, you can use dE76 but beware of its problems
- for graphics arts use we recommend dE94 and perhaps dE-CMC 2:1
- for textiles use dE-CMC

## Choosing the right tolerance (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 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 judgements - in other words, verify all calculations visually
- Always remember that nobody accepts or rejects color because of numbers - it's the way it looks that counts.

## Summary

I realize that this article is one of the more technical that I have written but delta-E is one of those topics that is worth understanding, and it can take a little work. I have also simplified the daylights out of some of my explanations. This is intended as an introduction to the concepts and not a detailed reference work.

At the very least, the next time you hear someone spouting off delta-E values you can ask them which delta-E. If there's a long, confused pause then you'll know what you're dealing with.

For more information and the actual equations I suggest you consult the following sources as I did for this article:

- Colour Engineering: Achieving Device Independent Colour - Edited by Phil Green & Lindsay MacDonald. Wiley. ISBN: 0471486884
- The Reproduction of Colour - R.W.G. Hunt, Wiley. ISBN: 0470024259
- Color Science: Concepts and Methods, Quantitative Data and Formulae - Gunther Wyszecki & WS Stiles. Wiley. ISBN: 0471399183
- A Guide to Understanding Color Communication - X-Rite PDF

Thanks for reading, Steve Upton