The CIE 1994 Colour Difference Model

Contributed by David Heggie, HeggieD@scot.hw.ac.uk
Scottish College of Textiles, Heriot Watt University

The new formula is called the CIE 1994 (DL*DC*DH*) color difference model, with the abbreviation CIE94, and symbol DE*94. The CIE have defined reference conditions under which the new metric with default parameters can be expected to perform well.

These are :

The specimens are homogeneous in colour.

The colour difference (CIELAB) is <= 5 units.

They are placed in direct edge contact.

Each specimen subtends an angle of >4 degrees to the assessor, whose colour vision is normal.

They are illuminated at 1000 lux, and viewed against a background of uniform grey, with L* of 50, under illumination simulating D65.

The new formula is similar in form to the CMC(l:c) colour difference formula, which is in widespread use, and is a BSI standard (BS 6923:1988). Both of these metrics are based in CIELAB space, with its perceptual correlates of lightness, chroma and hue differences. It is shown below:

DE*=( (DL* / kL.SL)^2 + (DC* / kC.SC)^2 + (DH* / kH.SH)^2 )^1/2

If you are familiar with the CMC(l:c) and BFD(l:c) formulae, you will recognise this form, in which the differences in Lightness (DL*), Chroma (DC*) and Hue (DH*) are weighted according to the size of a tolerance ellipsoid around the standard.

CIE94 differs from CMC(l:c) in the way these ellipsoid dimensions are calculated. In the CIE94 metric these are termed 'weighting functions', and are defined by the following linear equations:

SL = 1
SC = 1 + 0.045 C*
SH = 1 + 0.015 C*

where C* = value of standard's Chroma. If neither can be reasonably termed the standard, the geometric mean of the C values is used:
C* = (C*1.C*2)^1/2

The variables kL, kC and kH are called 'parametric factors' and are included in the formula to allow for adjustments to be made independently to each colour-difference term to account for any deviations from the reference viewing conditions, that cause component specific variations in the visual tolerances. Under the reference conditions explained above, they are set to

kL = kC = kH = 1.

References

CIE Publication 116-1995, 'Industrial Colour-Difference Evaluation' (Vienna: CIE 1995)
McDonald, R and Smith KJ, 'CIE94 - a new colour-difference formula', J. Soc. Dyers Col. Vol 111, Dec 1995, 376-379.

Ed note: I asked David if he'd be willing to contribute actual code that could be used to calculate CIE94, for the benefit of those like me, who are better programmers than mathematicians. He sent the following, which calculates CIE94, as well as CIELab, BFD, and CMC differences!

Bill:

I've included the program at the end of this mailing - bear in mind that it's a program (well, part of a program) I cobbled together to help me out with part of my work, so it's certainly *not* user-friendly! It's written in Turbo Pascal for DOS, but I should imagine with a couple of changes it should be OK elsewhere. You could easily modify it to enable user input - as it stands, you have to modify the program to input the sample / standard L* a* b* values - not exactly easy if it's already compiled, but as I said, it was never intended for this purpose. The actual functions which do the maths are OK 'though. Hope it's some use.

The actual program has been moved to its own page:

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