Fundamentals of Calculations · Formulary
Delta E
The numerals in the subscript indicate the belonging (original colour or comparison colour).
CIE 1976
Don't be afraid of the radical sign – the formula is quite understandable. Suppose the difference in brightness is zero. The result for the colour difference is the root of the deviance from a and b. Square the same and the results are:
ΔE² = Δa*² + Δb*²
The Pythagorean Theorem! One can interpret ΔE as the hypotenuse in a right-angled triangle, in which the length of both cathetus (a and b) are known – thus the distance between both endpoints. Delta E from 1976 is therefore nothing more than the spatial distance between two points in the L*a*b*-colour space.
Even though this formula is still the most widespread colour distance measure in the laboratory practice, it has its weaknesses. It weights colour hue differences as heavily as brightness or saturation difference in evaluation, even though the eye finds the latter two much more agreeable. Through modifications to this formula attempts are being made to approximate a visual equidistance in the dipicition.
CMC l:c
The "Colour Measurement Committee" of the "Society of Dyers and Colourists" published their formula in 1984, which contained the following, mostly relevant for the textile industry, correction factors:
- More heavily weighted lightness when dealing with very dark colours (SL)
- More heavily weighted saturation when dealing with very achromatic colours (SC)
- Correction of the hue in connection with the saturation (SH)
- Correction of the lightness (l)
- Correction of the saturation (c)
The parameters l (lightness) and c (chroma) are varied depending on each application. The combination CMC (2:1) is established in the textile industry. In non-textile work environments l = 1.3 or 1 is preferred, which means a smaller absorption of the lightness.
CIE 1994
In 1994 CIE published the colour distance formula CIE94. The CIE94 formula follows a similar approach as the CMC-formula, however it offers three correction parameters that are dependent on application:
| Coat of Paint | Textile | |
|---|---|---|
| kL | 1 | 2 |
| kC | 1 | 1 |
| kH | 1 | 1 |
| k1 | 0,045 | 0,048 |
| k2 | 0,015 | 0,014 |
CIE 2000
The CIEDE2000-formula is, through the influence of newer data sets, and compared to the little accepted CIE94-formula and also the CMCl:c, to achieve a refinement of the results.
Five correction factors were implemented:
- A hue rotation value (RT), in order to correct blue hues around 275°
- Compensation for neutral colours
- Compensation for lightness (SL)
- Compensation for saturation (SC)
- Compensation for hue (SH)
