Appendix B

The CIEDE2000 colour difference formula was published by the CIE in 2001 and is based on CIELAB colour space (see Chapter 5). It was developed to improve on the predictions of the CIELAB and further the CIE94 colour difference formulae, published by the CIE in 1976 and 1995 respectively. It includes lightness, chroma and hue weighting functions, and an interactive term between chroma and hue differences for improving the performance for blue colours, as well as a scaling factor for CIELAB a* scale for improving the performance in neutral regions.

Given two colour samples specified in CIELAB, the following steps are computed to derive the metric derived from the CIEDE2000 formula, ΔE₀₀:

Step 1. Calculate CIELAB L*, a*, b* and C* for both samples (described also in Chapter 5):

where f(x) is defined differently for very low and for normal and high ratios:

Step 2. Calculate L′, a′, b′, C′ and h′ for both samples:

where

where is the arithmetic mean of the values for the pair of samples.

Step 3. Calculate ΔL′, ΔC′ and ΔH′, where b and s refer to the test (batch) and standard colour samples respectively:

where

Step 4. Calculate ΔE₀₀:

where

with

and

The parametric factors k_L, k_C and k_H in Eqn B.17 are used to adjust the relative weighting of the lightness, chroma and hue components for various viewing conditions. In most imaging applications they are set equal to 1.0 – see Bibliography for more explanations.

are the arithmetic means of the and L′, C′ and h′ values for the pair of samples. For calculating caution needs to be taken for colours having hue angles in different quadrants. For example, a standard and a sample with hue angles of 90° and 300° would have a mean value of 195°, which is wrong. The correct value is 15°. It is obtained by:

1.   Calculating the absolute difference between the two hue angles. In the given example this is equal to 210.

2.   If the difference is less than 180°, the arithmetic mean should be used. In the given example the difference is more than 180°.

3.   If the difference is more than 180°, 360° should be subtracted from the larger angle, followed by calculating the arithmetic mean between the resulting value and the smaller angle. This gives 300° − 360° = −60° for the sample and a mean of (90° − 60°)/2 = 15°.

BIBLIOGRAPHY

CIE Technical Report, 2001. Improvement to Industrial Colour-Difference Evaluation. CIE Pub. No. 142-2001. Central Bureau of the CIE, Vienna.

Luo, M.R., Cui, G., Ring, B., 2001. The development of the CIE 2000 colour-difference formula: CIEDE2000. Color Research and Application 26 (5), 340–350.