Page 65 - Computational Colour Science Using MATLAB

52 COMPUTING COLOUR DIFFERENCE

u ¼ 4X=ðX þ 15Y þ 3ZÞ,
0
v ¼ 9Y=ðX þ 15Y þ 3ZÞ. ð5:8Þ
0
The subscript n in Equations (5.7) again refers to the neutral point. It is also
possible to compute polar coordinates for CIELUV,

2 2 1=2
C* uv ¼ðu* þ v* Þ ,
1
h uv ¼ tan ðv*=u*Þð180=pÞ. ð5:9Þ
Whereas CIELAB was recommended for use with surface colours, CIELUV was
recommended for use with self-luminous colours (surface colours are sometimes
referred to as related colours since we rarely see a surface in isolation but rather
as part of a scene). One of the reasons for this is that the CIELUV space retains a
chromaticity diagram which is derived by plotting u 0 against v .An
0
approximately uniform chromaticity space is useful since the additive mixtures
of two stimuli all lie on the straight line in chromaticity space between the points
that represent the two stimuli. However, in the last couple of decades CIELAB
has become almost exclusively used for colour specification and the vast majority
of work on the prediction of colour difference and colour appearance has been
based upon CIELAB. It has been noted that there seems no reason to use
CIELUV over CIELAB (Fairchild, 1998).

5.3 CIELAB colour difference

The CIELAB space has become popular largely because of the associated colour-
difference metric [Equation (5.10)] that is computed as the Euclidean distance
between two points in CIELAB space,
2 2 2 1=2
DE* ab ¼½ðDL*Þ þðDa*Þ þðDb*Þ Š , ð5:10Þ
where

DL* ¼ L* L*,
S
T
Da* ¼ a* a*,
T
S
Db* ¼ b* b*,
T S
and the subscripts refer to the standard (S) and the trial (T). In industrial
applications of colour difference it is common that one of the samples is a
standard and the other is a sample or trial that is supposed to be a visual match
to the standard.
An idea of the size of DE* ab units can be gained by considering that the
difference between a perfect white (L* ¼ 100, a* ¼ b* ¼ 0) and a perfect black