Page 63 - Computational Colour Science Using MATLAB

50 COMPUTING COLOUR DIFFERENCE
was never adopted by the CIE as a standard, however, and by the early 1990s
there was some concern that the formula might be overly complex and that its
predictions might be poor in certain areas of colour space. The CIE
recommended the CIE94 equation (Berns, 1993) for use before a concerted
effort was made to develop a new formula. CIEDE2000 (Luo et al., 2001) was
developed following collaboration between scientists working in several
countries and has now been adopted as a CIE recommendation for the
prediction of small colour differences.

5.2 CIELAB and CIELUV colour space

Between 1940 and 1976 a great number of colour spaces, transformations of
XYZ, were proposed as uniform colour spaces. Some of these, such as
HunterLab and ANLAB, were quite successful but in 1976 the CIE agreed
upon two transformations that led to CIELAB and CIELUV.
The formulae for computing CIELAB coordinates are given in Equations
(5.1):

1=3
16, if Y=Y n 4 0:008856,
L* ¼ 116ðY=Y n Þ
L* ¼ 903:3ðY=Y n Þ, if Y=Y n 4 0:008856,
ð5:1Þ
a* ¼ 500½fðX=X n Þ fðY=Y n ފ,
b* ¼ 200½fðY=Y n Þ fðZ=Z n ފ,
where

1=3
fðIÞ¼ðIÞ , if I 4 0:008856,
fðIÞ¼ 7.787ðIÞþ 16=116, if I4 0:008856,

and where X , Y and Z are the tristimulus values of a specified white object
n
n
n
colour. For surface colours the values of X , Y and Z usually are computed for
n
n
n
the perfect reflecting diffuser and are therefore equivalent to the illuminant itself.
Since white surfaces tend to look chromatically neutral under an illumination to
which the visual system is adapted the values of X , Y and Z sometimes are
n
n
n
referred to as the neutral point. The axes L*, a* and b* form a rectangular or
Cartesian coordinate space where L* represents lightness, a* represents redness-
greenness and b* represents yellowness-blueness. Sometimes it is useful to
represent colour stimuli in a cylindrical space and for these purposes it is possible
to compute the polar coordinates C* and h ab as shown in Equations (5.2) and
ab
(5.3),
2 2 1=2
,
C* ab ¼ða* þ b* Þ ð5.2Þ