Page 71 - Computational Colour Science Using MATLAB

58 COMPUTING COLOUR DIFFERENCE

T¼1 0:17cosðh 30Þþ0:24cosð2h Þþ0:32 cosð3h þ6Þ 0:20 cosð4h 63Þ.
0
0
0
0
Finally, the rotation term R is given by
T
R T ¼ sinð2DyÞR C ,
07 07 7 1=2 and Dy ¼ 30 expf ½ðh 275Þ=25Š g.
2
0
where R C ¼ 2ðC =ðC þ 25 ÞÞ
Note that the arithmetic mean of the CIELAB values of the standard and trial
are used to compute the values of the terms such as S . The CIEDE2000 formula
L
has been shown to outperform the CMC and CIE94 formulae by a large margin
(Luo et al., 2001).
Interestingly, the lightness component of the formula is very different from
those in earlier formulae. For example, the value of the function in the CMC
formula increases markedly as L* increases, implying that for equal differences in
L* the visual difference should be largest in the low L* region. The lightness
correction in the CIE94 formulae, on the other hand, implied that the CIELAB
L* scale was correct, so that equal differences in L* would yield equal visual
differences no matter what the value of L*. The S formula in CIEDE2000,
L
however, was based upon new data (Heptinstall, 1999; Chou et al., 2001) so that
S increases with L* only for L*450; for lower values of L* the value of S L
L
decreases as L* increases. It is still not at all clear why the new data upon which
CIEDE2000 was based should have been so different from the data upon which
the earlier formulae were based. Nevertheless, the evidence for CIEDE2000 is
convincing and there is strong confidence that the new formula is reliable (Cui et
al., 2001; Luo, 2002a).

5.5 Implementations and examples

5.5.1 Computing CIELAB and CIELUV coordinates

The function xyz2lab computes CIELAB L*a*b* coordinates from tristimulus
values. A typical call would be

[lab] = xyz2lab(xyz,’d65___64’);

where the variable xyz is a 361 vector of tristimulus values and lab returns the
CIELAB L*, a* and b* values. The white points are taken from Table 5 of the
ASTM standard (ASTM, 2001) which are reproduced in Table 4.2. Note that
the ASTM standard specifies that the white points listed at the bottom of each of
the tables in the standard should be used for the values of X , Y and Z during
n
n
n
computations where the neutral point is required. The listed white points
sometimes differ from the check sums for each of the tables because the tabulated