Page 68 - Computational Colour Science Using MATLAB

OPTIMIZED COLOUR-DIFFERENCE FORMULAE 55
compute colour difference report both possible hue-difference terms (redder/
bluer in the example).
Figure 5.1 emphasizes why the polar coordinates C* and h ab usually are
ab
preferred to the cartesian coordinates a* and b*. The fact that the trial has a
smaller a* value than the standard (Da* 5 0) could be misinterpreted as
indicating that the standard is redder than the trial and yet the opposite is true in
terms of hue; the trial is redder/bluer than the standard. The possible error
occurs because the dimensions of human colour perception are brightness,
colourfulness and hue and these correlate with the polar coordinates lightness,
chroma and hue. It can be misleading to consider differences in a* and b* in
isolation since these confound differences in chroma and hue.

5.4 Optimized colour-difference formulae

5.4.1 CMC(l:c)

In the late 1970s a number of different formulae were being used by practitioners,
one of which was known as the JPC79 formula (the name derives from J. & P.
Coats whose laboratories developed the formula). The JPC79 formula was
effective but was known to be deficient in some areas (Smith, 1997) and a revised
version of the formula was published in 1984 by members of the Colour
Measurement Committee of the Society of Dyers and Colourists (Clarke et al.,
1984). This revised formula became known as CMC(l:c) which, like most modern
optimized colour-difference formulae, is based upon the CIELAB colour-
difference components DL*, DC* and DH* ,
ab
ab
2 2 2 1=2
DE CMCðl:cÞ ¼½ðDL*=ðlS L ÞÞ þðDC* ab =ðcS C ÞÞ þðDH* ab =S H Þ Š , ð5:14Þ
where S L ¼ 0.040975L*=ð1 þ 0:01765L*Þ, if L*5 16,
S
S
S
but S L ¼ 0.511, if L* 5 16,
S
and
S C ¼ 0:638 þ 0:0638C* ab,S =ð1 þ 0.0131C* ab,S Þ,
S H ¼ S C ðTF þ 1 FÞ.

The terms T and F are given by
4 4 1=2
F ¼½ðC* ab,S Þ =ððC ab,S Þ þ 1900ފ
and
T ¼ 0:36 þj0:4 cosðh ab,S þ 35Þj, if h ab,S 4164 or h ab,S 5345,
T ¼ 0:56 þj0:2 cosðh ab,S þ 168Þj, if 164 5 h ab,S 5 345.