Page 103 - Computational Colour Science Using MATLAB

90 CHROMATIC-ADAPTATION TRANSFORMS AND COLOUR APPEARANCE
the white points of the illuminants to convert the RGB values of the sample to the
RGB values of the corresponding colour,

R C ¼½DðR WR =R WT Þþ 1 DŠR,
G C ¼½DðG WR =G WT Þþ 1 DŠG,
ð6:10Þ
½DðB WR =B Þþ 1 DŠB , if B C 4 0,
P P
WT
B C ¼ P P
½DðB WR =B Þþ 1 DŠjBj , otherwise,
WT
where
0:0834
P ¼ðB WT =B WR Þ .
Note that when D ¼ 1, the transform [Equations (6.10)] is quite close to the form
of a von Kries or diagonal transform except that a non-linearity is applied to the
B channel.
Finally, the corresponding RGB values are converted back to tristimulus
values by multiplying them by the inverse of M BFD to yield the normalized
tristimulus values which finally can be converted by multiplying each by the Y
tristimulus value of the sample under the test illuminant,
X C ¼ Yð0:9870R C 0:1471G C þ 0:1600B C Þ,
ð6:11Þ
Y C ¼ Yð0:4323R C þ 0:5184G C þ 0:0493B C Þ,
and
Z C ¼ Yð 0:0085R C þ 0:0400G C þ 0:9685B C Þ.

6.2.3 CMCCAT2000

There is some uncertainty over the reversibility of the CMCCAT97 transform
which arises because of the power function in Equations (6.10). Although this
problem has been solved by a small revision (Li et al., 2000) a further weakness
of the CMCCAT97 is that it was derived by fitting only a relatively small data
set. Further work resulted in the development of a new CAT that was accepted
by the Colour Measurement Committee and known as CMCCAT2000 (Li et al.,
2002). In CMCCAT2000 the power function was removed so that the transform
is fully reversible and the model was fitted to all available data sets.
Consequently the linear transform component, M CMCCAT2000 , of CMCCAT2000
is slightly different from that of CMCCAT97 and is shown below,
2 3
0:7982 0:3389 0:1371
0:5918 1:5512 0:0406 .
4 5
M CMCCAT2000 ¼
0:0008 0:0239 0:9753