Page 104 - Computational Colour Science Using MATLAB

CATS 91
The first step in CMCCAT2000 is to transform the tristimulus values of the
sample under the test illuminant to RGB values using Equations (6.12),
R ¼ 0:7982X=Y þ 0:3389Y=Y 0:1371Z=Y,
G ¼ 0:5918X=Y þ 1:5512Y=Y þ 0:0406Z=Y, ð6:12Þ

and
B ¼ 0:0008X=Y þ 0:0239Y=Y þ 0:9753Z=Y,

where X, Y and Z are the tristimulus values of the sample. Again, note that the
normalized tristimulus values are used as the input to the linear transform
[Equations (6.12)]. Similar transforms are computed for the test and reference
illuminants to produce R WT , G WT , B WT and R WR , G WR , B WR , respectively.
Note that this stage is equivalent to multiplying the 361 column matrix of
normalized tristimulus values by the 363 matrix M CMCCAT2000 . CMCCAT2000
incorporates the degree of adaptation D and this is computed by Equation (6.13),

D ¼ F 0:08 log½0:5ðL AT þ L AR ފ þ 0:76 0:45ðL AT L AR Þ=ðL AT þ L AR Þ ,
ð6:13Þ
where the parameter F ¼ 1.0 for average viewing conditions, F ¼ 0.8 for dim and
dark surround conditions and L AT and L AR are the luminances of the test and
reference adapting fields, respectively (note that CMCCAT97 did not account for
the luminance of the reference field).
The degree of adaptation D is then used 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, ð6:14Þ
B C ¼½DðB WR =B WT Þþ 1 DŠB.

Note that when D ¼ 1, the transform [Equations (6.14)] is simply a diagonal
transform of the RGB values.
Finally, the corresponding RGB values are converted back to tristimulus
values by multiplying them by the inverse of M CMCCAT2000 . This procedure yields
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 Yð1:0765R C 0:2377G C þ 0:1612B C Þ,
Y C ¼ Yð0:4110R C þ 0:5543G C þ 0:0347B C Þ, ð6:15Þ
Z C ¼ Yð 0:0110R C 0:0134G C þ 1:0243B C Þ.

A slight revision of CMCCAT2000, known as CAT02, has been developed
whereby the matrix M CAT02 was derived by fitting all the available data sets apart
from one (which was excluded on the basis that it refers to narrowband light
sources that are unlikely to be encountered in practical situations).