Page 100 - Computational Colour Science Using MATLAB

CATS 87

R ¼ 0.40024X þ 0.70760Y 0.08081Z,
G ¼ 0:22630X þ 1:16532Y þ 0:04570Z, ð6:3Þ
B ¼ 0:00000X þ 0:00000Y 0:91822Z.

The corresponding values R , G and B under the reference illuminant are
C
C
C
computed according to Equations (6.4),
R C ¼ðY 0 P R þ nÞK 1=bðR R Þ ½ðR þ nÞ=ðY 0 hPiþ nފ bðR T Þ=bðR R Þ n,
G C ¼ðY 0 Q R þ nÞK 1=bðG R Þ ½ðG þ nÞ=ðY 0 hQiþ nފ bðG T Þ=bðG R Þ n, ð6:4Þ
B C ¼ðY 0 S R þ nÞK 1=bðB R Þ ½ðB þ nÞ=ðY 0 hSiþ nފ bðB T Þ=bðB R Þ n,

where n is a noise term (n ¼ 0.1) and the other parameters are computed
according to the following steps:

Step 1: Compute the chromaticity correlates P , Q , S and P , Q , S using
R
T
T
T
R
R
P T ¼ð0.48105x T þ 0.78841y T 0.08081Þ=y T ,
Q T ¼ð 0.27200x T þ 1.11962y T 0.08081Þ=y T
S T ¼ð0.48105x T þ 0.78841y T 0.08081Þ=y T ,
and
P R ¼ð0.48105x R þ 0.78841y R 0.08081Þ=y R ,
Q R ¼ð 0.27200x R þ 1.11962y R 0.08081Þ=y R ,
S R ¼ð0.48105x R þ 0.78841y R 0.08081Þ=y R ,
where x , y and x , y are the chromaticity coordinates of the reference and test
R R T T
illuminants, respectively.

Step 2: Compute the coefficient a for adaptation using
a ¼ 0:115 logðL T Þþ 0:0025ðL* 50Þþ 0:22D þ 0:51,

where the factor D ¼ 1.0 for object colours and D ¼ 0.0 for luminous colours
(intermediate values of D may be used for projected colour slides) and the value
¼ 1.0. The value of L is the luminance
max T
of a is capped to have a maximum a
2
(cd/m ) of the adapting test field and L* is the CIE lightness of the sample under
the test illuminant.
Step 3: Compute the adapting chromaticity correlates hPi, hQi, and hSi using
hPi¼ aP T þð1 aÞP R ,
hQi¼ aQ T þð1 aÞQ R ,
hSi¼ aS T þð1 aÞS R .