Page 101 - Computational Colour Science Using MATLAB

88 CHROMATIC-ADAPTATION TRANSFORMS AND COLOUR APPEARANCE
Step 4: Compute the effective adapting responses of the test (R , G , B ) and
T
T
T
reference (R , G , B ) conditions using
R
R
R
R T ¼ L T hPi,
G T ¼ L T hQi,
B T ¼ L T hSi,
and

R R ¼ L R P R ,
G R ¼ L R Q R ,
B R ¼ L R S R .

Step 5: Compute the exponents of the red, green and blue transformations b(R ),
T
b(G ), b(B ) and b(R ), b(G ), b(B ) using
T
R
R
T
R
bðR T Þ¼ ð6.469 þ 6.326R 0:4495 Þ=ð6.469 þ R 0.4495 Þ,
T T
bðG T Þ¼ ð6.469 þ 6.326G 0.4495 Þ=ð6.469 þ G 0.4495 Þ,
T T
bðR R Þ¼ ð6.469 þ 6.326R 0.4495 Þ=ð6.469 þ R 0:4495 Þ,
R R
bðG R Þ¼ ð6.469 þ 6.326G 0.4495 Þ=ð6.469 þ G 0.4495 Þ,
R R
bðB T Þ¼ 0.7844ð8.414 þ 8.091B 0.5128 Þ=ð8.414 þ B 0.5128 Þ,
T T
bðB R Þ¼ 0.7844ð8.414 þ 8.091B 0:5128 Þ=ð8.414 þ B 0.5128 Þ.
R R
Step 6: Compute the coefficient K using
K ¼ p/q,

where

2bðR T Þ=3 bðG T Þ=3
p ¼½ðYhPiþ nÞ/ð20hPiþ nފ ½ðYhQiþ nÞ/ð20hQiþ nފ
and

2bðR R Þ=3 bðG R Þ=3
q ¼½ðYP R þ nÞ/ð20P R þ nފ ½ðYQ R þ nÞ/ð20Q R þ nފ ,
and where Y is the luminance factor (per cent) of the test adapting field.
Finally, the inverse of Equations (6.3) is used to transform the correlated RGB
values into correlated XYZ values,

X R ¼ 1.85995R R 1.12939G R þ 0.21990B R ,
Y R ¼ 0.36119R R þ 0.63881G R þ 0.00000B R , ð6:5Þ
Z R ¼ 0.00000R R þ 0.00000G R þ 1.08906B R .