Page 57 - Computational Colour Science Using MATLAB

44 COMPUTING CIE TRISTIMULUS VALUES

% note that 100/sum(cie(:,2)) is the normalising factor k
% so that Y = 100 for a perfect reflecting diffuser

The command load weights.mat loads the values of ASTM Table 5 and the
whos command would reveal the following variables:

Name Size Bytes Class
a___64 43x3 1032 double array
a___31 43x3 1032 double array
c___64 43x3 1032 double array
c___31 43x3 1032 double array
d50___64 43x3 1032 double array
d50___31 43x3 1032 double array
d55___64 43x3 1032 double array
d55___31 43x3 1032 double array
d65___64 43x3 1032 double array
d65___31 43x3 1032 double array
d75___64 43x3 1032 double array
d75___31 43x3 1032 double array
f2___64 43x3 1032 double array
f2___31 43x3 1032 double array
f7___64 43x3 1032 double array
f7___31 43x3 1032 double array
f9___64 43x3 1032 double array
f9___31 43x3 1032 double array

The file weights.mat therefore contains weights that represent the 1964 and 1931
colour-matching functions for the CIE illuminants A, C, D50, D55, D65, D75,
F2, F7 and F9. The leftmost column in the preceding list shows the valid
observer/illuminant options that can be used as the fourth argument in r2xyz.
The white points of the illuminants are given (ASTM, 2001) by Table 4.2.
Following some basic checks on the arguments to the function the issue of
truncation is addressed in the r2xyz code. If the reflectance data are only
available at 400 nm and higher, for example, then the values of the weights at
wavelengths lower than 400 nm are added to the value of the weights at 400 nm.
Summation of the product of the weights and the reflectance data is then
performed at 400 nm and upwards. This is equivalent to extending the reflectance
data below 400 nm using the value of reflectance at 400 nm. A similar process is
carried out for the upper wavelength that is available. This procedure is in
accordance with the CIE recommendation for dealing with truncated reflectance
data.