Page 192 - Computational Colour Science Using MATLAB

IMPLEMENTATIONS AND EXAMPLES 179

for i=1:404
pdspec(:,i) = pdspec(:,i)+mspec’;
end

% compute the reconstruction errors
de1 = zeros(404,1); de2 = zeros(404,1);
for i=1:404
xyzt = r2xyz(spectra(:,i),400,700,’d65___64’);
xyz1 = r2xyz(pspectra(:,i),400,700,’d65___64’);
xyz2 = r2xyz(pdspec(:,i),400,700,’d65___64’);
labt = xyz2lab(xyzt,’d65___64’);
lab1 = xyz2lab(xyz1,’d65___64’);
lab2 = xyz2lab(xyz2,’d65___64’);
thisde1 = cielabde(labt,lab1);
thisde2 = cielabde(labt,lab2);
de1(i) = thisde1;
de2(i) = thisde2;
end

result = [median(de1) max(de1) median(de2) max(de2)]

10.5.3 Estimation of reflectance spectra from tristimulus values

Despite the fact that spectral reflectance factors are almost always smooth
functions of wavelength and are highly constrained it is not possible to
accurately compute reflectance spectra from tristimulus values. Clearly, since
metamerism exists, the mapping from T!P, where T is a 36n matrix of
tristimulus values and P is a 316n matrix of reflectance values, is a one-to-many
mapping. However, the use of linear models and basis functions allows the
estimation of a possible reflectance spectrum corresponding to a target triplet of
tristimulus values.
We can represent the computation of the tristimulus values t for a given
reflectance spectrum p by the linear system

t ¼ Mp, ð10.20Þ
where M is a 3631 matrix whose rows contain the wavelength-by-wavelength
product of the illuminant with one of the three colour-matching functions. We
can try to solve Equation (10.20) directly by rearranging to give
p ¼ M t, ð10.21Þ
þ