Usability of Digital Cameras for Verifying Physically Based ...

3 Colorimetry
Colorimetry [WS82, Sto03, GM02, GJB80, Gre99, Gla95, Sha04, JMF94] is the
science of measuring, describing, and evaluating colors. It is based on empirical
studies of humans matching colors. This chapter gives a short overview of how
color can be specified and how color distances can be measured.
3.1 Color Spaces
3.1.1 CIE XYZ Color Space
In 1931, the Commission Internationale de l’Eclairage (CIE) standardized a set of
color-matching functions that can be used to convert spectral data to CIE XYZ
color space [WS82]. These color-matching functions are the result of color-
matching experiments. Three primary lights, which can vary in intensity, are
chosen. The observers then adjust these primary colors to create colors that match
a set of monochromatic colors of the spectrum. The CIE defined a transformation
to such kind of color-matching functions to make them more convenient to use.
These transformed functions are known as the CIE color-matching functions or
the CIE standard observer. The CIE tristimulus values X, Y, and Z are calculated
by multiplying the stimulus times the color-matching functions and integrating
the result, as shown in the following formulae:
X = k
Y = k
Z = k
λb �
λ=λa
λb �
λ=λa
λb �
λ=λa
β(λ)S(λ)¯x(λ)∆λ
β(λ)S(λ)¯y(λ)∆λ
β(λ)S(λ)¯z(λ)∆λ
where λ is the wavelength, β is the reflectance spectrum, S is the spectrum of
the light source and ¯x(λ), ¯y(λ) and ¯z(λ) are the color matching functions. The
constant k is equal to 638lmW −1 if tristimulus values are to be provided in units
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