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RGB color models as described in the next section rest on a scientific
foundation that has come about largely under the auspices of the Commission
Internationale de l'Eclairage (CIE), or the International Lighting
Committee, a Paris-based standards organization. Early in this century,
this organization sponsored research into color perception which lead to a
class of widely used mathematical models [Wyszecki \& Stiles 1982]. The basis
for all of these models is a number of color-matching experiments, where
an observer judges whether two parts of a visual stimulus match in
appearance, i.e., look identical or not (Figure ).
By varying the composition of the light projected onto either part of the
field of view, researchers can investigate properties of human color
vision. For instance, it has been found that light of almost any spectral
composition can be matched by mixtures of only three suitably chosen
monochromatic primaries (light of a single wavelength), which is the
principle behind color TV, as explained in the next section. By
repeating this type of experiment with many different observers and
averaging the results, and measuring the spectral composition and power of
each of the light sources, the CIE has defined a number of so-called
standard observer color matching functions.
Figure shows the color matching functions for a
particular choice of monochromatic primaries with an approximately red,
green, and blue appearance.
Assuming that the human visual system behaves linearly, the CIE then went
on to define the standard observer color matching functions in terms of
so-called virtual primaries. This amounts to a linear transformation
such that the color matching functions are all positive, which is desirable
for practical applications. The resulting primaries cannot be physically
realized, however. The result is usually referred to as the CIE 1931
standard observer color matching functions, and the individual functions
are labeled ,
, and
. These
functions are also chosen such that
is proportional to the
human photopic luminosity function, which is an experimentally determined
measure of the perceived brightness of monochromatic light of different
wavelengths (Figure
).
These functions are the basis for most quantitative work in color science
to date [Wyszecki \& Stiles 1982], even though there have been several
revisions since their original publication. The color TV spectral sensitivity functions
presented in the next section are linear transforms of the CIE functions
(they are also the functions I used in Section
).
According to the theory, the color matching functions are linear transforms
of the actual spectral sensitivity functions of the (average) human cone
photoreceptors (Section
). At the time of publication of
the CIE functions, the cone spectral sensitivities were not known yet, but
research done since then has shown good agreement with the predictions
[Boynton 1990][Wyszecki \& Stiles 1982][Boynton 1979].
If we know the spectral composition of a stimulus , we can now
determine its chromaticity coordinates as follows (see also
Section
). First, we calculate the tristimulus
values
,
, and
:
Next, we calculate the chromaticity coordinates:
Since the chromaticity coordinates are normalized, we lose all intensity
information, but all colors are otherwise representable in this form.
Usually the coordinates are plotted as a parametric --
plot, with
implicit as
. Such a diagram is known as a chromaticity
diagram (Figure
, left).
The chromaticity diagram has a number of interesting properties. It
represents every physically realizable color as a point, within a
well-defined boundary (representing the spectral colors). It has a white
point at its center, with more saturated colors radiating outwards from
white. When superimposing light coming from two different sources, the
resulting color percept lies on a straight line between the points
representing the component lights in the diagram. We can represent the
range of all colors that can be produced (the color gamut) by means
of three primaries as the triangular area of the chromaticity diagram whose
vertices have coordinates defined by the chromaticities of the primaries
(Figure , right). The right half of
Figure
, for instance, represents the gamut
defined by the NTSC
color TV
primaries. It is immediately obvious that not all physically realizable
colors can be realized by the NTSC primaries. In choosing primaries, one
generally tries to maximize the area of the chromaticity diagram covered,
subject to technical and other constraints
[McIlwain \& Dean 1956]. The same holds, mutatis mutandis, for other color
producing devices like printers and computer monitors. There is much more
to be said about chromaticity, but this will suffice for our purpose. The
interested reader can consult [Wyszecki \& Stiles 1982] for more details and
references.
More recently, the CIE has defined some additional color spaces, based on
the notion of perceptual color difference expressed as Euclidean distance
in the space (Appendix ). Color spaces with this
characteristic are generally referred to as uniform color spaces. The best
known examples of these are the CIE
(for additive light) and
(for reflected light) [Novak \& Shafer 1992][Wyszecki \& Stiles 1982].
[Robertson \& O'Callaghan 1986] report that linear interpolation in these spaces (for
computer graphics) is superior to the more common RGB and HSL spaces.
[Novak \& Shafer 1992] believe that it is unlikely that even the use of CIELUV
coordinates
will solve the fundamental problems of color image segmentation
and analysis.