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CIE chromaticity and related models

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.

lammens@cs.buffalo.edu