In 1931, the International Commission on Illumination (Commission Internationale de l'Eclairage, or CIE) developed a standard observer [CIE 1931] based on work by Wright [Wright 1928] and by Guild [Guild 1931]. Calculating the CIE standard observer assumes a brightness sensitivity function which is a linear combination of trichromatic stimuli. Guild's determination of the CIE standard observer measured the spectral sensitivity of three additive primaries in relation to each other by use of a small field (2-degree) bipartite matching to sample experiment where the reference stimulus was a white tungsten incandescent light of color--temperature of about 4800 degrees kelvin and the primaries were obtained by appropriate filters.

* Figure 11. Guild's mean color matching results for the chromaticity coordinates of the spectrum colors [from Wyszecki & Stiles 1967, page 264].*

Guild and Wright obtained similar results for their chromaticity coordinates and Guild transformed both his and Wright's data into a common coordinate system (see Figure 11). The 1931 CIE Standard Observer model is based on the mean of the transformed data from these two experiments. Each line in Figure 11 expresses the amount of light of the appropriate primary wavelength (nm, nm, nm) required to match a sample of wavelength on the **X** axis.

* Figure 12. The CIE color space. X = Red. Y = Green. Z = Blue. If we assume that X + Y + Z = 1, we see that Z = 1 - (X + Y). Then an equiluminant slice through the CIE color space can be plotted using just X and Y [from Gonzalez 1977].*

By holding the total illuminance constant, a two dimensional diagram of the CIE color space can be plotted. The standard representation rewrites the coordinate for blue in terms of the red and green coordinates. Thus if **X** is red, **Y** is green, and **Z** is blue, and if we assume that **X + Y + Z = 1**, we can write . This results in a CIE Chromaticity Diagram as shown in Figure 12.

Stiles [Stiles 1946] proposed a method for the calculation of a metric for perceptual color space; a distance function between two perceptual colors which is called a * line element*, a term from tensor calculus [Synge & Schild 1978]. The line element is derived from the following hypothesis: if and are two neighboring just noticeably different colors, then some line element **ds** connecting the two pairs has the same constant value along its length. Stiles formulation of **ds** is

where

This formulation of a metric for the CIE color space has performed relatively well and results in what is known as discrimination ellipses as illustrated in Figure 13.

Stiles' line element metric has proven to be a fair fit to isoluminant color information but has problems with non--isoluminant colors. Some current work tends to suggest that the search for a metric in a three dimensional color space may be problematic.

* Figure 13. CIE chromaticity diagram showing discrimination ellipses derived from Stiles' line element [from Wyszecki & Stiles 1967, page 521].*

Sun Feb 12 19:24:36 EST 1995