As mentioned in the preceding page, CIE considered the tristimulus values for red, green, and blue to be undesirable for creating a standardized color model. Instead, they used a mathematical formula to convert the RGB data to a system that uses only positive integers as values. The reformulated tristimulus values were indicated as XYZ. These values do not directly correspond to red, green, and blue, but are approximately so. The curve for the Y tristimulus value is equal to the curve that indicates the human eye's response to the total power of a light source. For this reason the value Y is called the luminance factor and the XYZ values have been normalized so that Y always has a value of 100.
Obtaining the XYZ tristimulus values is only part of defining the color. The color itself is more readily understood in terms of hue and chroma (to use Munsell's terms). To make this possible, CIE used the XYZ tristimulus values to formulate a new set of chromaticity coordinates that are denoted xyz.
|Note: The tristumulus values XYZ are always indicated in upper case while the chromaticity coordinates, xyz, are always in lower case.
The chromaticity coordinates are used in conjunction with a chromaticity diagram, the most familiar one being CIE's 1931 xyY Chromaticity Diagram:
The horseshoe-shaped color space is set in a grid using the chromaticity coordinates x and y as a locator for any value of hue and chroma. These correspond to the color itself (e.g., reddish-orange) and the fullness of the color or saturation. The coordinate z is not used, but can be inferred from the other two since the sum of the coordinates x + y + z is always 1.
The white spot in the following diagram represents the location of the illuminant.
The third dimension is indicated by the tristimulus value Y. As previously mentioned, this value indicates the lightness or luminance of the color. The scale for Y extends from the white spot in a line perpendicular to the plane formed by x and y using a scale that runs from 0 to 100. The fullest range of color exists at 0 where the white point is equal to CIE Illuminant C. As the Y value increases and the color becomes lighter, the range of color, or gamut, decreases so that the color space at 100 is just a sliver of the original area:
Using the xyY values, any two colors can be compared to determine whether they matchwhich is the whole purpose of CIE's standards. It needs to be noted that CIE did not create their system as a means for describing colors or producing a line of swatches for use in color production.
It is not possible to use the xyY chromaticity diagram as a map for showing the relationships between colors. The diagram is a flat representation of what is really a curved surface. So, like a Mercator projection map of the world, parts of it are visibly distorted in relationship to others. Colors of equal amounts of difference appear farther apart in the green part of the diagram than they do in the red or violet part.
To resolve the problem of non-uniform color scaling, CIE adopted two different uniform diagrams that became the 1976 specifications for CIELUV and CIELAB.