1.2.2 The CIE Chromaticity Diagram

The negative values in the representation of color by R-G-B-values is unpleasant. Thus the Commission Internationale de l'Éclairage (CIE) defined in 1931 another base in terms of (virtual) primaries $\mathbf X$, (the luminous-efficiency function) $\mathbf Y$ and $\mathbf Z$, which allows to match all visible colors as linear combinations with positive coefficients only (the so called CHROMATICITY VALUES $X,Y,Z$), i.e. any visible color $\mathbf C$ can be expressed as $\mathbf C=X\mathbf X+Y\mathbf Y+Z\mathbf Z$, see

Figure: CIE 1931 primaries

Normalization to $X+Y+Z=1$ gives new coordinates $x$, $y$ (and $z=1-x-y$), which are independent on luminous energy $X+Y+Z$. The visible chromatic values in this coordinate system form a horseshoe shaped region, with the spectrally pure colors on the curved boundary. Warning: brown is orange-red at very low luminance (hence is not shown in this diagram). Standard white light (approximative sunlight) is located at point $C$ near $x=y=z=1/3$.

Figure: CIE 1931 Chromaticity Diagram
From:cie-1.html

    

Figure: Horseshoe of visible colors
From:www.adobe.com/.../ciexyz.html

The DOMINANT WAVELENGTH of some color is given by the intersection of the ray from $C$ to the color with the curved boundary formed by the pure colors.

Some colors (purples and magentas) are non-spectral, i.e. have no dominant wavelength (since the intersection of the rays hit the boundary in the flat part). But they have have a COMPLEMENTARY DOMINANT WAVELENGTH, lying on the opposite side.

COLOR COMPLEMENTARY to some color are opposite to $C$ on the line through $C$. E.g. we have the following complementary pairs: red-cyan, green-magenta, and blue-yellow.

EXCITATION PURITY is a ratio of the distances from the color and the dominant wavelength to $C$.

Figure: Dominant wavelength and complementary colors

The CIE chromaticity diagram can also be used to visualize the COLOR GAMUTS (i.e. the ranges of producible colors) for various output devices:

Figure: Color gamut
From:cie-1.html

Figure: Color gamuts for PAL, NTSC and HDTV and their chromaticity values

    

The chromaticity values for standard NTSC RGB phosphor are:

	R	G	B
x	0.67	0.21	0.14
y	0.33	0.71	0.08

The color-printer gamut is rather small in comparison to the color-monitor gamut. Thus we can print much fewer colors that we can display on the screen.

A disadvantage of the CIE 1931 standard is that equal distances in the $X-Y$ coordinates are not perceived as being equal. This was corrected by 1976 CIE LUV standard.

Figure: Chromaticity diagrams of 1931 and of 1976

    

Figure: Chromaticity diagrams of 1960 and 1976
From:Chromaticity.htm

    

Figure: Equally perceived color distances and chromaticity diagram of 1960
From:www.adobe.com/.../cieluv.html

    

Figure: Equally perceived color distances and chromaticity diagram of 1976
From:www.adobe.com/.../cieluv.html