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
Image /home/andreas/tex/Books/computer-graphics/img//ciexyz31_1.png

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
Image /home/andreas/tex/Books/computer-graphics/img//cie3.gif      Image /home/andreas/tex/Books/computer-graphics/img//cie4.gif

Figure: Horseshoe of visible colors

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
Image /home/andreas/tex/Books/computer-graphics/img//cie.gif

Figure: Color gamuts for PAL, NTSC and HDTV and their chromaticity values
\includegraphics[width=0.45\textwidth]{ppmcie-ebu}      \includegraphics[width=0.45\textwidth]{ppmcie-ntsc}


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
\includegraphics[width=0.45\textwidth]{ppmcie-ebu}     \includegraphics[width=0.45\textwidth]{ppmcie-uv-ebu}

Figure: Chromaticity diagrams of 1960 and 1976
\includegraphics[width=0.45\textwidth]{CIE1960-inv}     \includegraphics[width=0.45\textwidth]{CIE1976-inv}

Figure: Equally perceived color distances and chromaticity diagram of 1960
Image /home/andreas/tex/Books/computer-graphics/img//xyz_scale.jpg     \includegraphics[width=0.45\textwidth]{cie_luv1960-inv}

Figure: Equally perceived color distances and chromaticity diagram of 1976
Image /home/andreas/tex/Books/computer-graphics/img//luv_scale.jpg     \includegraphics[width=0.45\textwidth]{cieluv-inv}

Andreas Kriegl 2003-07-23