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Colorimetry: Primaries and Gamut

Excerpt from Field Guide to Visual and Ophthalmic Optics

The points R709, G709, B709 and D65 are the standard red, green, blue primaries and white point for HDTV. The chromaticity coordinates for these values are

 RedGreenBlueWhite, D65

Primaries form a triangular region on the chromaticity diagram. The triangular region defines the gamut of the primaries, or in other words, colors within the region are obtained by the appropriate mixture of the three primaries. Colors outside of the gamut cannot be obtained.

Standard image formats such as BMP and JPEG provide color information in RGB format, typically ranging in values from 0 for unsaturated to 255 for fully saturated for 8-bit images. If the image has been calibrated to the R709,
G709, B709 primaries, then a simple matrix conversion can be used to obtain XYZ tristimulus values. First, each RGB value must be normalized by 255, so they range from 0 to 1; then the following matrix conversion can be used:

Matrix Conversion 1

The operation can be reversed as well to calculate RGB values from tristimulus values. However, some XYZ coordinates lie outside of the gamut of the primaries. The RGB values obtained with the matrix below must be multiplied by 255 for display on a calibrated monitor. RGB values less than zero or greater than 255 represent colors outside of the gamut of the primaries and cannot be properly displayed:

Matrix Conversion 1


J. Schwiegerling, Field Guide to Visual and Ophthalmic Optics, SPIE Press, Bellingham, WA (2004).

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