Luminance (relative)

Relative luminance follows the photometric definition of luminance, but with the values normalized to 1 or 100 for a reference white. Like the photometric definition, it is related to the luminous flux density in a particular direction, which is radiant flux density weighted by the luminosity function y(λ) of the CIE Standard Observer.

The use of relative values is useful in systems where absolute reproduction is impractical. For example, in prepress for print media, the absolute luminance of light reflecting off the print depends on the illumination and therefore absolute reproduction cannot be assured.

For color spaces such as XYZ, xyY, etc. the letter Y refers to relative luminance. No computation is required to find relative luminance when it is explicit in a color representation in such spaces.

For RGB color spaces that use the ITU-R BT.709 primaries (or sRGB, which defines the same primaries), relative luminance can be calculated from linear RGB components: first convert the gamma-compressed RGB values to linear RGB, and then

The formula reflects the luminosity function: green light contributes the most to the intensity perceived by humans, and blue light the least.

For other sets of primary chromaticities (defined by their x and y chromaticity coordinates), different linear coefficients are needed to get relative luminance. In general, the coefficients are all positive, the green coefficient is largest and blue smallest, and the three form the middle row of the RGB-to-XYZ color transformation matrix.

For nonlinear gamma-compressed R′G′B′ color spaces as typically used for computer images, a linearization of the R′G′B′ components to RGB is needed before the linear combination.

For L*a*b* space, the L* component is the lightness; a perceptual scale of the brightness as a nonlinear function of the relative luminance Y.

Note that relative luminance should not be confused with luma, the weighted sum of the nonlinear gamma-compressed R′G′B′ components. For color spaces that use luma, such as Y′UV or Y′CbCr (where Y′ represents luma), computation of relative luminance can still be done. The R′G′B′ components can be transformed into RGB linear components by undoing the gamma compression; these linear components can then be used to calculate luminance.

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