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Luminance (relative)

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Relative luminance follows the photometric definition of luminance, but with the values normalized to 1 or 100 for a reference white[1]. 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 \overline{y}(\lambda) 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.

Relative luminance in colorimetric spaces

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:[2]

Y = 0.2126 R + 0.7152 G + 0.0722 B

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' spaces as typically used for computer images, a linearization of the R'G'B' components to RGB is needed before the linear combination.[3]

For L*a*b* space, the L* component is simply a nonlinear version of the relative luminance Y, so Y is easy to compute as a function of L*.

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 linear light components by undoing the gamma compression; these linear primary components can then be used to calculate luminance.

References

  1. Poynton, Charles (2003). Digital Video and HDTV: Algorithms and Interfaces.
  2. Michael Stokes, Matthew Anderson, Srinivasan Chandrasekar, and Ricardo Motta, "A Standard Default Color Space for the Internet - sRGB", online see matrix at end of Part 2.
  3. Maureen C. Stone (2003). A Field Guide to Digital Color, A K Peters, Ltd.

See also


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