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Relative luminance Y follows the photometric definition of luminance L including spectral weighting for human vision, but while luminance L is a measure of light in units such as cd/m^2, Relative luminance Y values are normalized as 0.0 to 1.0 (or 1 to 100), with 1.0 (or 100) being a theoretical perfect reflector of 100% 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
luminous efficiency function A luminous efficiency function or luminosity function represents the average spectral sensitivity of human visual perception of light. It is based on subjective judgements of which of a pair of different-colored lights is brighter, to describ ...
(''λ'') of the CIE Standard Observer. The use of relative values is useful in color or appearance models that describe perception relative to the eye's adaptation state and a reference white. For example, in prepress for print media, the absolute luminance of light reflecting off the print depends on the specific illumination, but a
color appearance model A color appearance model (CAM) is a mathematical model that seeks to describe the perceptual aspects of human color vision, i.e. viewing conditions under which the appearance of a color does not tally with the corresponding physical measurement of ...
using relative luminance can predict the appearance by referencing the given light source.


Relative luminance and colorimetric spaces

For CIE colorspaces XYZ and xyY, the letter Y refers to relative luminance. If the maximum luminance for a given example is L_ or L_, and the subject luminance is L_ then the relative luminance is :Y = \ \ or \ \ Y_ = \ \times \ 100


Relative luminance and "gamma encoded" colorspaces

Y (and L) are both linear to changes in the volume of light. Conversions from color spaces where light or lightness are encoded with a power curve, such as most image and video formats, must be linearized before being transformed to Y or the XYZ space. The simple method is to apply the inverse power curve to each of the color channels, as an example for several common RGB color spaces, a 2.2 power curve is applied: : R_ = ^\ \ G_ = ^\ \ B_ = ^ Y can then be calculated for these colorspaces by using the coefficients for the Y component of the transform matrix. For instance, for ITU-R BT.709 and
sRGB sRGB is a standard RGB (red, green, blue) color space that HP and Microsoft created cooperatively in 1996 to use on monitors, printers, and the World Wide Web. It was subsequently standardized by the International Electrotechnical Commission ( ...
both of which use the same primaries and whitepoint, relative luminance can be calculated from RGB components: first convert the gamma-compressed RGB values to linear RGB, and then : Y = 0.2126*R_ + 0.7152*G_ + 0.0722*B_ The formula reflects the
luminous efficiency function A luminous efficiency function or luminosity function represents the average spectral sensitivity of human visual perception of light. It is based on subjective judgements of which of a pair of different-colored lights is brighter, to describ ...
as "green" light is the major component of luminance, responsible for the majority of light perceived by humans, and "blue" light the smallest component. Different linear coefficients are needed to determine luminance for a given colorspace, which are calculated from their primary chromaticities (defined by their x&y or uʹ&vʹ chromaticity coordinates). For RGB spaces that use real colors for primaries, these coefficients will be positive for the conversion into XYZ space, but may be negative for transforming back to RGB. The green coefficient is normally the largest and blue normally smallest, and normally 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. Relative luminance should not be confused with '' luma'' Y^\prime (Y prime), which is a weighted sum of ''nonlinear'' (gamma encoded) R′G′B′ components, where in some implementations the weighting coefficients are applied to the gamma encoded signal. Some colorspaces that use luma include
Y′UV YUV is a color model typically used as part of a color image pipeline. It encodes a color image or video taking human perception into account, allowing reduced bandwidth for chrominance components, compared to a "direct" RGB-representation. ...
, Y′IQ, and
Y′CbCr YCbCr, Y′CbCr, or Y Pb/Cb Pr/Cr, also written as YCBCR or Y′CBCR, is a family of color spaces used as a part of the color image pipeline in video and digital photography systems. Y′ is the luma component and CB and CR are the blue-diff ...
. To determine relative luminance, The Y^\prime must be used with the subcomponents to create the gamma encoded R′G′B′ components, which are then linearized to RGB by inverting the
gamma correction Gamma correction or gamma is a nonlinear operation used to encode and decode luminance or tristimulus values in video or still image systems. Gamma correction is, in the simplest cases, defined by the following power-law expression: : V_\text ...
. These linearized RGB channels can then have the appropriate linear coefficients applied (based on the primary chromaticities) and summed to relative luminance Y.


Relative luminance and perceptual spaces

Y is linear to light, but human perception has a non-linear response to lightness/darkness/brightness. For
L*a*b* The CIELAB color space, also referred to as ''L*a*b*'' , is a color space defined by the International Commission on Illumination (abbreviated CIE) in 1976. (Referring to CIELAB as "Lab" without asterisks should be avoided to prevent confusion ...
and
L*u*v* In colorimetry, the CIE 1976 ''L''*, ''u''*, ''v''* color space, commonly known by its abbreviation CIELUV, is a color space adopted by the International Commission on Illumination (CIE) in 1976, as a simple-to-compute transformation of the 1931 C ...
space, the L^* component is perceptual
lightness Lightness is a visual perception of the luminance (L) of an object. It is often judged relative to a similarly lit object. In colorimetry and color appearance models, lightness is a prediction of how an illuminated color will appear to a stan ...
(also known as "Lstar" and not to be confused with L luminance). L^* is intended to be linear to human perception of lightness/darkness, and since human perception of light is non-linear, L^* is a nonlinear function of relative luminance Y.


See also

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Luminance Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted from, or is reflected from a particular area, and falls withi ...
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CIE 1931 color space The CIE 1931 color spaces are the first defined quantitative links between distributions of wavelengths in the electromagnetic visible spectrum, and physiologically perceived colors in human color vision. The mathematical relationships that defin ...
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Chromaticity Chromaticity is an objective specification of the quality of a color regardless of its luminance. Chromaticity consists of two independent parameters, often specified as hue (h) and colorfulness (s), where the latter is alternatively called s ...


References

{{Color space Color Photometry Film and video technology