Editing Grayscale (section)

== Converting color to grayscale ==
[[File:Auschwitz_channel_mixer.jpg|thumb|Examples of conversion from a full-color image to grayscale using [[Adobe Photoshop]]'s ''Channel Mixer'', compared to the original image and colorimetric conversion to grayscale]]
Conversion of an arbitrary color image to grayscale is not unique in general; different weighting of the color channels effectively represent the effect of shooting black-and-white film with different-colored [[photographic filter]]s on the cameras.

=== Colorimetric (perceptual luminance-preserving) conversion to grayscale ===
A common strategy is to use the principles of [[photometry (optics)|photometry]] or, more broadly, [[colorimetry]] to calculate the grayscale values (in the target grayscale colorspace) so as to have the same luminance (technically relative luminance) as the original color image (according to its colorspace).<ref>{{cite conference |last= Poynton |first= Charles A. |date= 2022-03-14 |title= Rehabilitation of Gamma |editor-last1= Rogowitz |editor-first1= B. E. |editor-last2= Pappas |editor-first2= T. N. |conference= SPIE/IS&T Conference 3299: Human Vision and Electronic Imaging III; January 26–30, 1998 |location= San Jose, Calif. |publisher= SPIE |publication-place= Bellingham, Wash. |doi= 10.1117/12.320126 |url= https://poynton.ca/PDFs/Rehabilitation_of_gamma.pdf |archive-url= https://web.archive.org/web/20230423034709/https://poynton.ca/PDFs/Rehabilitation_of_gamma.pdf |archive-date= 2023-04-23 |url-status= live }}</ref><ref>{{cite web |last= Poynton |first= Charles A. |date= 2004-02-25 |title= Constant Luminance |url= http://poynton.ca/notes/video/Constant_luminance.html |website= Video Engineering |archive-url= https://web.archive.org/web/20230316214443/https://poynton.ca/notes/video/Constant_luminance.html |archive-date= 2023-03-16 |url-status= live}}</ref>  In addition to the same (relative) luminance, this method also ensures that both images will have the same [[Luminance|absolute luminance]] when displayed, as can be measured by instruments in its [[SI]] units of  [[candela per square metre|candelas per square meter]], in any given area of the image, given equal [[whitepoint]]s.  Luminance itself is defined using a standard model of human vision, so preserving the luminance in the grayscale image also preserves other perceptual [[Lightness#Relationship between lightness, value, and luminance|lightness measures]], such as {{math|''L''<sup>*</sup>}} (as in the 1976 CIE [[Lab color space#CIELAB|''L''ab color space]]) which is determined by the linear luminance {{math|''Y''}} itself (as in the [[CIE 1931 color space#Definition of the CIE XYZ color space|CIE 1931 ''XYZ'' color space]]) which we will refer to here as {{math|''Y''<sub>linear</sub>}} to avoid any ambiguity.

To convert a color from a colorspace based on a typical [[gamma correction|gamma-compressed]] (nonlinear) [[RGB color model]] to a grayscale representation of its luminance, the gamma compression function must first be removed via gamma expansion (linearization) to transform the image to a linear RGB colorspace, so that the appropriate [[weighted sum]] can be applied to the linear color components (<math>R_\mathrm{linear},G_\mathrm{linear},B_\mathrm{linear}</math>) to calculate the linear luminance {{math|''Y''<sub>linear</sub>}}, which can then be gamma-compressed back again if the grayscale result is also to be encoded and stored in a typical nonlinear colorspace.<ref>{{cite web |last= Lindbloom |first= Bruce |date= 2017-04-06 |title= RGB Working Space Information |url= http://www.brucelindbloom.com/index.html?WorkingSpaceInfo.html |archive-url= https://web.archive.org/web/20230601091400/http://www.brucelindbloom.com/index.html?WorkingSpaceInfo.html |archive-date= 2023-06-01 |url-status= live}}</ref>

For the common [[sRGB]] color space,  gamma expansion is defined as
<math display="block">C_\mathrm{linear}=
\begin{cases}\frac{C_\mathrm{srgb}}{12.92}, & \text{if } C_\mathrm{srgb}\le0.04045\\
\left(\frac{C_\mathrm{srgb}+0.055}{1.055}\right)^{2.4}, & \text{otherwise}
\end{cases}
</math>

where {{math|''C''<sub>srgb</sub>}} represents any of the three gamma-compressed sRGB primaries ({{math|''R''<sub>srgb</sub>}}, {{math|''G''<sub>srgb</sub>}}, and {{math|''B''<sub>srgb</sub>}}, each in range [0,1]) and {{math|''C''<sub>linear</sub>}} is the corresponding linear-intensity value ({{math|''R''<sub>linear</sub>}}, {{math|''G''<sub>linear</sub>}}, and {{math|''B''<sub>linear</sub>}}, also in range [0,1]). Then, linear luminance is calculated as a weighted sum of the three linear-intensity values. The [[sRGB]] color space is defined in terms of the [[CIE 1931 color space|CIE 1931]] linear luminance {{math|''Y''<sub>linear</sub>}}, which is given by<ref>{{cite web |last1= Stokes |first1= Michael |last2= Anderson |first2= Matthew |last3= Chandrasekar |first3= Srinivasan |last4= Motta |first4= Ricardo |date= 1996-11-05 |title= A Standard Default Color Space for the Internet – sRGB |website= [[World Wide Web Consortium]] – Graphics on the Web |url= http://www.w3.org/Graphics/Color/sRGB |archive-url= https://web.archive.org/web/20230524195001/https://www.w3.org/Graphics/Color/sRGB |archive-date= 2023-05-24 |url-status= live |at= Part 2, matrix in equation 1.8}}</ref>

<math display="block">Y_\mathrm{linear} = 0.2126 R_\mathrm{linear} + 0.7152 G_\mathrm{linear} + 0.0722 B_\mathrm{linear}.</math>

These three particular coefficients represent the intensity (luminance) perception of typical [[trichromat]] humans to light of the precise [[Rec. 709]] additive primary colors (chromaticities) that are used in the definition of sRGB. Human vision is most sensitive to green, so this has the greatest coefficient value (0.7152), and least sensitive to blue, so this has the smallest coefficient (0.0722).  To encode grayscale intensity in linear RGB, each of the three color components can be set to equal the calculated linear luminance <math>Y_\mathrm{linear}</math> (replacing <math>R_\mathrm{linear},G_\mathrm{linear},B_\mathrm{linear}</math> by the values <math>Y_\mathrm{linear},Y_\mathrm{linear},Y_\mathrm{linear}</math> to get this linear grayscale), which then typically needs to be [[gamma correction|gamma compressed]] to get back to a conventional non-linear representation.<ref name="Wilhelm Burger, Mark J. Burge">{{cite book |last1= Burger |first1= Wilhelm |last2= Burge |first2= Mark J. |date= 2010 |title= Principles of Digital Image Processing Core Algorithms |url= https://books.google.com/books?id=s5CBZLBakawC&pg=PA |publisher= Springer Science & Business Media |isbn= 978-1-84800-195-4 |pages= 110–111}}</ref>  For sRGB, each of its three primaries is then set to the same gamma-compressed {{math|''Y''<sub>srgb</sub>}} given by the inverse of the gamma expansion above as

<math display="block">Y_\mathrm{srgb}=\begin{cases}
12.92\ Y_\mathrm{linear}, & \text{if } Y_\mathrm{linear} \le 0.0031308\\
1.055\ Y_\mathrm{linear}^{1/2.4}-0.055, & \text{otherwise}
\end{cases}
</math>

Because the three sRGB components are then equal, indicating that it is actually a gray image (not color), it is only necessary to store these values once, and we call this the resulting grayscale image.  This is how it will normally be stored in sRGB-compatible image formats that support a single-channel grayscale representation, such as JPEG or PNG.  Web browsers and other software that recognizes sRGB images should produce the same rendering for such a grayscale image as it would for a "color" sRGB image having the same values in all three color channels.

=== Luma coding in video systems ===
{{Main|luma (video)}}

For images in color spaces such as [[Y'UV]] and its relatives, which are used in standard color TV and video systems such as [[PAL]], [[SECAM]], and [[NTSC]], a nonlinear [[luma (video)|luma]] component {{math|(''Y{{prime}}'')}} is calculated directly from gamma-compressed primary intensities as a weighted sum, which, although not a perfect representation of the colorimetric luminance, can be calculated more quickly without the gamma expansion and compression used in photometric/colorimetric calculations. In the [[Y'UV]] and [[YIQ|Y'IQ]] models used by PAL and NTSC, the [[Rec. 601|rec601]] luma {{math|(''Y{{prime}}'')}} component is computed as
<math display="block">Y' =  0.299 R' + 0.587 G' + 0.114 B'</math>
where we use the prime to distinguish these nonlinear values from the sRGB nonlinear values (discussed above) which use a somewhat different gamma compression formula, and from the linear RGB components.  The [[Rec. 709|ITU-R BT.709]] standard used for [[High-definition television|HDTV]] developed by the [[Advanced Television Systems Committee standards|ATSC]] uses different color coefficients, computing the luma component as
<math display="block">Y' =  0.2126 R' + 0.7152 G' + 0.0722 B'.</math>
Although these are numerically the same coefficients used in sRGB above, the effect is different  because here they are being applied directly to gamma-compressed values rather than to the linearized values.  The [[Rec. 2100|ITU-R BT.2100]] standard for [[High Dynamic Range|HDR]] television uses yet different coefficients, computing the luma component as
<math display="block">Y' =  0.2627 R' + 0.6780 G' + 0.0593 B'.</math>

Normally these colorspaces are transformed back to nonlinear R'G'B' before rendering for viewing.  To the extent that enough precision remains, they can then be rendered accurately.

But if the luma component Y' itself is instead used directly as a grayscale representation of the color image, luminance is not preserved: two colors can have the same luma {{math|''Y{{prime}}''}} but different CIE linear luminance {{math|''Y''}} (and thus different nonlinear {{math|''Y''<sub>srgb</sub>}} as defined above) and therefore appear darker or lighter to a typical human than the original color.  Similarly, two colors having the same luminance {{math|''Y''}} (and thus the same {{math|''Y''<sub>srgb</sub>}}) will in general have different luma by either of the {{math|''Y{{prime}}''}} luma definitions above.<ref>{{cite web |last= Poynton |first= Charles A. |date= 1997-07-15 |title= The Magnitude of Nonconstant Luminance Errors |url= http://poynton.ca/PDFs/Mag_of_nonconst_luminance.pdf}}</ref>