Editing Primary color (section)

== Color space primaries ==
[[File:Colormatch.svg|thumb|A conceptual visualization of a color matching experiment. A circular foveal bipartite field (about the size one's thumbnail an arm's length away<ref>{{cite web |title=What is Meant by the Term "Observer Angle"? |url=https://www.xrite.com/service-support/what_is_meant_by_the_term_observer_angle |website=X-Rite |access-date=12 May 2021 |language=en}}</ref>) is presented to the observer in a dark surround. One part of the field is illuminated by a monochromatic test stimulus. The participant adjusts the intensities of the three coincident monochromatic primary lights (which are usually red, green and blue hues) on either field until both the test stimulus and match stimulus appear as the exact same color. In this case the participant has added red to the 480 nm test stimulus and has almost matched the match stimulus made of only the green and blue lights of comparable intensities. The specific monochromatic primaries shown here are from the Stiles-Burch 1955 experiment.<ref>{{cite journal |last1=Stiles |first1=W.S. |last2=Burch |first2=J. M. |title=Interim Report to the Commission Internationale de l'Eclairage, Zurich, 1955, on the National Physical Laboratory's Investigation of Colour-matching (1955) |journal=Optica Acta: International Journal of Optics |date=December 1955 |volume=2 |issue=4 |pages=168–181 |doi=10.1080/713821039|bibcode=1955AcOpt...2..168S }}</ref>]]

[[File:Canonical color matching functions.png|thumb|The [[CIE RGB]],<ref>{{cite journal |last1=Stiles |first1=W.S. |last2=Burch |first2=J. M. |title=Interim Report to the Commission Internationale de l'Eclairage, Zurich, 1955, on the National Physical Laboratory's Investigation of Colour-matching (1955) |journal=Optica Acta: International Journal of Optics |date=December 1955 |volume=2 |issue=4 |pages=168–181 |doi=10.1080/713821039|bibcode=1955AcOpt...2..168S }}</ref><ref>{{cite web |title=Colour matching functions - Stiles & Burch (1955) 2-deg, RGB CMFs |url=http://cvrl.ioo.ucl.ac.uk/cmfs.htm |website=cvrl.ioo.ucl.ac.uk}}</ref> [[CIE XYZ]]<ref>{{cite web |title=Colour matching functions - 2-deg XYZ CMFs transformed from the CIE (2006) 2-deg LMS cone fundamentals |url=http://cvrl.ioo.ucl.ac.uk/cmfs.htm |website=cvrl.ioo.ucl.ac.uk}}</ref> color matching functions and [[LMS color space|LMS]] cone fundamentals.<ref>{{cite book |title=Fundamental chromaticity diagram with physiological axes. Part 1. |date=2006 |publisher=Commission internationale de l'eclairage |location=Vienna, Austria |isbn=9783901906466}}</ref><ref>{{cite web |title=CVRL functions - 2-deg fundamentals based on the Stiles and Burch 10-deg CMFs adjusted to 2-deg |url=http://www.cvrl.org/cvrlfunctions.htm |website=www.cvrl.org}}</ref> The curves are all for 2° fields.]]
A [[color space]] is a subset of a [[color model]], where the primaries have been defined, either directly as photometric spectra, or indirectly as a function of other color spaces. For example, [[sRGB]] and [[Adobe RGB]] are both color spaces based on the [[RGB color model]]. However, the green primary of Adobe RGB is more saturated than the equivalent in sRGB, and therefore yields a larger [[gamut]].<ref name="sRGBVsAdobeRGB">{{cite web|url=https://www.cambridgeincolour.com/tutorials/sRGB-AdobeRGB1998.htm|title=sRGB vs. Adobe RGB 1998|website=Cambridge in Colour}}</ref> Otherwise, choice of color space is largely arbitrary and depends on the utility to a specific application.<ref name="handprintprimaries"/>

=== Imaginary primaries ===
Color space primaries are derived from canonical colorimetric experiments that represent a standardized model of an observer (i.e., a set of ''color matching functions'') adopted by [[International Commission on Illumination|Commission Internationale de l'Eclairage]] (CIE) standards. The abbreviated account of color space primaries in this section is based on descriptions in ''Colorimetry - Understanding The CIE System''.<ref name="Schanda2007">{{cite book |editor1-last=Schanda |editor1-first=János |title=Colorimetry : understanding the CIE system |date=2007 |publisher=CIE/Commission internationale de l'eclairage |location=[Vienna, Austria] |isbn=978-0-470-04904-4}}</ref>

The [[CIE 1931]] standard observer is derived from experiments in which participants observe a foveal secondary bipartite [[field of view|field]] with a dark surround. Half of the field is illuminated with a monochromatic ''test stimulus'' (ranging from 380&nbsp;nm to 780&nbsp;nm) and the other half is the ''matching stimulus'' illuminated with three coincident monochromatic primary lights: 700&nbsp;nm for red (R), 546.1&nbsp;nm for green (G), and 435.8&nbsp;nm for blue (B).<ref name="Schanda2007"/>{{rp|29}} These primaries correspond to [[CIE RGB|CIE RGB color space]]. The intensities of the primary lights could be adjusted by the participant observer until the matching stimulus matched the test stimulus, as predicted by Grassman's laws of additive mixing. Different standard observers from other color matching experiments have been derived since 1931. The variations in experiments include choices of primary lights, field of view, number of participants etc.<ref>{{cite journal |last1=Li |first1=Jiaye |last2=Hanselaer |first2=Peter |last3=Smet |first3=Kevin A. G. |title=Impact of Color-Matching Primaries on Observer Matching: Part I – Accuracy |journal=LEUKOS |date=17 February 2021 |volume=18 |issue=2 |pages=104–126 |doi=10.1080/15502724.2020.1864395|doi-access=free }}</ref> but the presentation below is representative of those results.

Matching was performed across many participants in incremental steps along the range of test stimulus wavelengths (380&nbsp;nm to 780&nbsp;nm) to ultimately yield the color matching functions: <math>\overline{r}(\lambda)</math>, <math>\overline{g}(\lambda)</math> and <math>\overline{b}(\lambda)</math> that represent the relative intensities of red, green, and blue light to match each wavelength (<math>\lambda</math>). These functions imply that <math>[C]</math> units of the test stimulus with ''any'' spectral power distribution, <math>P(\lambda)</math>, can be matched by {{math|[R]}}, {{math|[G]}}, and {{math|[B]}} units of each primary where:<ref name="Schanda2007"/>{{rp|28}}

{{NumBlk|:|<math>
[C] =
\int_{380\text{ nm}}^{780\text{ nm}} \overline{r}(\lambda) P(\lambda)\,d\lambda \cdot [R] +
\int_{380\text{ nm}}^{780\text{ nm}} \overline{g}(\lambda) P(\lambda)\,d\lambda \cdot [G] +
\int_{380\text{ nm}}^{780\text{ nm}} \overline{b}(\lambda) P(\lambda)\,d\lambda \cdot [B].
</math>|{{EquationRef|Eq. 1}}}}

Each integral term in the above equation is known as a ''tristimulus value'' and measures amounts in the adopted units. No set of real primary lights can match another monochromatic light under additive mixing so at least one of the color matching functions is negative for each wavelength. A negative tristimulus value corresponds to that primary being added to the test stimulus instead of the matching stimulus to achieve a match.

The negative tristimulus values made certain types of calculations difficult, so the CIE put forth new color matching functions <math>\overline{x}(\lambda)</math>, <math>\overline{y}(\lambda)</math>, and <math>\overline{z}(\lambda)</math> defined by the following [[linear map|linear transformation]]:<ref name="Schanda2007"/>{{rp|30}}

{{NumBlk|:|<math>
\begin{bmatrix}
 \overline{x}(\lambda) \\
 \overline{y}(\lambda) \\
 \overline{z}(\lambda)
\end{bmatrix}
=
\begin{bmatrix}
 2.768892 & 1.751748 & 1.130160 \\
 1.000000 & 4.590700 & 0.060100 \\
 0 & 0.056508 & 5.594292 \\
\end{bmatrix}
\begin{bmatrix}
 \overline{r}(\lambda) \\
 \overline{g}(\lambda) \\
 \overline{b}(\lambda)
\end{bmatrix}.
</math>|{{EquationRef|Eq. 2}}}}

These new color matching functions correspond to ''imaginary'' primary lights X, Y, and Z ([[CIE XYZ|CIE XYZ color space]]). All colors can be matched by finding the amounts {{math|[X]}}, {{math|[Y]}}, and {{math|[Z]}} analogously to {{math|[R]}}, {{math|[G]}}, and {{math|[B]}} as defined in {{EquationNote|Eq. 1}}. The functions <math>\overline{x}(\lambda)</math>, <math>\overline{y}(\lambda)</math>, and <math>\overline{z}(\lambda)</math> based on the specifications that they should be nonnegative for all wavelengths, <math>\overline{y}(\lambda)</math> be equal to [[luminous efficiency function|photometric luminance]], and that <math>[X]=[Y]=[Z]</math> for an equienergy (i.e., a uniform spectral power distribution) test stimulus.<ref name="Schanda2007"/>{{rp|30}}

Derivations use the color matching functions, along with data from other experiments, to ultimately yield the ''cone fundamentals'': <math>\overline{l}(\lambda)</math>, <math>\overline{m}(\lambda)</math> and <math>\overline{s}(\lambda)</math>. These functions correspond to the response curves for the three types of color [[photoreceptor cell|photoreceptors]] found in the human retina: long-wavelength (L), medium-wavelength (M), and short-wavelength (S) [[cone cell|cones]]. The three cone fundamentals are related to the original color matching functions by the following linear transformation (specific to a 10° field):<ref name="Schanda2007"/>{{rp|227}}
 
{{NumBlk|:|<math>
\begin{bmatrix}
 \overline{l}(\lambda) \\
 \overline{m}(\lambda) \\
 \overline{s}(\lambda)
\end{bmatrix}
=
\begin{bmatrix}
 0.192325269 & 0.749548882 & 0.0675726702 \\
 0.0192290085 & 0.949098496 & 0.113830196 \\
 0 & 0.0105107859 & 0.991427669 \\
\end{bmatrix}
\begin{bmatrix}
 \overline{r}(\lambda) \\
 \overline{g}(\lambda) \\
 \overline{b}(\lambda)
\end{bmatrix}.
</math>|{{EquationRef|Eq. 3}}}}

[[LMS color space]] comprises three primary lights (L, M, and S) that stimulate only the L-, M-, and S-cones respectively. A real primary that stimulates only the M-cone is impossible, and therefore these primaries are imaginary. The [[LMS color space]] has significant physiological relevance as these three photoreceptors mediate trichromatic color vision in humans.

Both XYZ and LMS color spaces are ''complete'' since all colors in the gamut of the standard observer are contained within their color spaces. Complete color spaces must have imaginary primaries, but color spaces with imaginary primaries are not necessarily complete (e.g. [[ProPhoto RGB color space]]).

=== Real primaries ===
[[File:CIE1931xy_gamut_comparison.svg |thumb|300px|various RGB color spaces are represented as [[color triangle]]s with vertices that represent the primaries. The [[CIE 1931 color space|1931 CIE chromaticity diagram]] shows the gamut of the standard observer. Primaries outside of the colored region are imaginary.]]

Color spaces used in [[color reproduction]] must use real primaries that can be reproduced by practical sources, either lights in additive models, or pigments in subtractive models. Most [[RGB color spaces]] have real primaries, though some maintain imaginary primaries. For example, all the [[sRGB]] primaries fall within the gamut of human perception, and so can be easily represented by practical light sources, including CRT and LED displays, hence why sRGB is still the color space of choice for digital displays.

A color in a color space is defined as a combination of its primaries, where each primary must give a non-negative contribution. Any color space based on a finite number of real primaries is ''incomplete'' in that it cannot reproduce every color within the gamut of the standard observer.

Practical color spaces such as [[sRGB]]<ref name="sRGB_orig">{{cite web|author1=Michael Stokes|author2=Matthew Anderson|author3=Srinivasan Chandrasekar|author4=Ricardo Motta|date=5 November 1996|title=A Standard Default Color Space for the Internet – sRGB, Version 1.10|url=https://www.w3.org/Graphics/Color/sRGB.html <!-- ALTERNATIVE URL: http://www.color.org/sRGB.xalter -->|archive-url=|archive-date=|access-date=|website=}}</ref> and [[scRGB]]<ref name="iec-standard">{{Cite web|url=https://webstore.iec.ch/publication/6171|title=Multimedia systems and equipment - Colour measurement and management - Part 2-2: Colour management - Extended RGB colour space - scRGB|date=23 January 2003|access-date=18 April 2021|author1=HP|author-link1=Hewlett-Packard|author2=Microsoft|author-link2=Microsoft|author3=IEC|author-link3=International Electrotechnical Commission|editor=IEC|website=IEC}}</ref> are typically (at least partially) defined in terms of linear transformations from CIE XYZ, and [[color management]] often uses CIE XYZ as a middle point for transformations between two other color spaces.

Most color spaces in the color-matching context (those defined by their relationship to CIE XYZ) inherit its three-dimensionality. However, more complex [[color appearance model]]s like [[CIECAM02]] require extra dimensions to describe colors appear under different viewing conditions.<ref>{{cite book |last1=Fairchild |first1=Mark D. |title=Color Appearance Models. |date=2013 |publisher=Wiley |location=Hoboken |isbn=9781119967033 |page=287 |edition=3rd}}</ref>

{{clear}}