SRGB

sRGB is a standard numerical encoding of colors, based on the RGB (red, green, blue) color model, for use on monitors, printers, and the World Wide Web. It was initially proposed by HP and Microsoft in 1996 and became an official standard of the International Electrotechnical Commission (IEC) as IEC 61966-2-1:1999. It is the current defined standard colorspace for the web, and it is usually the assumed colorspace for images that are neither tagged for a colorspace nor have an embedded color profile.

The sRGB standard uses the same color primaries and white point as the ITU-R BT.709 standard for HDTV, but a different transfer function (or gamma) compatible with the era's CRT displays, and assumes a viewing environment closer to typical home and office viewing conditions.

The sRGB color space is also the basis of the sYCC color encoding, which is a remapping of the R, G, and B components of sRGB to a luminance (brightness) value $Y$ and two chroma channels similar to those of the CIE YCbCr encoding.

sRGB definition

Gamut

Chromaticity	Red	Green	Blue	White point
x	0.6400	0.3000	0.1500	0.3127
y	0.3300	0.6000	0.0600	0.3290
Y	0.2126	0.7152	0.0722	1.0000

The sRGB standard defines the chromaticities of the red, green, and blue primaries, the colors where one of the three channels is nonzero and the other two are zero. The gamut of chromaticities that can be represented in sRGB is the color triangle defined by these primaries, which are set such that the range of colors inside the triangle is well within the range of colors visible to a human with normal trichromatic vision. As with any RGB color space, for non-negative values of R, G, and B it is not possible to represent colors outside this triangle.

The primaries come from HDTV (ITU-R BT.709), which are somewhat different from those for older color TV systems (ITU-R BT.601). These values were chosen to reflect the approximate color of consumer CRT phosphors at the time of its design. Since flat-panel displays at the time were generally designed to emulate CRT characteristics, the values also reflected prevailing practice for other display devices as well.

Transfer function ("gamma")

Plot of the sRGB intensities (red), and this function's slope in log-log space (blue), which is the instantaneous gamma. Below a compressed value of 0.04045 or a linear intensity of 0.00313, the curve is linear so the gamma is 1. Behind the red curve is a dashed black curve showing an exact gamma = 2.2 power law.

On an sRGB display, each solid bar should look as bright as the surrounding striped dither. (Note: must be viewed at original, 100% size)

The sRGB standard specifies a non-linear encoding of physical brightness values (proportional to luminous power emitted per unit of area) into the integer R, G, and B values that are to be stored in computer memory or image files. This transfer function commonly called gamma encoding, is the combination of a linear function at low brightness values and a displaced power law for the rest of the range.

Specifically, let $z$ be the encoded R, G, or B value, assumed to be an integer ranging from 0 (meaning no light) to some maximum $M$ (meaning the maximum displayable intensity of that channel). Typically $M$ is 255 when $z$ as an 8-bit integer, or generally $2^N-1$ for an $N$-bit integer. The physical intensity represented by $z$ is defined as $v=D(z/M)$, where the decoding function $D$ is defined as

$D(u)=\{\begin{array}{cc}u/12.92,& u\le 0.04045\\ {\left(\frac{u+0.055}{1.055}\right)}^{2.4},& u>0.04045\end{array}$

The result is 0 for no light, and 1 for the maximum intensity. The value $v=D(z/M)$ is sometimes called the "linear value" or "linear-light value" corresponding to the encoded sample $z$.

Conversely, given a value $v$ between 0 and 1 that is proportional to the physical R, G, or B intensity to be displayed, the encoded integer intensity will be $z=\text{round}(ME(v))$, where encoding function $E$ is defined as

$E(v)=\{\begin{array}{cc}12.92v,& v\le 0.0031308\\ (1.055)v^{1/2.4}-0.055,& v>0.0031308\end{array}$

These sRGB encoding and decoding functions $D$ and $E$ above are similar in form to those of BT.709, but the values are noticeably different. Because of the rounding of the parameters, they have small discontinuities at the transition between the linear and non-linear part, on the order of 10⁻⁸ — which are too small to matter in most practical situations.

For medium and large values of the argument $u$, the decoding function $D$ is actually quite close to a pure power law with exponent (gamma) of 2.2. However, for low values (around and below the breakpoint $U$) the difference is perceptible.

If needed, the encoding and decoding functions $D$, $E$ can be used for arguments greater than 1. They are also extended to negative values by the identities $D(-u)=-D(u)$, $E(-v)=-E(v)$.

In practice, there is still debate and confusion about the formulas used for encoding and decoding image colors from or into "sRGB" files. Also, programmers may choose use the "pure" power law $D(u)=u^{2.2}$ instead of the correct piecewise formulas above, for the sake of code simplicity or efficiency, but that would introduce some issues near black. Also, some operating systems and programs may directly send sRGB encoded images to monitors which actually have a different effective decoding function, such as pure power law with 2.2 exponent, this is further complicated by the standard saying that reference CRT display should use 2.2 gamma.

Correspondence to CIE XYZ stimulus

The sRGB standard specifies also the colors and relative intensities of the three primaries R, G, and B, by defining the mapping between these values (in linear brightness scale, before the gamma encoding) and the CIE XYZ perceptual color coordinates. This mapping is the same specified by the BT.709 standard; in matrix notation,

$\left[\begin{array}{c}{X}_{D65}\\ Y_{D65}\\ Z_{D65}\end{array}\right]=\left[\begin{array}{ccc}0.4124& 0.3576& 0.1805\\ 0.2126& 0.7152& 0.0722\\ 0.0193& 0.1192& 0.9505\end{array}\right]\left[\begin{array}{c}{R}_{\text{linear}}\\ G_{\text{linear}}\\ B_{\text{linear}}\end{array}\right]$

These coefficients should be considered exact and assume the 2° standard colorimetric observer for CIE XYZ. In particular, the second row of this matrix specifies the computation of the BT.709-2 luma (brightness) value from the linear R, G, and B values. (BT.709-1 had a typo in these coefficients.)

The inverse conversion, from from CIE XYZ to (linear) sRGB, can be obtained by inverting the matrix above to a suitable numerical accuracy. The 1999 standard provides the matrix

$\left[\begin{array}{c}{R}_{\text{linear}}\\ G_{\text{linear}}\\ B_{\text{linear}}\end{array}\right]=\left[\begin{array}{ccc}+3.2406& -1.5372& -0.4986\\ -0.9689& +1.8758& +0.0415\\ +0.0557& -0.2040& +1.0570\end{array}\right]\left[\begin{array}{c}{X}_{D65}\\ Y_{D65}\\ Z_{D65}\end{array}\right]$

which is not the exact inverse of the sRGB to XYZ transformation, but was expected to be accurate enough for 8-bit encoded samples (with $M=255$).

The 2003 amended version of the sRGB standard points out that higher accuracy is needed when the samples are encoded with more than 8 bits. It provides the matrix

$\left[\begin{array}{c}{R}_{\text{linear}}\\ G_{\text{linear}}\\ B_{\text{linear}}\end{array}\right]=\left[\begin{array}{ccc}+3.2406255& -1.5372080& -0.4986286\\ -0.9689307& +1.8757561& +0.0415175\\ +0.0557101& -0.2040211& +1.0569959\end{array}\right]\left[\begin{array}{c}{X}_{D65}\\ Y_{D65}\\ Z_{D65}\end{array}\right]$.

which is claimed to be sufficiently accurate for samples with $N=16$ bits ($M=65535$).

For these formulas, the X, Y, and Z values must be scaled so that the Y of D65 ("white") is 1.0 (X = 0.9505, Y = 1.0000, Z = 1.0890). This is usually true but some color spaces use 100 or other values (such as in CIELAB, when using specified white points).

Viewing environment

CIE 1931 xy chromaticity diagram showing the gamut of the sRGB color space (the triangle). The outer curved boundary is the spectral (or monochromatic) locus, with wavelengths shown in nanometers (labeled in blue). This image is drawn using sRGB, so colors outside the triangle cannot be accurately colored and have been interpolated. The D65 white point is shown in the center, and the Planckian locus is shown with color temperatures labeled in kelvins. D65 is not an ideal 6504-kelvin black body because it is based on atmospheric filtered daylight.

The sRGB specification assumes a dimly lit encoding (creation) environment with an ambient correlated color temperature (CCT) of 5003 K:

Parameter	Value
Screen luminance level	80 cd/m2
Illuminant white point	x = 0.3127, y = 0.3290 (D65)
Image surround reflectance	20% (~medium gray)
Encoding ambient illuminance level	64 lux
Encoding ambient white point	x = 0.3457, y = 0.3585 (D50)
Encoding viewing flare	1.0%
Typical ambient illuminance level	200 lux
Typical ambient white point	x = 0.3457, y = 0.3585 (D50)
Typical viewing flare	5.0%

The assumed ambient CCT differs from that of the BT.709 standard illuminant (D65), which is still retained for the screen white point. Using D50 for both would have made the white point of most photographic paper appear excessively blue. The other parameters, such as the luminance level, are representative of a typical CRT monitor.

For optimal results, the ICC recommends using the encoding viewing environment (i.e., dim, diffuse lighting) rather than the less-stringent typical viewing environment.

The bg-sRGB space

Annex G of the 2003 amendment of the sRGB standard describes an alternative encoding of color values, called bg-sRGB, that is recommended when the number of bits per channel $N$ is 10 or more.

In this alternative encoding, an integer encoded sample value $z$ and the corresponding linear R, G, or B value $v$ are related by the formulas

$v=D\left(\frac{z-K}{W-K}\right)$

and

$z=\text{round}(K+(W-K)E(v))$

where the $D$ and $E$ functions are the same as in the sRGB space. The standard specifies $K=384$ and $W=894$ for $N=10$, and generally

$K=3\times 2^{N-3}W=K+255\times 2^{N-9}$

for $N>10$. In the bg-sRGB color space, the null intensity $v=0$ is encoded as the integer $K$, and the maximum displayable intensity $v=1$ is encoded as the integer $W$. This encoding is useful for color space manipulations (like the conversion from sYCC) that can generate values $v$ that are negative or greater than 1.

History

The non-linear encoding of physical data samples is a common digital signal processing technique that aims to make better use of the bits available for the encoded signal, taking into account the non-linear way human senses perceive physical stimuli. Using smaller increments for smaller signals reduces the quantization artifacts.

This principle was incorporated into the digital-to-analog converters and the analog circuitry of early computer monitors, resulting in an effective decoding function (the mapping from digital sample values to the displayed intensity) which was roughly a power law with an exponent between 2 and 3. The exponent was commonly denoted with the letter $\gamma$, hence the common name "gamma correction" (or similar) for this function. This mapping initially varied according to CRT manufacturers, but was normalized in 1993 for use in HDTV systems, as the ITU BT.709 standard The BT.709 standard specified a decoding function with a linear section near zero, transitioning to a shifted power law with exponent 1/0.45 ≈ 2.2222....

The sRGB encoding was created a few years later by Hewlett-Packard and Microsoft. It was meant to describe the decoding function of most CRT computer monitors used with Windows operating systems at the time, which was still different from that assumed by BT.709. The first draft of the standard was published in 1996. A fourth draft, still incomplete, is available online. Like the BT.709, the sRGB decoding function was defined as a linear section near zero that transitions to a shifted power law

Justification for the formulas

In theory, the parameters of the encoding and decoding functions should be chosen so that the transition from the linear section to the power law section is continuous (without a sudden step) and smooth (without a sudden change of slope).

To derive the decoding function, one considers that the general formula for a linear function, whose graph is a straight line that passes through Template:Math, is $y=x/A$, and a shifted power law curve that passes through Template:Math is $y={\left(\frac{x+C}{1+C}\right)}^{\mathrm{\Gamma }}$

To obtain a seamless transition between the two functions when $x$ has a value $U$, we must have

$\frac{x}{A}={\left(\frac{U+C}{1+C}\right)}^{\mathrm{\Gamma }}$

To avoid a sudden change of slope where the two segments meet, the derivatives must be equal at this point:

$\frac{1}{A}=\mathrm{\Gamma }{\left(\frac{U+C}{1+C}\right)}^{\mathrm{\Gamma }-1}\left(\frac{1}{1+C}\right)$

Solving the two equations for $U$ and $A$ we get

$U=\frac{C}{\mathrm{\Gamma }-1}A=\frac{(1+C{)}^{\mathrm{\Gamma }}(\mathrm{\Gamma }-1{)}^{\mathrm{\Gamma }-1}}{(C^{\mathrm{\Gamma }-1})({\mathrm{\Gamma }}^{\mathrm{\Gamma }})}$

Parameter values

The first draft of the sRGB standard initially set the parameters at $C=0.055$ and $\mathrm{\Gamma }=2.4$ so that the resulting decoding function $D$ closely resembled a pure power law with exponent (gamma) 2.2, assimed to be typical of computer monitors at the time. This choice implies a breakpoint $U\approx 0.0392857...$ and a linear coefficient $A\approx 12.9232102...$. These values, rounded to $U=0.03928$ and $A=12.92321$ are still incorrectly given in some publications. However, the value of $A$ was rounded to $12.92$ already in the sRGB draft standard, resulting in a small discontinuity in the curve.

The first official version of the standard was defined and published by the IEC in 1999. In this version, the rounded value of $A=12.92$ was retained, but the breakpoint $U$ was redefined as $0.04045$ to make the curve approximately continuous. With these values, there is still a discontinuity in the slope, from $1/12.92$ just below the intersection to $1/12.70$ just above it. The final standard also corrected some small rounding errors present in the draft.

The 1999 IEC standard was amended in 2003. The sRGB to CIE XYZ matrix was retained, but the inverse transformation above was replaced by a more accurate version, with seven decimal fraction digits. The amended standard also included the definition of the sYCC encoding, using brightness (Y) and two chroma coordinates (CC) instead of R, G, and B coordinates, and a bg-sRGB encoding for 10-bit components which allows some component values outside the 0-1 range.

Usage

Comparison of some RGB and CMYK colour gamuts on a CIE 1931 xy chromaticity diagram

Due to the standardization of sRGB on the Internet, on computers, and on printers, many low- to medium-end consumer digital cameras and scanners use sRGB as the default (or only available) working color space. However, consumer-level CCDs are typically uncalibrated, meaning that even though the image or device is being labeled as "sRGB", one cannot assume that the encoded values or the colors of displayed images are accurate as specified by the standard. Recently that changed and smartphones and TVs have very good calibration out of the box.

If the color space of an image is unknown and the R, G, and B samples are encoded with 8 bits each, the sRGB encoding usually the assumed default.

As the sRGB gamut mostly meets or exceeds the gamut of a low-end inkjet printer, an sRGB image is often regarded as satisfactory for home printing. The sRGB color space is sometimes avoided by high-end print publishing professionals because its color gamut is not big enough, especially in the blue-green colors, to include all the colors that can be reproduced in CMYK printing. Images intended for professional printing via a fully color-managed workflow (e.g. prepress output) sometimes use another color space such as Adobe RGB (1998), which accommodates a wider gamut and CMYK color space like Fogra39. Such CMYK and sRGB images used on the Internet may be converted to sRGB using color management tools that are usually included with software that works in these other color spaces.

Programming interface support

The two dominant programming interfaces for 3D graphics, OpenGL and Direct3D, have both incorporated support for the sRGB gamma curve. OpenGL supports textures with sRGB gamma encoded color components (first introduced with EXT_texture_sRGB extension, added to the core in OpenGL 2.1) and rendering into sRGB gamma encoded framebuffers (first introduced with EXT_framebuffer_sRGB extension, added to the core in OpenGL 3.0). Correct mipmapping and interpolation of sRGB gamma textures has direct hardware support in texturing units of most modern GPUs (for example nVidia GeForce 8 performs conversion from 8-bit texture to linear values before interpolating those values), and does not have any performance penalty.

ICC profiles

A lookup table may be used to efficiently convert sRGB to other color spaces.Template:Citation needed The International Color Consortium (ICC) has published color profiles for this purpose, which are widely used. There are several variants, including ICCmax, version 4, and version 2.

Version 4 is generally recommended, but version 2 is still commonly used and is the most compatible with other software including browsers. However, inconsistencies have been pointed out between those ICC profiles and the IEC sRGB standard. In particular, version 2 of the ICC profile specification does not implement the piecewise parametric curve encoding ("para") as specified by the IEC sRGB standard, and has to implement the linear spline using 1DLUT. What is worse in some cases "simplified sRGB" is used which is just 2.2 gamma.

The sYCC color space

Amendment 1 to IEC 61966-2-1:1999, approved in 2003, includes the definition of a Y′Cb′Cr′ color representation called sYCC. Although the RGB color primaries are based on BT.709, the equations for transformation from sRGB to sYCC and vice versa are based on BT.601. The sYCC standard specifies 8 bits for the encoded components, and the matrices result in a range of approximately 0–1 for Y; -0.5–0.5 for C.

As this conversion can result in sRGB values outside the range 0–1, the amendment describes how to apply the gamma correction to negative values, by applying Template:Math when Template:Mvar is negative (and Template:Mvar is the sRGB↔linear functions described above). This is also used by scRGB.

External links

• Test that shows whether your display is pure 2.2 gamma or sRGB (~2.2 gamma) on Shadertoy