RGB conversion

R'G'B' to Y′PbPr

RGB to YCbCr conversion

Y′CbCr signals (prior to scaling and offsets to place the signals into digital form) are called YPbPr, and are created from the corresponding gamma-adjusted RGB (red, green and blue) source using three defined constants K_R, K_G, and K_B as follows:

${\displaystyle {\begin{aligned}Y'&=K_{R}\cdot R'+K_{G}\cdot G'+K_{B}\cdot B'\\P_{B}&={\frac {1}{2}}\cdot {\frac {B'-Y'}{1-K_{B}}}\\P_{R}&={\frac {1}{2}}\cdot {\frac {R'-Y'}{1-K_{R}}}\end{aligned}}}$

where K_R, K_G, and K_B are ordinarily derived from the definition of the corresponding RGB space, and required to satisfy ${\displaystyle K_{R}+K_{G}+K_{B}=1}$.

The equivalent matrix manipulation is often referred to as the "color matrix":

${\displaystyle {\begin{bmatrix}Y'\\P_{B}\\P_{R}\end{bmatrix}}={\begin{bmatrix}K_{R}&K_{G}&K_{B}\\-{\frac {1}{2}}\cdot {\frac {K_{R}}{1-K_{B}}}&-{\frac {1}{2}}\cdot {\frac {K_{G}}{1-K_{B}}}&{\frac {1}{2}}\\{\frac {1}{2}}&-{\frac {1}{2}}\cdot {\frac {K_{G}}{1-K_{R}}}&-{\frac {1}{2}}\cdot {\frac {K_{B}}{1-K_{R}}}\end{bmatrix}}{\begin{bmatrix}R'\\G'\\B'\end{bmatrix}}}$

And its inverse:

${\displaystyle {\begin{bmatrix}R'\\G'\\B'\end{bmatrix}}={\begin{bmatrix}1&0&2-2\cdot K_{R}\\1&-{\frac {K_{B}}{K_{G}}}\cdot (2-2\cdot K_{B})&-{\frac {K_{R}}{K_{G}}}\cdot (2-2\cdot K_{R})\\1&2-2\cdot K_{B}&0\end{bmatrix}}{\begin{bmatrix}Y'\\P_{B}\\P_{R}\end{bmatrix}}}$

Here, the prime (′) symbols mean gamma correction is being used; thus R′, G′ and B′ nominally range from 0 to 1, with 0 representing the minimum intensity (e.g., for display of the color black) and 1 the maximum (e.g., for display of the color white). The resulting luma (Y) value will then have a nominal range from 0 to 1, and the chroma (P_B and P_R) values will have a nominal range from -0.5 to +0.5. The reverse conversion process can be readily derived by inverting the above equations.

ITU-R BT.601 conversion

The form of Y′CbCr that was defined for standard-definition television use in the ITU-R BT.601 (formerly CCIR 601) standard for use with digital component video is derived from the corresponding RGB space (ITU-R BT.470-6 System M primaries) as follows:

${\displaystyle {\begin{aligned}K_{R}&=0.299\\K_{G}&=0.587\\K_{B}&=0.114\end{aligned}}}$

From the above constants and formulas, the following can be derived for ITU-R BT.601.

Analog YPbPr from analog R'G'B' is derived as follows:

${\displaystyle {\begin{aligned}Y'&=&0.299\cdot R'&+&0.587\cdot G'&+&0.114\cdot B'\\P_{B}&=-&0.168736\cdot R'&-&0.331264\cdot G'&+&0.5\cdot B'\\P_{R}&=&0.5\cdot R'&-&0.418688\cdot G'&-&0.081312\cdot B'\end{aligned}}}$

Digital Y′CbCr (8 bits per sample) is derived from analog R'G'B' as follows:

${\displaystyle {\begin{aligned}Y'&=&16&+&(65.481\cdot R'&+&128.553\cdot G'&+&24.966\cdot B')\\C_{B}&=&128&+&(-37.797\cdot R'&-&74.203\cdot G'&+&112.0\cdot B')\\C_{R}&=&128&+&(112.0\cdot R'&-&93.786\cdot G'&-&18.214\cdot B')\end{aligned}}}$

or simply componentwise

${\displaystyle {\begin{aligned}(Y',C_{B},C_{R})&=&(16,128,128)+(219\cdot Y,224\cdot P_{B},224\cdot P_{R})\\\end{aligned}}}$

The resultant signals range from 16 to 235 for Y′ (Cb and Cr range from 16 to 240); the values from 0 to 15 are called footroom, while the values from 236 to 255 are called headroom.

Alternatively, digital Y′CbCr can derived from digital R'dG'dB'd (8 bits per sample, each using the full range with zero representing black and 255 representing white) according to the following equations:

${\displaystyle {\begin{aligned}Y'&=&16&+&{\frac {65.481\cdot R'_{D}}{255}}&+&{\frac {128.553\cdot G'_{D}}{255}}&+&{\frac {24.966\cdot B'_{D}}{255}}\\C_{B}&=&128&-&{\frac {37.797\cdot R'_{D}}{255}}&-&{\frac {74.203\cdot G'_{D}}{255}}&+&{\frac {112.0\cdot B'_{D}}{255}}\\C_{R}&=&128&+&{\frac {112.0\cdot R'_{D}}{255}}&-&{\frac {93.786\cdot G'_{D}}{255}}&-&{\frac {18.214\cdot B'_{D}}{255}}\end{aligned}}}$

In the formula below, the scaling factors are multiplied by ${\displaystyle {\frac {256}{255}}}$. This allows for the value 256 in the denominator, which can be calculated by a single bitshift.

${\displaystyle {\begin{aligned}Y'&=&16&+&{\frac {65.738\cdot R'_{D}}{256}}&+&{\frac {129.057\cdot G'_{D}}{256}}&+&{\frac {25.064\cdot B'_{D}}{256}}\\C_{B}&=&128&-&{\frac {37.945\cdot R'_{D}}{256}}&-&{\frac {74.494\cdot G'_{D}}{256}}&+&{\frac {112.439\cdot B'_{D}}{256}}\\C_{R}&=&128&+&{\frac {112.439\cdot R'_{D}}{256}}&-&{\frac {94.154\cdot G'_{D}}{256}}&-&{\frac {18.285\cdot B'_{D}}{256}}\end{aligned}}}$

If the R'd G'd B'd digital source includes footroom and headroom, the footroom offset 16 needs to be subtracted first from each signal, and a scale factor of ${\displaystyle {\frac {255}{219}}}$ needs to be included in the equations.

The inverse transform is:

${\displaystyle {\begin{aligned}R'_{D}&=&{\frac {298.082\cdot Y'}{256}}&&&+&{\frac {408.583\cdot C_{R}}{256}}&-&222.921\\G'_{D}&=&{\frac {298.082\cdot Y'}{256}}&-&{\frac {100.291\cdot C_{B}}{256}}&-&{\frac {208.120\cdot C_{R}}{256}}&+&135.576\\B'_{D}&=&{\frac {298.082\cdot Y'}{256}}&+&{\frac {516.412\cdot C_{B}}{256}}&&&-&276.836\end{aligned}}}$

The inverse transform without any roundings (using values coming directly from ITU-R BT.601 recommendation) is:

${\displaystyle {\begin{aligned}R'_{D}={\frac {255}{219}}\cdot (Y'-16)&&&&&&&+{\frac {255}{224}}\cdot 1.402\cdot (C_{R}-128)\\G'_{D}={\frac {255}{219}}\cdot (Y'-16)&-&{\frac {255}{224}}\cdot 1.772&&\cdot {\frac {0.114}{0.587}}&&\cdot (C_{B}-128)&-{\frac {255}{224}}\cdot 1.402\cdot {\frac {0.299}{0.587}}\cdot (C_{R}-128)\\B'_{D}={\frac {255}{219}}\cdot (Y'-16)&+&{\frac {255}{224}}\cdot 1.772&&&&\cdot (C_{B}-128)\end{aligned}}}$

This form of Y′CbCr is used primarily for older standard-definition television systems, as it uses an RGB model that fits the phosphor emission characteristics of older CRTs.

ITU-R BT.709 conversion

Rec. 709 compared with Rec. 2020

A different form of Y′CbCr is specified in the ITU-R BT.709 standard, primarily for HDTV use. The newer form is also used in some computer-display oriented applications, as sRGB (though the matrix used for sRGB form of YCbCr, sYCC, is still BT.601). In this case, the values of Kb and Kr differ, but the formulas for using them are the same. For ITU-R BT.709, the constants are:

${\displaystyle {\begin{aligned}K_{B}&=0.0722\\K_{R}&=0.2126\\(K_{G}&=1-K_{B}-K_{R}=0.7152)\end{aligned}}}$

This form of Y′CbCr is based on an RGB model that more closely fits the phosphor emission characteristics of newer CRTs and other modern display equipment. The conversion matrices for BT.709 are these:

${\displaystyle {\begin{aligned}{\begin{bmatrix}Y'\\C_{B}\\C_{R}\end{bmatrix}}&={\begin{bmatrix}0.2126&0.7152&0.0722\\-0.1146&-0.3854&0.5\\0.5&-0.4542&-0.0458\end{bmatrix}}{\begin{bmatrix}R'\\G'\\B'\end{bmatrix}}\\{\begin{bmatrix}R'\\G'\\B'\end{bmatrix}}&={\begin{bmatrix}1&0&1.5748\\1&-0.1873&-0.4681\\1&1.8556&0\end{bmatrix}}{\begin{bmatrix}Y'\\C_{B}\\C_{R}\end{bmatrix}}\end{aligned}}}$

The definitions of the R', G', and B' signals also differ between BT.709 and BT.601, and differ within BT.601 depending on the type of TV system in use (625-line as in PAL and SECAM or 525-line as in NTSC), and differ further in other specifications. In different designs there are differences in the definitions of the R, G, and B chromaticity coordinates, the reference white point, the supported gamut range, the exact gamma pre-compensation functions for deriving R', G' and B' from R, G, and B, and in the scaling and offsets to be applied during conversion from R'G'B' to Y′CbCr. So proper conversion of Y′CbCr from one form to the other is not just a matter of inverting one matrix and applying the other. In fact, when Y′CbCr is designed ideally, the values of K_B and K_R are derived from the precise specification of the RGB color primary signals, so that the luma (Y′) signal corresponds as closely as possible to a gamma-adjusted measurement of luminance (typically based on the CIE 1931 measurements of the response of the human visual system to color stimuli).^[4]

ITU-R BT.2020 conversion

The ITU-R BT.2020 standard uses the same gamma function as BT.709. It defines:^[5]

• Non-constant luminance Y'CbCr, similar to the previous entries, except with different K_B and K_R.
• Constant luminance Y'cCbcCrc, a formulation where Y' is the gamma-codec version of the true luminance.^[5]

For both, the coefficients derived from the primaries are:

${\displaystyle {\begin{aligned}K_{B}&=0.0593\\K_{R}&=0.2627\\(K_{G}&=1-K_{B}-K_{R}=0.6780)\end{aligned}}}$

For NCL, the definition is classical: Y' = 0.2627R' + 0.6780 G' + 0.0593 B'; Cb = (B' - Y)' / 1.8814; Cr = (R' - Y') / 1.4746. The encoding conversion can, as usual, be written as a matrix.^[5] The decoding matrix for BT.2020-NCL is this with 14 decimal places:

${\displaystyle {\begin{aligned}{\begin{bmatrix}R\\G\\B\end{bmatrix}}&={\begin{bmatrix}1&0&1.4746\\1&-0.16455312684366&-0.57135312684366\\1&1.8814&0\end{bmatrix}}{\begin{bmatrix}Y'\\C_{B}\\C_{R}\end{bmatrix}}\end{aligned}}}$

The smaller values in the matrix are not rounded; they are precise values. For systems with limited precision (8 or 10 bit, for example) a lower precision of the above matrix could be used, for example, retaining only 6 digits after decimal point.^[6]

The CL version, YcCbcCrc, codes:^[5]

• Y'c = (0.2627R + 0.6780 G + 0.0593 B)'. This is the gamma function applied to the true luminance calculated from linear RGB.
• Cbc = (B'-Y'c) / (-2 Nb) if B' < Y'c; (B'-Y'c) / (2 Pb) otherwise. Nb and Pb are the theoretical minimum and maximum of (B'-Y'c) corresponding to the gamut. The rounded "practical" values are Pb = 0.7910, Nb = -0.9702. The full derivation can be found in the recommendation.^[5]
• Crc = (R'-Y'c) / (-2 Nr) if R' < Y'c; (R'-Y'c) / (2 Pr) otherwise. Again, Pr and Nr are theoretical limits. The rounded values are Pr 0.4969, Nr = -0.8591.

The CL function can be used when preservation of luminance is of primary importance (see: Chroma subsampling § Gamma luminance error), or when "there is an expectation of improved coding efficiency for delivery." The specification refers to Report ITU-R BT.2246 on this matter.^[5] BT.2246 states that CL has improved compression efficiency and luminance preservation, but NCL will be more familiar to a staff that has previously handled color mixing and other production practices in HDTV YCbCr.^[7]

BT.2020 does not define PQ and thus HDR, it is further defined in SMPTE ST 2084 and BT.2100. BT.2100 will introduce the use of IC_TC_P, a semi-perceptual colorspace derived from linear RGB with good hue linearity. It is "near-constant luminance".^[8]

SMPTE 240M conversion

The SMPTE 240M standard (used on the MUSE analog HD television system) defines YCC with these coefficients:

${\displaystyle {\begin{aligned}K_{B}&=0.087\\K_{R}&=0.212\end{aligned}}}$

The coefficients are derived from SMPTE 170M primaries and white point, as used in 240M standard.

JPEG conversion

JFIF usage of JPEG supports a modified Rec. 601 Y′CbCr where Y′, C_B and C_R have the full 8-bit range of [0...255].^[9] Below are the conversion equations expressed to six decimal digits of precision. (For ideal equations, see ITU-T T.871.^[10]) Note that for the following formulae, the range of each input (R,G,B) is also the full 8-bit range of [0...255].

${\displaystyle {\begin{aligned}Y'&=&0&+(0.299&\cdot R'_{D})&+(0.587&\cdot G'_{D})&+(0.114&\cdot B'_{D})\\C_{B}&=&128&-(0.168736&\cdot R'_{D})&-(0.331264&\cdot G'_{D})&+(0.5&\cdot B'_{D})\\C_{R}&=&128&+(0.5&\cdot R'_{D})&-(0.418688&\cdot G'_{D})&-(0.081312&\cdot B'_{D})\end{aligned}}}$

And back:

${\displaystyle {\begin{aligned}R'_{D}&=&Y'&&&+1.402&\cdot (C_{R}-128)\\G'_{D}&=&Y'&-0.344136&\cdot (C_{B}-128)&-0.714136&\cdot (C_{R}-128)\\B'_{D}&=&Y'&+1.772&\cdot (C_{B}-128)&\end{aligned}}}$

The above conversion is identical to sYCC when the input is given as sRGB, except that IEC 61966-2-1:1999/Amd1:2003 only gives four decimal digits.

JPEG also defines a "YCCK" format from Adobe for CMYK input. In this format, the "K" value is passed as-is, while CMY are used to derive YCbCr with the above matrix by assuming R=1-C, G=1-M, and B=1-Y. As a result, a similar set of subsampling techniques can be used.^[11]

Coefficients for BT.470-6 System B, G primaries

${\displaystyle {\begin{aligned}K_{B}&=0.0713\\K_{R}&=0.2220\end{aligned}}}$

These coefficients are not in use and were never in use.^[12]

Chromaticity-derived luminance systems

H.273 also describes constant and non-constant luminance systems which are derived strictly from primaries and white point, so that situations like sRGB/BT.709 default primaries of JPEG that use BT.601 matrix (that is derived from BT.470-6 System M) do not happen.

Approximate 8-bit matrices for BT.601

These matrices round all factors to the closest 1/256 unit. As a result, only one 16-bit intermediate value is formed for each component, and a simple right-shift with rounding (x + 128) >> 8 can take care of the division.^[13]

For studio-swing:

${\displaystyle {\begin{bmatrix}Y'\\C_{B}\\C_{R}\end{bmatrix}}={\frac {1}{256}}{\begin{bmatrix}66&129&25\\-38&-74&112\\112&-94&-18\end{bmatrix}}{\begin{bmatrix}R'\\G'\\B'\end{bmatrix}}+{\begin{bmatrix}16\\128\\128\end{bmatrix}}}$

For full-swing:

${\displaystyle {\begin{bmatrix}Y'\\C_{B}\\C_{R}\end{bmatrix}}={\frac {1}{256}}{\begin{bmatrix}77&150&29\\-43&-84&127\\127&-106&-21\end{bmatrix}}{\begin{bmatrix}R'\\G'\\B'\end{bmatrix}}+{\begin{bmatrix}0\\128\\128\end{bmatrix}}}$

Google's Skia used to use the above 8-bit full-range matrix, resulting in a slight greening effect on JPEG images encoded by Android devices, more noticeable on repeated saving. The issue was fixed in 2016, when the more accurate version was used instead. Due to SIMD optimizations in libjpeg-turbo, the accurate version is actually faster.^[14]

4:4:4

4:4:4 is straightforward, as no pixel-grouping is done: the difference lies solely in how many bits each channel is given, and their arrangement. The basic YUV3 scheme uses 3 bytes per pixel, with the order y0, u0, v0, y1, u1, v1 (using "u" for Cb and "v" for Cr; the same applies to content below).^[17] In computers, it is more common to see a AYUV format, which adds an alpha channel and goes a0, y0, u0, v0, a1, y1, u1, v1, because groups of 32-bits are easier to deal with.^[15]

4:2:2

4:2:2 groups 2 pixels together horizontally in each conceptual "container". Two main arrangements are:^[16]

• YUY2: also called YUYV, runs in the format y0, u, y1, v.
  

  YUY2 format
• UYVY: the byte-swapped reverse of YUY2, runs in the format u, y0, v, y1.

4:1:1

4:1:1 is rarely used. Pixels are in horizontal groups of 4.^[16]

4:2:0

4:2:0 is very commonly used. The main formats are IMC2, IMC4, YV12, and NV12.^[16] All of these four formats are "planar", meaning that the Y, U, and V values are grouped together instead of interspersed. They all occupy 12 bits per pixel, assuming a 8-bit channel.

• IMC2 first lays the full images out in Y. It then arranges each line of chroma in the order of V₀ ... V_n, U₀ ... U_n, where n is the number of chroma samples per line, equal to half the width of Y.
• IMC4 is similar to IMC2, except it runs in U₀ ... U_n, V₀ ... V_n.
• YV12 is a simpler design and is more commonly used. The entire image in Y is written out, followed by the image in V, then by the whole image in U.
  

  YV12 layout
• NV12 is possibly the most commonly-used 8-bit 4:2:0 format. It is the default for Android camera preview.^[18] The entire image in Y is written out, followed by interleaved lines that go U₀, V₀, U₁, V₁, etc.

There are also "tiled" variants of planar formats.^[19]