# 2.17. Detailed Colorspace Descriptions¶

## 2.17.1. Colorspace SMPTE 170M (V4L2_COLORSPACE_SMPTE170M)¶

The SMPTE 170M standard defines the colorspace used by NTSC and PAL and by SDTV in general. The default transfer function is V4L2_XFER_FUNC_709. The default Y’CbCr encoding is V4L2_YCBCR_ENC_601. The default Y’CbCr quantization is limited range. The chromaticities of the primary colors and the white reference are:

SMPTE 170M Chromaticities

Color

x

y

Red

0.630

0.340

Green

0.310

0.595

Blue

0.155

0.070

White Reference (D65)

0.3127

0.3290

The red, green and blue chromaticities are also often referred to as the SMPTE C set, so this colorspace is sometimes called SMPTE C as well.

The transfer function defined for SMPTE 170M is the same as the one defined in Rec. 709.

L' = -1.099(-L)^{0.45} + 0.099 \text{, for } L \le-0.018 L' = 4.5L \text{, for } -0.018 < L < 0.018 L' = 1.099L^{0.45} - 0.099 \text{, for } L \ge 0.018

Inverse Transfer function:

L = -\left( \frac{L' - 0.099}{-1.099} \right) ^{\frac{1}{0.45}} \text{, for } L' \le -0.081 L = \frac{L'}{4.5} \text{, for } -0.081 < L' < 0.081 L = \left(\frac{L' + 0.099}{1.099}\right)^{\frac{1}{0.45} } \text{, for } L' \ge 0.081

The luminance (Y’) and color difference (Cb and Cr) are obtained with the following V4L2_YCBCR_ENC_601 encoding:

Y' = 0.2990R' + 0.5870G' + 0.1140B' Cb = -0.1687R' - 0.3313G' + 0.5B' Cr = 0.5R' - 0.4187G' - 0.0813B'

Y’ is clamped to the range [0…1] and Cb and Cr are clamped to the range [-0.5…0.5]. This conversion to Y’CbCr is identical to the one defined in the ITU BT.601 standard and this colorspace is sometimes called BT.601 as well, even though BT.601 does not mention any color primaries.

The default quantization is limited range, but full range is possible although rarely seen.

## 2.17.2. Colorspace Rec. 709 (V4L2_COLORSPACE_REC709)¶

The ITU BT.709 standard defines the colorspace used by HDTV in general. The default transfer function is V4L2_XFER_FUNC_709. The default Y’CbCr encoding is V4L2_YCBCR_ENC_709. The default Y’CbCr quantization is limited range. The chromaticities of the primary colors and the white reference are:

Rec. 709 Chromaticities

Color

x

y

Red

0.640

0.330

Green

0.300

0.600

Blue

0.150

0.060

White Reference (D65)

0.3127

0.3290

The full name of this standard is Rec. ITU-R BT.709-5.

Transfer function. Normally L is in the range [0…1], but for the extended gamut xvYCC encoding values outside that range are allowed.

L' = -1.099(-L)^{0.45} + 0.099 \text{, for } L \le -0.018 L' = 4.5L \text{, for } -0.018 < L < 0.018 L' = 1.099L^{0.45} - 0.099 \text{, for } L \ge 0.018

Inverse Transfer function:

L = -\left( \frac{L' - 0.099}{-1.099} \right)^\frac{1}{0.45} \text{, for } L' \le -0.081 L = \frac{L'}{4.5}\text{, for } -0.081 < L' < 0.081 L = \left(\frac{L' + 0.099}{1.099}\right)^{\frac{1}{0.45} } \text{, for } L' \ge 0.081

The luminance (Y’) and color difference (Cb and Cr) are obtained with the following V4L2_YCBCR_ENC_709 encoding:

Y' = 0.2126R' + 0.7152G' + 0.0722B' Cb = -0.1146R' - 0.3854G' + 0.5B' Cr = 0.5R' - 0.4542G' - 0.0458B'

Y’ is clamped to the range [0…1] and Cb and Cr are clamped to the range [-0.5…0.5].

The default quantization is limited range, but full range is possible although rarely seen.

The V4L2_YCBCR_ENC_709 encoding described above is the default for this colorspace, but it can be overridden with V4L2_YCBCR_ENC_601, in which case the BT.601 Y’CbCr encoding is used.

Two additional extended gamut Y’CbCr encodings are also possible with this colorspace:

The xvYCC 709 encoding (V4L2_YCBCR_ENC_XV709, xvYCC) is similar to the Rec. 709 encoding, but it allows for R’, G’ and B’ values that are outside the range [0…1]. The resulting Y’, Cb and Cr values are scaled and offset according to the limited range formula:

Y' = \frac{219}{256} * (0.2126R' + 0.7152G' + 0.0722B') + \frac{16}{256} Cb = \frac{224}{256} * (-0.1146R' - 0.3854G' + 0.5B') Cr = \frac{224}{256} * (0.5R' - 0.4542G' - 0.0458B')

The xvYCC 601 encoding (V4L2_YCBCR_ENC_XV601, xvYCC) is similar to the BT.601 encoding, but it allows for R’, G’ and B’ values that are outside the range [0…1]. The resulting Y’, Cb and Cr values are scaled and offset according to the limited range formula:

Y' = \frac{219}{256} * (0.2990R' + 0.5870G' + 0.1140B') + \frac{16}{256} Cb = \frac{224}{256} * (-0.1687R' - 0.3313G' + 0.5B') Cr = \frac{224}{256} * (0.5R' - 0.4187G' - 0.0813B')

Y’ is clamped to the range [0…1] and Cb and Cr are clamped to the range [-0.5…0.5] and quantized without further scaling or offsets. The non-standard xvYCC 709 or xvYCC 601 encodings can be used by selecting V4L2_YCBCR_ENC_XV709 or V4L2_YCBCR_ENC_XV601. As seen by the xvYCC formulas these encodings always use limited range quantization, there is no full range variant. The whole point of these extended gamut encodings is that values outside the limited range are still valid, although they map to R’, G’ and B’ values outside the [0…1] range and are therefore outside the Rec. 709 colorspace gamut.

## 2.17.3. Colorspace sRGB (V4L2_COLORSPACE_SRGB)¶

The sRGB standard defines the colorspace used by most webcams and computer graphics. The default transfer function is V4L2_XFER_FUNC_SRGB. The default Y’CbCr encoding is V4L2_YCBCR_ENC_601. The default Y’CbCr quantization is limited range.

Note that the sYCC standard specifies full range quantization, however all current capture hardware supported by the kernel convert R’G’B’ to limited range Y’CbCr. So choosing full range as the default would break how applications interpret the quantization range.

The chromaticities of the primary colors and the white reference are:

sRGB Chromaticities

Color

x

y

Red

0.640

0.330

Green

0.300

0.600

Blue

0.150

0.060

White Reference (D65)

0.3127

0.3290

These chromaticities are identical to the Rec. 709 colorspace.

Transfer function. Note that negative values for L are only used by the Y’CbCr conversion.

L' = -1.055(-L)^{\frac{1}{2.4} } + 0.055\text{, for }L < -0.0031308 L' = 12.92L\text{, for }-0.0031308 \le L \le 0.0031308 L' = 1.055L ^{\frac{1}{2.4} } - 0.055\text{, for }0.0031308 < L \le 1

Inverse Transfer function:

L = -((-L' + 0.055) / 1.055) ^{2.4}\text{, for }L' < -0.04045 L = L' / 12.92\text{, for }-0.04045 \le L' \le 0.04045 L = ((L' + 0.055) / 1.055) ^{2.4}\text{, for }L' > 0.04045

The luminance (Y’) and color difference (Cb and Cr) are obtained with the following V4L2_YCBCR_ENC_601 encoding as defined by sYCC:

Y' = 0.2990R' + 0.5870G' + 0.1140B' Cb = -0.1687R' - 0.3313G' + 0.5B' Cr = 0.5R' - 0.4187G' - 0.0813B'

Y’ is clamped to the range [0…1] and Cb and Cr are clamped to the range [-0.5…0.5]. This transform is identical to one defined in SMPTE 170M/BT.601. The Y’CbCr quantization is limited range.

## 2.17.4. Colorspace opRGB (V4L2_COLORSPACE_OPRGB)¶

The opRGB standard defines the colorspace used by computer graphics that use the opRGB colorspace. The default transfer function is V4L2_XFER_FUNC_OPRGB. The default Y’CbCr encoding is V4L2_YCBCR_ENC_601. The default Y’CbCr quantization is limited range.

Note that the opRGB standard specifies full range quantization, however all current capture hardware supported by the kernel convert R’G’B’ to limited range Y’CbCr. So choosing full range as the default would break how applications interpret the quantization range.

The chromaticities of the primary colors and the white reference are:

opRGB Chromaticities

Color

x

y

Red

0.6400

0.3300

Green

0.2100

0.7100

Blue

0.1500

0.0600

White Reference (D65)

0.3127

0.3290

Transfer function:

L' = L ^{\frac{1}{2.19921875}}

Inverse Transfer function:

L = L'^{(2.19921875)}

The luminance (Y’) and color difference (Cb and Cr) are obtained with the following V4L2_YCBCR_ENC_601 encoding:

Y' = 0.2990R' + 0.5870G' + 0.1140B' Cb = -0.1687R' - 0.3313G' + 0.5B' Cr = 0.5R' - 0.4187G' - 0.0813B'

Y’ is clamped to the range [0…1] and Cb and Cr are clamped to the range [-0.5…0.5]. This transform is identical to one defined in SMPTE 170M/BT.601. The Y’CbCr quantization is limited range.

## 2.17.5. Colorspace BT.2020 (V4L2_COLORSPACE_BT2020)¶

The ITU BT.2020 standard defines the colorspace used by Ultra-high definition television (UHDTV). The default transfer function is V4L2_XFER_FUNC_709. The default Y’CbCr encoding is V4L2_YCBCR_ENC_BT2020. The default Y’CbCr quantization is limited range. The chromaticities of the primary colors and the white reference are:

BT.2020 Chromaticities

Color

x

y

Red

0.708

0.292

Green

0.170

0.797

Blue

0.131

0.046

White Reference (D65)

0.3127

0.3290

Transfer function (same as Rec. 709):

L' = 4.5L\text{, for }0 \le L < 0.018 L' = 1.099L ^{0.45} - 0.099\text{, for } 0.018 \le L \le 1

Inverse Transfer function:

L = L' / 4.5\text{, for } L' < 0.081 L = \left( \frac{L' + 0.099}{1.099}\right) ^{\frac{1}{0.45} }\text{, for } L' \ge 0.081

Please note that while Rec. 709 is defined as the default transfer function by the ITU BT.2020 standard, in practice this colorspace is often used with the Transfer Function SMPTE 2084 (V4L2_XFER_FUNC_SMPTE2084). In particular Ultra HD Blu-ray discs use this combination.

The luminance (Y’) and color difference (Cb and Cr) are obtained with the following V4L2_YCBCR_ENC_BT2020 encoding:

Y' = 0.2627R' + 0.6780G' + 0.0593B' Cb = -0.1396R' - 0.3604G' + 0.5B' Cr = 0.5R' - 0.4598G' - 0.0402B'

Y’ is clamped to the range [0…1] and Cb and Cr are clamped to the range [-0.5…0.5]. The Y’CbCr quantization is limited range.

There is also an alternate constant luminance R’G’B’ to Yc’CbcCrc (V4L2_YCBCR_ENC_BT2020_CONST_LUM) encoding:

Luma:

\begin{align*} Yc' = (0.2627R + 0.6780G + 0.0593B)'& \\ B' - Yc' \le 0:& \\ &Cbc = (B' - Yc') / 1.9404 \\ B' - Yc' > 0: & \\ &Cbc = (B' - Yc') / 1.5816 \\ R' - Yc' \le 0:& \\ &Crc = (R' - Y') / 1.7184 \\ R' - Yc' > 0:& \\ &Crc = (R' - Y') / 0.9936 \end{align*}

Yc’ is clamped to the range [0…1] and Cbc and Crc are clamped to the range [-0.5…0.5]. The Yc’CbcCrc quantization is limited range.

## 2.17.6. Colorspace DCI-P3 (V4L2_COLORSPACE_DCI_P3)¶

The SMPTE RP 431-2 standard defines the colorspace used by cinema projectors that use the DCI-P3 colorspace. The default transfer function is V4L2_XFER_FUNC_DCI_P3. The default Y’CbCr encoding is V4L2_YCBCR_ENC_709. The default Y’CbCr quantization is limited range.

Note

Note that this colorspace standard does not specify a Y’CbCr encoding since it is not meant to be encoded to Y’CbCr. So this default Y’CbCr encoding was picked because it is the HDTV encoding.

The chromaticities of the primary colors and the white reference are:

DCI-P3 Chromaticities

Color

x

y

Red

0.6800

0.3200

Green

0.2650

0.6900

Blue

0.1500

0.0600

White Reference

0.3140

0.3510

Transfer function:

L' = L^{\frac{1}{2.6}}

Inverse Transfer function:

L = L'^{(2.6)}

Y’CbCr encoding is not specified. V4L2 defaults to Rec. 709.

## 2.17.7. Colorspace SMPTE 240M (V4L2_COLORSPACE_SMPTE240M)¶

The SMPTE 240M standard was an interim standard used during the early days of HDTV (1988-1998). It has been superseded by Rec. 709. The default transfer function is V4L2_XFER_FUNC_SMPTE240M. The default Y’CbCr encoding is V4L2_YCBCR_ENC_SMPTE240M. The default Y’CbCr quantization is limited range. The chromaticities of the primary colors and the white reference are:

SMPTE 240M Chromaticities

Color

x

y

Red

0.630

0.340

Green

0.310

0.595

Blue

0.155

0.070

White Reference (D65)

0.3127

0.3290

These chromaticities are identical to the SMPTE 170M colorspace.

Transfer function:

L' = 4L\text{, for } 0 \le L < 0.0228 L' = 1.1115L ^{0.45} - 0.1115\text{, for } 0.0228 \le L \le 1

Inverse Transfer function:

L = \frac{L'}{4}\text{, for } 0 \le L' < 0.0913 L = \left( \frac{L' + 0.1115}{1.1115}\right) ^{\frac{1}{0.45} }\text{, for } L' \ge 0.0913

The luminance (Y’) and color difference (Cb and Cr) are obtained with the following V4L2_YCBCR_ENC_SMPTE240M encoding:

Y' = 0.2122R' + 0.7013G' + 0.0865B' Cb = -0.1161R' - 0.3839G' + 0.5B' Cr = 0.5R' - 0.4451G' - 0.0549B'

Y’ is clamped to the range [0…1] and Cb and Cr are clamped to the range [-0.5…0.5]. The Y’CbCr quantization is limited range.

## 2.17.8. Colorspace NTSC 1953 (V4L2_COLORSPACE_470_SYSTEM_M)¶

This standard defines the colorspace used by NTSC in 1953. In practice this colorspace is obsolete and SMPTE 170M should be used instead. The default transfer function is V4L2_XFER_FUNC_709. The default Y’CbCr encoding is V4L2_YCBCR_ENC_601. The default Y’CbCr quantization is limited range. The chromaticities of the primary colors and the white reference are:

NTSC 1953 Chromaticities

Color

x

y

Red

0.67

0.33

Green

0.21

0.71

Blue

0.14

0.08

White Reference (C)

0.310

0.316

Note

This colorspace uses Illuminant C instead of D65 as the white reference. To correctly convert an image in this colorspace to another that uses D65 you need to apply a chromatic adaptation algorithm such as the Bradford method.

The transfer function was never properly defined for NTSC 1953. The Rec. 709 transfer function is recommended in the literature:

L' = 4.5L\text{, for } 0 \le L < 0.018 L' = 1.099L ^{0.45} - 0.099\text{, for } 0.018 \le L \le 1

Inverse Transfer function:

L = \frac{L'}{4.5} \text{, for } L' < 0.081 L = \left( \frac{L' + 0.099}{1.099}\right) ^{\frac{1}{0.45} }\text{, for } L' \ge 0.081

The luminance (Y’) and color difference (Cb and Cr) are obtained with the following V4L2_YCBCR_ENC_601 encoding:

Y' = 0.2990R' + 0.5870G' + 0.1140B' Cb = -0.1687R' - 0.3313G' + 0.5B' Cr = 0.5R' - 0.4187G' - 0.0813B'

Y’ is clamped to the range [0…1] and Cb and Cr are clamped to the range [-0.5…0.5]. The Y’CbCr quantization is limited range. This transform is identical to one defined in SMPTE 170M/BT.601.

## 2.17.9. Colorspace EBU Tech. 3213 (V4L2_COLORSPACE_470_SYSTEM_BG)¶

The EBU Tech 3213 standard defines the colorspace used by PAL/SECAM in 1975. Note that this colorspace is not supported by the HDMI interface. Instead EBU Tech 3321 recommends that Rec. 709 is used instead for HDMI. The default transfer function is V4L2_XFER_FUNC_709. The default Y’CbCr encoding is V4L2_YCBCR_ENC_601. The default Y’CbCr quantization is limited range. The chromaticities of the primary colors and the white reference are:

EBU Tech. 3213 Chromaticities

Color

x

y

Red

0.64

0.33

Green

0.29

0.60

Blue

0.15

0.06

White Reference (D65)

0.3127

0.3290

The transfer function was never properly defined for this colorspace. The Rec. 709 transfer function is recommended in the literature:

L' = 4.5L\text{, for } 0 \le L < 0.018 L' = 1.099L ^{0.45} - 0.099\text{, for } 0.018 \le L \le 1

Inverse Transfer function:

L = \frac{L'}{4.5} \text{, for } L' < 0.081 L = \left(\frac{L' + 0.099}{1.099} \right) ^{\frac{1}{0.45} }\text{, for } L' \ge 0.081

The luminance (Y’) and color difference (Cb and Cr) are obtained with the following V4L2_YCBCR_ENC_601 encoding:

Y' = 0.2990R' + 0.5870G' + 0.1140B' Cb = -0.1687R' - 0.3313G' + 0.5B' Cr = 0.5R' - 0.4187G' - 0.0813B'

Y’ is clamped to the range [0…1] and Cb and Cr are clamped to the range [-0.5…0.5]. The Y’CbCr quantization is limited range. This transform is identical to one defined in SMPTE 170M/BT.601.

## 2.17.10. Colorspace JPEG (V4L2_COLORSPACE_JPEG)¶

This colorspace defines the colorspace used by most (Motion-)JPEG formats. The chromaticities of the primary colors and the white reference are identical to sRGB. The transfer function use is V4L2_XFER_FUNC_SRGB. The Y’CbCr encoding is V4L2_YCBCR_ENC_601 with full range quantization where Y’ is scaled to [0…255] and Cb/Cr are scaled to [-128…128] and then clipped to [-128…127].

Note

The JPEG standard does not actually store colorspace information. So if something other than sRGB is used, then the driver will have to set that information explicitly. Effectively V4L2_COLORSPACE_JPEG can be considered to be an abbreviation for V4L2_COLORSPACE_SRGB, V4L2_XFER_FUNC_SRGB, V4L2_YCBCR_ENC_601 and V4L2_QUANTIZATION_FULL_RANGE.

# 2.18. Detailed Transfer Function Descriptions¶

## 2.18.1. Transfer Function SMPTE 2084 (V4L2_XFER_FUNC_SMPTE2084)¶

The SMPTE ST 2084 standard defines the transfer function used by High Dynamic Range content.

Constants:

m1 = (2610 / 4096) / 4

m2 = (2523 / 4096) * 128

c1 = 3424 / 4096

c2 = (2413 / 4096) * 32

c3 = (2392 / 4096) * 32

Transfer function:

L’ = ((c1 + c2 * Lm1) / (1 + c3 * Lm1))m2

Inverse Transfer function:

L = (max(L’1/m2 - c1, 0) / (c2 - c3 * L’1/m2))1/m1

Take care when converting between this transfer function and non-HDR transfer functions: the linear RGB values [0…1] of HDR content map to a luminance range of 0 to 10000 cd/m2 whereas the linear RGB values of non-HDR (aka Standard Dynamic Range or SDR) map to a luminance range of 0 to 100 cd/m2.

To go from SDR to HDR you will have to divide L by 100 first. To go in the other direction you will have to multiply L by 100. Of course, this clamps all luminance values over 100 cd/m2 to 100 cd/m2.