Application #5

6 Data structures🔗

6.1 Color volume transform structure🔗

6.1.1 Introduction🔗

A color volume transform structure defines the parameters for the color volume transformation informatively described in Annex A.

A color volume transform structure is parameterized by:

a real value $L_{white}$ representing HDR reference white in cd/m²
an optional headroom-adaptive tone map structure defining a function $𝖳𝗈𝗇𝖾𝖬𝖺𝗉 : ℝ^{3} \times ℝ_{\geq 0} \to ℝ^{3}$

6.1.2 Parameter constraints🔗

The value of $L_{white}$ shall be in the interval $(0, 10000]$ .

6.2 Headroom-adaptive tone mapping structure🔗

6.2.1 Introduction🔗

A headroom-adaptive tone map structure defines a function $𝖳𝗈𝗇𝖾𝖬𝖺𝗉 : ℝ^{3} \times ℝ_{\geq 0} \to ℝ^{3}$ which takes as parameters an input color $C \in ℝ^{3}$ in the gain application color space and a targeted HDR headroom $H_{target}$ , and returns a tone mapped color.

NOTE —⁠ The function $𝖳𝗈𝗇𝖾𝖬𝖺𝗉$ performs the headroom-adaptive tone mapping, so when it is applied to the baseline image the resulting image will have an HDR headroom equal to the specified targeted HDR headroom.

This structure is parameterized by:

a real value $H_{baseline}$ representing the baseline HDR headroom
an integer $N_{alt}$ number of alternate images
real values $H_{alt, i}$ for $i \in ℤ_{N_{alt}}$ representing the alternate HDR headroom of each alternate image
color gain function structures that define the function ${𝖦𝖺𝗂𝗇}_{alt, i}$ for each $i \in ℤ_{N alt}$ representing the color gain function associated with each alternate image
real valued vectors $χ_{red}$ , $χ_{green}$ , $χ_{blue}$ , and $χ_{white}$ , indicating the ISO/CIE 11664-1:2019 CIE 1931 $x y$ chromaticity coordinates from of the red, green, and blue color primaries and white point of the gain application color space

6.2.2 Parameter constraints🔗

The value of $H_{baseline}$ shall be in the interval $[0, 6]$ .

The value of $N_{alt}$ shall be greater than or equal to 0 and less than or equal to 4.

For $i \in ℤ_{N_{alt}}$ , the value of $H_{alt, i}$ shall be in the interval $[0, 6]$ .

For $i \in ℤ_{N_{alt}}$ it shall be the case that $H_{alt, i} \neq H_{baseline}$ .

For $i \in ℤ_{N_{alt} - 1}$ it shall be the case that $H_{alt, i} < H_{alt, i + 1}$ .

The length of the vectors $χ_{red}$ , $χ_{green}$ , $χ_{blue}$ , and $χ_{white}$ shall be 2.

The values of the components of the vectors $χ_{red}$ , $χ_{green}$ , $χ_{blue}$ , and $χ_{white}$ shall be in the interval $[0, 1]$ .

6.2.3 Gain curve constraints🔗

This clause lists constraints that are useful for achieving coherent headroom-adaptive tone mapping behavior. Implementations may adjust metadata items so that they satisfy these constraints.

For each $i \in ℤ_{N_{alt}}$ , let ${𝖦𝖺𝗂𝗇𝖢𝗎𝗋𝗏𝖾}_{i}$ be the function defined by the gain curve structure parameter to ${𝖦𝖺𝗂𝗇}_{alt, i}$ . It should be the case that:

${𝖦𝖺𝗂𝗇𝖢𝗎𝗋𝗏𝖾}_{i} (2^{H_{baseline}}) = H_{alt,i} - H_{baseline}$

This has the effect that when a headroom-adaptive tone mapping is performed with the targeted HDR headroom parameter set equal to an alternate HDR headroom, pixels in the baseline image with values equal to the baseline HDR headroom are mapped to values equal to that alternate HDR headroom.
For all $x \in ℝ$ :
- If $H_{alt, i} > H_{baseline}$ , then ${𝖦𝖺𝗂𝗇𝖢𝗎𝗋𝗏𝖾}_{i} (x) \geq 0$ .
- If $H_{alt, i} < H_{baseline}$ , then ${𝖦𝖺𝗂𝗇𝖢𝗎𝗋𝗏𝖾}_{i} (x) \leq 0$ .
- If $i + 1 \in ℤ_{N_{alt}}$ then, ${𝖦𝖺𝗂𝗇𝖢𝗎𝗋𝗏𝖾}_{i} (x) \leq {𝖦𝖺𝗂𝗇𝖢𝗎𝗋𝗏𝖾}_{i + 1} (x)$ .
This has the effect that, for a given pixel value in the baseline image, the headroom-adaptive tone mapped pixel values monotonically increases as the targeted HDR headroom increases.
If $H_{alt, i} < H_{baseline}$ , then the tone curve function $f (x) = x \times 2^{{𝖦𝖺𝗂𝗇𝖢𝗎𝗋𝗏𝖾}_{i} (x)}$ is monotonically decreasing.
If $H_{alt, i} > H_{baseline}$ , then the tone curve function $f (x) = x \times 2^{{𝖦𝖺𝗂𝗇𝖢𝗎𝗋𝗏𝖾}_{i} (x)}$ is monotonically increasing.

6.2.4 Computation of alternate images🔗

When tone mapping to a targeted HDR headroom that is equal to an alternate HDR headroom, the result of tone mapping is the corresponding alternate image. In symbols, for any $i \in ℤ_{N_{alt}}$ , the function $𝖳𝗈𝗇𝖾𝖬𝖺𝗉$ shall satisfy the equality in Formula (1).

𝖳𝗈𝗇𝖾𝖬𝖺𝗉 (C, H_{alt, i}) = C \times 2^{{𝖦𝖺𝗂𝗇}_{alt, i} (C)}

(1)

The equality in Formula (1) is satisfied by the function defined in Formula (5).

6.2.5 Computation of the headroom-adaptive tone map 🔗

This clause describes the evaluation of the function $𝖳𝗈𝗇𝖾𝖬𝖺𝗉$ given an input color $C \in ℝ^{3}$ in the gain application color space and a targeted HDR headroom $H_{target} \in ℝ_{\geq 0}$ .

Create a new list of HDR headrooms by inserting the baseline HDR headroom $H_{baseline}$ into the list of alternate HDR headrooms $H_{alt, 0}, \dots, H_{alt, N_{alt} - 1}$ in its sorted position. Let $N = N_{alt} + 1$ be the length of this new list and let $H_{0}, \dots, H_{N - 1}$ be the list. Let ${𝖦𝖺𝗂𝗇}_{0}, \dots, {𝖦𝖺𝗂𝗇}_{N - 1}$ be the list ${𝖦𝖺𝗂𝗇}_{alt, 0}, \dots, {𝖦𝖺𝗂𝗇}_{alt, N - 1}$ with the zero color gain function inserted at the position where $H_{baseline}$ was inserted.

NOTE —⁠

These lists are constructed in order to simplify the presentation by reducing the number of special cases. In this formulation, the presentation does not need to distinguish between the case of interpolating between the baseline image and an alternate image and the case of interpolating between two alternate images, because they are unified into a single list.

Implementations can avoid explicitly forming these unified lists as an optimization.

A visualization of an example in which $H_{baseline}$ is inserted at the end of the list is shown in Figure B.1. A visualization of an example in which $H_{baseline}$ is inserted at the beginning of the list is shown in Figure B.3. A visualization of an example in which $H_{baseline}$ is the only entry in the list (because $N_{alt} = 0$ ) is shown in Figure B.4.

Let $G \in ℝ^{3}$ be the per-component gain in $\log_{2}$ space. This is computed as a weighted combination of color gain functions evaluated at $C$ . The weighting depends on the value of $H_{target}$ parameter.

If there exists a value $i$ such that $H_{i} = clamp (H_{target}, H_{0}, H_{N - 1})$ then $G$ shall be equivalent to the result of the definition in Formula (2).

$G = {𝖦𝖺𝗂𝗇}_{i} (C)$ (2)
Otherwise, there exists exactly one value $i \in ℤ_{N - 1}$ such that $H_{i} < H_{target} < H_{i + 1}$ .

Let $w_{i}$ and $w_{i + 1}$ be the weights of the $i$ -th and $i + 1$ -th color gain functions. These weights shall be computed as defined in Formula (3).

$\begin{matrix} w_{i} = \frac{H_{target} - H_{i + 1}}{H_{i} - H_{i + 1}} & w_{i + 1} = \frac{H_{target} - H_{i}}{H_{i + 1} - H_{i}} = 1 - w_{i} \end{matrix}$ (3)

The value of $G$ shall be equivalent to the result of the definition in Formula (4).

$G = w_{i} \times {𝖦𝖺𝗂𝗇}_{i} (C) + w_{i + 1} \times {𝖦𝖺𝗂𝗇}_{i + 1} (C)$ (4)

The headroom-adaptive tone mapping function shall be equivalent to the definition in Formula (5).

𝖳𝗈𝗇𝖾𝖬𝖺𝗉 (C, H_{target}) = C \times 2^{G}

(5)

6.2.6 Visualization🔗

Figure 2 provides a visualization of the computation of an alternate image as described in 6.2.4.

Figure 2 — Computation of the $i$ -th alternate image

Figure 3 provides a visualization of the evaluation of the $𝖳𝗈𝗇𝖾𝖬𝖺𝗉$ function as described in 6.2.5.

Figure 3 — Headroom-adaptive tone map computation

6.3 Color gain function structure🔗

6.3.1 Introduction🔗

A color gain function structure defines a color gain function $𝖦𝖺𝗂𝗇 : ℝ^{3} \to ℝ^{3}$ .

A color gain function structure is parameterized by:

a component mixing function structure, which defines the function $𝖢𝗈𝗆𝗉𝗈𝗇𝖾𝗇𝗍𝖬𝗂𝗑𝗂𝗇𝗀$
a gain curve structure, which defines the function $𝖦𝖺𝗂𝗇𝖢𝗎𝗋𝗏𝖾$

NOTE —⁠ The resulting color gain function is equivalent to an adaptive gain curve from ICC Adaptive Gain Curve.

6.3.2 Function evaluation🔗

This clause describes the evaluation of the function $𝖦𝖺𝗂𝗇$ , given an input parameter $C \in ℝ^{3}$ .

Let $M = [m_{r}, m_{g}, m_{b}] \in ℝ^{3}$ be the component mixing function evaluated at $C$ , as defined in Formula (6)

M = [\begin{matrix} m_{r} \\ m_{g} \\ m_{b} \end{matrix}] = 𝖢𝗈𝗆𝗉𝗈𝗇𝖾𝗇𝗍𝖬𝗂𝗑𝗂𝗇𝗀 (C)

(6)

The function $𝖦𝖺𝗂𝗇$ shall be equivalent to the definition in Formula (7).

𝖦𝖺𝗂𝗇 (C) = [\begin{matrix} 𝖦𝖺𝗂𝗇𝖢𝗎𝗋𝗏𝖾 (m_{r}) \\ 𝖦𝖺𝗂𝗇𝖢𝗎𝗋𝗏𝖾 (m_{g}) \\ 𝖦𝖺𝗂𝗇𝖢𝗎𝗋𝗏𝖾 (m_{b}) \end{matrix}]

(7)

NOTE —⁠ If it is the case that all components of $M$ are equal, then the function $𝖦𝖺𝗂𝗇𝖢𝗎𝗋𝗏𝖾$ needs to be evaluated only once.

6.3.3 Zero color gain function🔗

The zero color gain function shall equal the color gain function defined in Formula (8).

𝖦𝖺𝗂𝗇 (C) = [0,0,0]

(8)

NOTE —⁠ The zero color gain function is the color gain function that is applied to the baseline image when performing headroom-adaptive tone mapping with the targeted HDR headroom parameter equal to the baseline HDR headroom.

6.3.4 Visualization🔗

Figure 4 provides a visualization of the evaluation of the $𝖦𝖺𝗂𝗇$ function as described in 6.3.2.

Figure 4 — Visualization of the evaluation of the color gain function. Each arrow represents an individual color component.

6.4 Component mixing function structure🔗

6.4.1 Introduction🔗

A component mixing function structure defines a function $𝖢𝗈𝗆𝗉𝗈𝗇𝖾𝗇𝗍𝖬𝗂𝗑𝗂𝗇𝗀 : ℝ^{3} \to ℝ^{3}$ .

A component mixing function structure is parameterized by:

a real value $k_{red}$ representing the weighting of the red color component
a real value $k_{green}$ representing the weighting of the green color component
a real value $k_{blue}$ representing the weighting of the blue color component
a real value $k_{max}$ representing the weighting of the maximum color component
a real value $k_{min}$ representing the weighting of the minimum color component
a real value $k_{component}$ representing the weighting of each color component

NOTE 1 —⁠ The $𝖢𝗈𝗆𝗉𝗈𝗇𝖾𝗇𝗍𝖬𝗂𝗑𝗂𝗇𝗀$ function is constructed such that for any $x \in ℝ$ , there exists a $y \in ℝ$ such that $𝖢𝗈𝗆𝗉𝗈𝗇𝖾𝗇𝗍𝖬𝗂𝗑𝗂𝗇𝗀 ([x, x, x]) = [y, y, y]$ . This means that, when applied to color values, $𝖢𝗈𝗆𝗉𝗈𝗇𝖾𝗇𝗍𝖬𝗂𝗑𝗂𝗇𝗀$ maps grey values to grey values.

NOTE 2 —⁠ This function and its parameterization are the same as the adaptive gain curve input evaluator from Annex 1 of ICC Adaptive Gain Curve.

6.4.2 Parameter constraints🔗

The values of $k_{red}$ , $k_{green}$ , $k_{blue}$ , $k_{max}$ , $k_{min}$ , and $k_{component}$ shall be in the interval $[0, 1]$ .

It shall be the case that $k_{red} + k_{green} + k_{blue} + k_{max} + k_{min} + k_{component} = 1$ .

6.4.3 Function evaluation🔗

This clause describes the evaluation of the function $𝖢𝗈𝗆𝗉𝗈𝗇𝖾𝗇𝗍𝖬𝗂𝗑𝗂𝗇𝗀$ , given an input parameter $C = [c_{r}, c_{g}, c_{b}] \in ℝ^{3}$ .

Let $f_{common} : ℝ^{3} \to ℝ$ be the part of the component mixing function that is common to all components. It shall be equivalent to the definition in Formula (9).

\begin{matrix} f_{common} (C) = & c_{r} \times k_{red} + \\ c_{g} \times k_{green} + \\ c_{b} \times k_{blue} + \\ max (c_{r}, c_{g}, c_{b}) \times k_{max} + \\ min (c_{r}, c_{g}, c_{b}) \times k_{min} \end{matrix}

(9)

The function $𝖢𝗈𝗆𝗉𝗈𝗇𝖾𝗇𝗍𝖬𝗂𝗑𝗂𝗇𝗀$ shall be equivalent to the definition in Formula (10).

𝖢𝗈𝗆𝗉𝗈𝗇𝖾𝗇𝗍𝖬𝗂𝗑𝗂𝗇𝗀 (C) = [\begin{matrix} c_{r} \times k_{component} + f_{common} (C) \\ c_{g} \times k_{component} + f_{common} (C) \\ c_{b} \times k_{component} + f_{common} (C) \end{matrix}]

(10)

NOTE —⁠ If the parameter $k_{component}$ is equal to zero, then all three components of $𝖢𝗈𝗆𝗉𝗈𝗇𝖾𝗇𝗍𝖬𝗂𝗑𝗂𝗇𝗀 (C)$ will be equal.

6.5 Gain curve structure🔗

6.5.1 Introduction🔗

A gain curve structure defines a function $𝖦𝖺𝗂𝗇𝖢𝗎𝗋𝗏𝖾 : ℝ \to ℝ$ .

A gain curve structure is parameterized by:

an integer $N_{cp}$ number of control points
real values $x_{i}$ , $y_{i}$ , and $m_{i}$ for $i \in ℤ_{N}_{cp}$ representing input, output, and slope of the control points

6.5.2 Parameter constraints🔗

The value of $N_{cp}$ shall be greater than or equal to 1 and less than or equal to 32.

For $i \in ℤ_{N_{cp}}$ , the value of $x_{i}$ shall be in the interval $[0, 64]$ .

For $i \in ℤ_{N_{cp}}$ , the value of $y_{i}$ shall be in the interval $[- 6, 6]$ .

For $i \in ℤ_{N_{cp} - 1}$ it shall be the case that $x_{i} \leq x_{i + 1}$ . If it is the case that $x_{i} = x_{i + 1}$ then it shall also be the case that $y_{i} = y_{i + 1}$ .

6.5.3 Function evaluation🔗

This clause describes the evaluation of the function $𝖦𝖺𝗂𝗇𝖢𝗎𝗋𝗏𝖾$ , given an input parameter $x \in ℝ$ .

For $i \in ℤ_{N_{cp} - 1}$ , let $f_{i} : [x_{i}, x_{i + 1}] \to ℝ$ be the $i$ th component of the gain curve, as defined in Formula (11).

\begin{matrix} f_{i} (x) & = c_{3} \times t^{3} + c_{2} \times t^{2} + c_{1} \times t + c_{0} & where \\ {\hat{m}}_{i} & = (x_{i + 1} - x_{i}) \times m_{i} \\ {\hat{m}}_{i + 1} & = (x_{i + 1} - x_{i}) \times m_{i + 1} \\ c_{3} & = 2 y_{i} + {\hat{m}}_{i} - 2 y_{i + 1} + {\hat{m}}_{i + 1} \\ c_{2} & = - 3 y_{i} + 3 y_{i + 1} - 2 {\hat{m}}_{i} - {\hat{m}}_{i + 1} \\ c_{1} & = {\hat{m}}_{i} \\ c_{0} & = y_{i} \\ t & = (x - x_{i}) / (x_{i + 1} - x_{i}) \end{matrix}

(11)

The function $𝖦𝖺𝗂𝗇𝖢𝗎𝗋𝗏𝖾$ shall be equivalent to the definition in Formula (12).

𝖦𝖺𝗂𝗇𝖢𝗎𝗋𝗏𝖾 (x) = {\begin{matrix} y_{0} & : x < x_{0} \\ y_{i} & : there exists i \in ℤ_{N_{cp}} such that x = x_{i} \\ f_{i} (x) & : there exists i \in ℤ_{N_{cp} - 1} such that x_{i} < x < x_{i + 1} \\ y_{_{N_{cp} - 1}} + \log_{2} (\frac{x_{_{N_{cp} - 1}}}{x}) & : x_{_{N_{cp} - 1}} \leq x \end{matrix}

(12)

7 Application constraints🔗

7.1 Metadata set🔗

A metadata set shall comprise exactly one of each of the following:

ApplicationIdentifier
ApplicationVersion
TimeInterval
ProcessingWindow
ColorVolumeTransform

The TimeInterval group shall include exactly one of each of the following metadata items defined in Clause 8 of SMPTE ST 2094-1:2016:

TimeIntervalStart
TimeIntervalDuration

The ProcessingWindow group shall include exactly one of each of the following metadata items defined in Clause 9 of SMPTE ST 2094-1:2016:

UpperLeftCorner
LowerRightCorner
WindowNumber

The ColorVolumeTransform group shall include the following metadata items:

HdrReferenceWhite, of which there shall be exactly one.
HeadroomAdaptiveToneMap, of which there shall be at most one.

The HeadroomAdaptiveToneMap group shall include exactly one of each of the following metadata items:

BaselineHdrHeadroom
NumAlternateImages
AlternateImage[a] for each $a \in {0, . . .,$ NumAlternateImages $- 1}$
GainApplicationChromaticities[r] for each $r \in {0, . . ., 7}$

Each AlternateImage[a] group shall include exactly one of each of the following metadata items:

AlternateHdrHeadroom[a]
ColorGainFunction[a]

Each ColorGainFunction[a] group shall include exactly one of each of the following metadata items:

ComponentMix[a]
GainCurve[a]

Each ComponentMix[a] group shall include exactly one of each of the following metadata items:

ComponentMixRed[a]
ComponentMixGreen[a]
ComponentMixBlue[a]
ComponentMixMax[a]
ComponentMixMin[a]
ComponentMixComponent[a]

Each GainCurve[a] group shall include exactly one of each of the following metadata items:

GainCurveNumControlPoints[a]
GainCurveControlPoint[a][c] for each $c \in {0, . . .,$ GainCurveNumControlPoints[a] $- 1}$

Each GainCurveControlPoint[a][c] group shall include exactly one of each of the following metadata items:

GainCurveControlPointX[a][c]
GainCurveControlPointY[a][c]
GainCurveControlPointM[a][c]

7.2 Metadata set constraints🔗

This clause specifies the constraints on the metadata set from 7.1, and defines the association between the items of the metadata set and data structures and parameters defined in Clause 6.

The ApplicationIdentifier metadata item shall equal 5.

The ApplicationVersion metadata item shall equal 0.

The ProcessingWindow shall be subject to the following constraints.

The WindowNumber metadata item shall equal 0.
The UpperLeftCorner metadata item shall equal [0, 0].
The LowerRightCorner metadata item shall equal the size of the input image essence in pixels.

The ColorVolumeTransform metadata group specifies a color volume transform structure. The metadata items in this metadata group specify the parameters listed in 6.1.1, and are subject to the constraints listed in 6.1.2.

$L_{white}$ shall be assigned the value HdrReferenceWhite
$𝖳𝗈𝗇𝖾𝖬𝖺𝗉$ shall be assigned as specified by the headroom-adaptive tone map structure parameterized by the HeadroomAdaptiveToneMap metadata group, if present.

The HeadroomAdaptiveToneMap metadata group, if present, specifies a headroom-adaptive tone map structure. The metadata items in this metadata group specify the parameters listed in 6.2.1, and are subject to the constraints listed in 6.2.2.

$H_{baseline}$ shall be assigned the value BaselineHdrHeadroom.
$N_{alt}$ shall be assigned the value NumAlternateImages.
$H_{alt, a}$ shall be assigned the value AlternateHdrHeadroom[a].
${𝖦𝖺𝗂𝗇}_{a}$ shall be assigned as specified by the gain curve structure parameterized by the ColorGainFunction[a] metadata group.
$χ_{red}$ shall be assigned the value $[$ GainApplicationChromaticities[0], GainApplicationChromaticities[1] $]$ .
$χ_{green}$ shall be assigned the value $[$ GainApplicationChromaticities[2], GainApplicationChromaticities[3] $]$ .
$χ_{blue}$ shall be assigned the value $[$ GainApplicationChromaticities[4], GainApplicationChromaticities[5] $]$ .
$χ_{white}$ shall be assigned the value $[$ GainApplicationChromaticities[6], GainApplicationChromaticities[7] $]$ .

The ColorGainFunction[a] metadata group specifies a color gain function structure. The metadata items in this metadata group specify the parameters listed in 6.3.1.

$𝖢𝗈𝗆𝗉𝗈𝗇𝖾𝗇𝗍𝖬𝗂𝗑𝗂𝗇𝗀$ shall be assigned as specified by the component mixing function structure parameterized by the ComponentMix[a] metadata group.
$𝖦𝖺𝗂𝗇𝖢𝗎𝗋𝗏𝖾$ shall be assigned as specified by the gain curve structure parameterized by the GainCurve[a] metadata group.

The ComponentMix[a] metadata group specifies a component mixing function structure. The metadata items in this metadata group specify the parameters listed in 6.4.1, and are subject to the constraints listed in 6.4.2.

$k_{red}$ shall be assigned the value ComponentMixRed[a].
$k_{green}$ shall be assigned the value ComponentMixGreen[a].
$k_{blue}$ shall be assigned the value ComponentMixBlue[a].
$k_{max}$ shall be assigned the value ComponentMixMax[a].
$k_{min}$ shall be assigned the value ComponentMixMin[a].
$k_{component}$ shall be assigned the value ComponentMixComponent[a].

The GainCurve[a] metadata group specifies a gain curve structure. The metadata items in this metadata group specify the parameters listed in 6.5.1, and are subject to the constraints listed in 6.5.2.

$N_{cp}$ shall be assigned the value GainCurveNumControlPoints[a].
$x_{c}$ shall be assigned the value GainCurveControlPointX[a][c].
$y_{c}$ shall be assigned the value GainCurveControlPointY[a][c].
$m_{c}$ shall be assigned the value GainCurveControlPointM[a][c].

7.3 Metadata carriage🔗

The metadata set for Application #5 may be carried by mechanisms that use the Recommendation ITU-T T.35 codes for non-standard facilities.

When using such mechanisms, Application #5 shall be identified by country code 0xB5 (United States), terminal provider code 0x0090 (SMPTE), and terminal provider oriented code 0x0001. The metadata set shall be encoded using the binary encoding described in Annex C.

In systems that support metadata carriage using Recommendation ITU-T T.35 codes in both the codec and the container, carriage in the container shall take precedence over and be preferred over carriage in the codec.

Annex A
Computation of color volume transformation (Informative)🔗

A.1 Introduction🔗

This annex describes the computations to apply the color volume transformation to an input image essence. Figure A.1 illustrates this specification's headroom-adaptive tone mapping algorithm in the framework of the Generalized Color Transform Model described in Annex A and visualized in Figure A.1 of SMPTE ST 2094-1:2016.

Figure A.1 — The generalized color volume transform model

The individual stages of Figure A.1 correspond to Figure A.2, followed by Figure 3, followed by Figure A.3.

A.2 Conversion to gain application color space 🔗

This clause describes the computation of the function $𝖳𝗈𝖦𝖺𝗂𝗇𝖠𝗉𝗉𝗅𝗂𝖼𝖺𝗍𝗂𝗈𝗇𝖲𝗉𝖺𝖼𝖾 : ℝ^{3} \to ℝ^{3}$ , which converts an input signal to a color in the gain application color space.

Throughout this clause, the input signal is assumed to have three components corresponding to its red, green, and blue primaries, scaled such that the nominal peak signal is $1$ and the black signal is $0$ . It is also assumed to have transfer characteristics that determine its non-linear encoding and opto-optical transfer function. This corresponds a normalized $R^{'}, G^{'}, B^{'}$ coded signal according to Recommendation ITU-R BT.2100-3. These assumptions are to simplify the presentation, and are not a limitation on the types of input signal that can be used with this color volume transform. Similar computations can be used for non-normalized input signals (e.g., quantized and limited range signals) and for different coded input signals (e.g., $Y^{'}, C_{B}^{'}, C_{R}^{'}$ or $I, C_{T}, C_{P}$ ).

The computation is visualized in Figure A.2, and represents the "Convert to Gain Application Color Space" block of Figure A.1.

Figure A.2 — Conversion of an input signal to gain application color space processing block. The intermediate results of the RGB components of luminance and color value in the relative linear color space with the signal's color primaries are shown at the bottom of the figure.

Let $E \in ℝ^{3}$ be this input signal value.

NOTE 1 —⁠ Components of $E$ can be outside of the $[0,1]$ interval. This can occur due to multiple reasons, including coding and chroma format conversion. For example, a signal coded using a narrow range representation can intentionally contain values greater than the nominal peak signal or values less than the black signal as mentioned in Note 9a of Recommendation ITU-R BT.2100-3. Further information can be found in Section 2.4 of Report ITU-R BT.2408-8.

NOTE 2 —⁠ Scalar functions applied to vector arguments are applied component-wise.

Let $L_{white}$ be the value of the HDR reference white parameter specified by the HdrReferenceWhite metadata item.

Let $𝖤𝗈𝗍𝖿 : ℝ^{3} \to ℝ^{3}$ be the electro-optical transfer function which converts an input signal value to RGB components of luminance in cd/m².

NOTE 3 —⁠ When referring to the luminance of a single color component, it means the luminance of an equivalent achromatic color with all three color components having that same value.

The function $𝖤𝗈𝗍𝖿$ for some common video signal transfer characteristics is as follows:

If the baseline image indicates Recommendation ITU-R BT.709-6 or Recommendation ITU-R BT.2020-2 transfer characteristics, then let $𝖤𝗈𝗍𝖿$ be defined as in Formula (A.1), which is equivalent to the reference electro-optical transfer function defined in Annex 1 of Recommendation ITU-R BT.1886, with parameters $L_{W} = L_{white}$ and $L_{B} = 0$ .

$𝖤𝗈𝗍𝖿 (E) = L_{white} \times {(E)}^{2.4}$ (A.1)

NOTE 4 —⁠ For this and other standard dynamic range transfer characteristics, the function $𝖤𝗈𝗍𝖿$ evaluated at the nominal peak signal value $E = 1$ will equal $L_{white}$ . The resulting color value in gain application color space, after applying Formula (A.3), will be $1$ .

NOTE 5 —⁠ An input image essence that originates from video that did not indicate its transfer characteristics is often assumed to have Recommendation ITU-R BT.709-6 transfer characteristics.

NOTE 6 —⁠ This formulation is equivalent to the display referred mappings described in Section 5.1.2, Section 5.1.3.1, Figure 5, and Figure 7 of Report ITU-R BT.2408-8, and in MovieLabs Best Practice: SDR to HDR Conversion. When in a context dominated by Recommendation ITU-R BT.2100-3 Hybrid Log-Gamma (HLG) content, some systems can choose to include an extra OOTF gamma adjustment step (using $γ = 1.15 - 1.16$ ) in Formula (A.1), as described in Section 5.1.3.2 and Figure 8 of Report ITU-R BT.2408-8. Implementations can use the formulation indicated by the content or the application context for this and other standard dynamic range transfer characteristics.
If the baseline image indicates IEC 61966-2-1 sRGB transfer characteristics, then let $𝖤𝗈𝗍𝖿$ be defined as in Formula (A.2), which is $L_{white}$ multiplied by the function listed in Equations 5 and 6 of Chapter 5 of IEC 61966-2-1.

$𝖤𝗈𝗍𝖿 (E) = {\begin{matrix} L_{white} \times (\frac{E}{12.92}) & : E \leq 0.04045 \\ L_{white} \times {(\frac{E + 0.055}{1.055})}^{2.4} & : E > 0.04045 \end{matrix}$ (A.2)
If the baseline image indicates Recommendation ITU-R BT.2100-3 Perceptual Quantization (PQ) transfer characteristics, then let $𝖤𝗈𝗍𝖿$ be the PQ Reference EOTF as described in Table 4 of Recommendation ITU-R BT.2100-3.
If the baseline image indicates Recommendation ITU-R BT.2100-3 Hybrid Log-Gamma (HLG) transfer characteristics, then let $𝖤𝗈𝗍𝖿$ be the HLG Reference EOTF as described in Table 5 of Recommendation ITU-R BT.2100-3, with parameters $L_{W} = 1000$ , $L_{B} = 0$ , and $γ = 1.2$ .

NOTE 7 —⁠ The HLG Reference OOTF in this formulation must be applied using the color primaries indicated in Table 2 of Recommendation ITU-R BT.2100-3.

Let $M_{input,gain}$ be the 3x3 matrix that converts color primaries from the baseline image color primaries to the color primaries of the gain application color space. The matrix is computed using chromatic adaptation (if needed) as defined in Annex E of Specification ICC.1:2022.

The function $𝖳𝗈𝖦𝖺𝗂𝗇𝖠𝗉𝗉𝗅𝗂𝖼𝖺𝗍𝗂𝗈𝗇𝖲𝗉𝖺𝖼𝖾$ can be computed as defined in Formula (A.3).

𝖳𝗈𝖦𝖺𝗂𝗇𝖠𝗉𝗉𝗅𝗂𝖼𝖺𝗍𝗂𝗈𝗇𝖲𝗉𝖺𝖼𝖾 (E) = M_{input,gain} \times \frac{1}{L_{white}} \times 𝖤𝗈𝗍𝖿 (E)

(A.3)

A.3 Headroom-adaptive tone mapping in gain application color space 🔗

This clause describes the computation of the headroom-adaptive tone mapping algorithm.

Let $H_{target} \in ℝ_{\geq 0}$ be the targeted HDR headroom that characterizes the capabilities of the target display. This can be computed as $\log_{2}$ of the ratio of the peak luminance of the display to the luminance at which HDR reference white will be displayed, or it can be computed by other means outside of the scope of this specification.

Since the Application #5 metadata is modular by design, the HeadroomAdaptiveToneMap metadata group could have been omitted by the content creator. In this case, the headroom-adaptive tone mapping can be decided by the output system.

Otherwise, let $𝖳𝗈𝗇𝖾𝖬𝖺𝗉 : ℝ^{3} \times ℝ_{\geq 0} \to ℝ^{3}$ be defined by the headroom-adaptive tone map structure parameter specified by the HeadroomAdaptiveToneMap metadata group.

Let $C \in ℝ^{3}$ be a color from the baseline image, in the gain application color space. Let $T \in ℝ^{3}$ be the color resulting from applying the headroom-adaptive tone mapping algorithm to that color. The value of $T$ can be computed as defined in Formula (A.4).

T = 𝖳𝗈𝗇𝖾𝖬𝖺𝗉 (C, H_{target})

(A.4)

A.4 Conversion from gain application color space to the target display🔗

The transformation from gain application color space to the targeted system color volume can account for viewer preferences, non-reference ambient viewing environments, and other factors. The details of this transformation are outside of the scope of this document.

This clause describes a simplified illustrative example transformation from gain application color space to the targeted system color volume using linear scaling. The computation is visualized in Figure A.3, and represents the "Convert to Target Color Volume" block of Figure A.1.

Figure A.3 — Conversion to target display color volume processing block

Let the function $𝖳𝗈𝖳𝖺𝗋𝗀𝖾𝗍𝖢𝗈𝗅𝗈𝗋𝖵𝗈𝗅𝗎𝗆𝖾 : ℝ^{3} \to ℝ^{3}$ be the function that computes the components of the luminance in the targeted system color volume. Let $T \in ℝ^{3}$ be the input tone mapped color in the gain application color space. Let $L_{white,target}$ be the targeted system white display luminance, which is the luminance at which HDR reference white will be displayed given the current user settings and ambient viewing environment. Let $M_{gain,target}$ be the 3x3 matrix that converts color primaries from the gain application color space primaries to the targeted system color primaries.

The function $𝖳𝗈𝖳𝖺𝗋𝗀𝖾𝗍𝖢𝗈𝗅𝗈𝗋𝖵𝗈𝗅𝗎𝗆𝖾$ can be computed as defined in Formula (A.5).

𝖳𝗈𝖳𝖺𝗋𝗀𝖾𝗍𝖢𝗈𝗅𝗈𝗋𝖵𝗈𝗅𝗎𝗆𝖾 (T) = L_{white,target} \times M_{gain,target} \times T

(A.5)

NOTE —⁠ Any colors that do not fit in the targeted display color volume (any colors with components greater than $2^{H_{target}}$ in the relative linear color space with color primaries of the targeted display color volume), can be projected (often by clamping component-wise) to the targeted display color volume.

Annex B
Examples (Informative)🔗

B.1 Simple tone mapping🔗

Figure B.1 illustrates the color gain functions and associated tone mapping functions of a headroom-adaptive tone mapping with a baseline high dynamic range headroom $H_{baseline} = \log_{2} (4) = 2$ , and a standard dynamic range alternate image with $H_{alt, 0} = \log_{2} (1) = 0$ .

On the left side of Figure B.1 are the underlying color gain functions in the $\log_{2}$ domain. The zero color gain function inserted corresponding to the baseline image is indicated with a solid line. The alternate image's color gain function is indicated with a dashed line. The control points for the gain curve parameter of the color gain function are indicated using filled circles.

On the right side of Figure B.1 are the tone mapping curves that are computed from the color gain functions. The zero color gain function results in an identity tone mapping function. The alternate image's color gain function results in a tone mapping curve that maps $2^{H_{baseline}} = 4$ to $2^{H_{altr, 0}} = 1$ , which corresponds to the standard dynamic range version. The mapping of the color gain function's gain curve's control points are indicated using empty circles.

Adaptation to a different targeted HDR headroom of $H_{target} = \log_{2} (2) = 1$ is indicated using a dotted line. Its adapted color gain function is computed as a weighted averaging of the color gain functions on the left. The weighting parameters are $w_{0} = w_{1} = \frac{1}{2}$ . The resulting adapted tone mapping curve on the right maps $2^{H_{baseline}} = 4$ to $2^{H_{target}} = 2$ .

Figure B.1 — Simple headroom-adaptive tone mapping from high dynamic range to standard dynamic range

B.2 Tone mapping with two alternate images🔗

Figure B.2 illustrates a slightly more complicated example of headroom-adaptive tone mapping with an additional alternate image with $H_{alt, 1} = \log_{2} (2) = 1$ . This new alternate image indicates that, when tone mapping to a targeted HDR headroom of $1$ , the color values below 1 in the relative linear color space (signal values below HDR reference white) are preserved and that highlights (signal values above HDR reference white) are to be compressed more aggressively.

An example adaptation to a targeted HDR headroom of $H_{target} = \log_{2} (1.5) \approx 0.58$ is included. The adapted color gain function in this instance is a weighted averaging of the two alternate images' color gain functions. The weights in this example are $w_{0} \approx 0.42$ and $w_{1} \approx 0.58$ . The resulting adapted tone mapping curve on the right maps $2^{H_{baseline}} = 4$ to $2^{H_{target}} = 1.5$ .

Figure B.2 — Headroom-adaptive tone mapping from high dynamic range to standard dynamic range with two alternate images

B.3 Inverse tone mapping🔗

Figure B.3 illustrates an example of inverse tone mapping with a standard dynamic range baseline image with $H_{baseline} = \log_{2} (1) = 0$ , and a high dynamic range alternate image with $H_{alt, 0} = \log_{2} (4) = 2$ .

This example is the inverse of the transformation performed in the example in Clause B.1. That is to say that a baseline image set to the alternate image from the example in Clause B.1 (the tone mapping to standard dynamic range), with this metadata, would appear identical to the example in Clause B.1, up to any quantization errors.

Note in the legend that in this example, $H_{1} = H_{alt, 0}$ because $H_{baseline}$ is inserted at the beginning of the merged list of HDR headrooms in 6.2.5.

Adaptation to the targeted HDR headroom of $H_{target} = \log_{2} (2) = 1$ is indicated using a dotted line, as was also done in the example in Clause B.1.

Figure B.3 — Headroom-adaptive tone mapping from standard dynamic range to high dynamic range

B.4 No tone mapping (projection or clamping)🔗

The way to indicate that no tone mapping is to be performed, and that the baseline image is to be projected (clamped) to the target color volume, regardless of the targeted HDR headroom, is to specify that the number of alternate images is 0. This clause illustrates this behavior by working through the details of the computation.

In the context of the headroom-adaptive tone map computation described in in 6.2.5, this means that $N_{alt} = 0$ and therefore $N = 1$ . The only entry in the constructed list of HDR headrooms is $H_{0} = H_{baseline}$ , and the only entry in the constructed list of color gain functions is $G_{0}$ , which equals the zero color gain function. The value of $G$ is set by Formula (2) and is $G = [0,0,0]$ . Finally, the function $𝖳𝗈𝗇𝖾𝖬𝖺𝗉$ as defined in Formula (5) evaluates to be the identity, as worked out in Formula (B.1).

𝖳𝗈𝗇𝖾𝖬𝖺𝗉 (C, H_{target}) = C \times 2^{G} = C \times 2^{0} = C

(B.1)

This means that the image resulting from the headroom-adaptive tone mapping in the color volume transform step in Clause A.3 is the unchanged baseline image. After this, the image is converted to the target display as described in Clause A.4, and the resulting image is projected to the targeted color volume, as described in Clause A.4, Note. The result of this operation is to clamp the baseline image to the targeted HDR headroom.

Figure B.4 illustrates this case, where the color gain function is always equal to the zero color gain function and the headroom-adaptive tone mapping is the identity.

Figure B.4 — Headroom-adaptive tone mapping from high dynamic range to standard dynamic range with zero alternate images

Figure B.5 illustrates the result of this operation described in Clause A.4, Note, which is to project (or clamp) the baseline image to the targeted HDR headroom.

Figure B.5 — Projection of the baseline image to target color volumes with various targeted HDR headrooms

Annex C
Binary encoding (Normative)🔗

C.1 Introduction🔗

The metadata for Application #5 may be stored in binary form according to the syntax structure in Clause C.2. The assignment of values to the items of the metadata set based on the syntax elements is in Clause C.3.

The syntax structures are presented in a tabular form. The type of each syntax element in the bitstream is indicated in the Type column. A syntax element with type u(N) is stored as an N-bit unsigned integer. The bits of each syntax element shall be read in order from most significant to least significant.

NOTE —⁠ All syntax elements that are one full byte or larger are byte aligned. For syntax elements that are 16-bit unsigned integers, this representation is equivalent to storing those syntax elements in big-endian form.

Syntax elements with the name reserved_zero shall be equal to zero.

C.2 Syntax🔗

C.2.1 Application syntax🔗

Table C.1 presents the syntax structures related to Application #5.

The smpte_st_2094_50_application_info metadata bitstream may have padding after the end of the structure. Parsers shall stop reading after the last recognized syntax element of smpte_st_2094_50_application_info and ignore all remaining data.

The minimum_application_version syntax element indicates the minimum application version that a parser needs to support in order to parse the smpte_st_2094_50_application_info metadata bitstream and perform headroom-adaptive tone mapping. Future updates to this specification may add new metadata to the smpte_st_2094_50_application_info metadata bitstream. If these changes are done in a backwards-compatible manner, then the minimum_application_version will be kept unchanged.

A parser encountering an unrecognized minimum_application_version shall ignore the entire smpte_st_2094_50_application_info metadata bitstream. The minimum_application_version syntax element shall be 0 in this version of the specification.

Table C.1 — Application #5 syntax structure
smpte_st_2094_50_application_info() {	Type
application_version	u(3)
minimum_application_version	u(3)
reserved_zero	u(2)
smpte_st_2094_50_color_volume_transform()
}

C.2.2 Color volume transform syntax🔗

Table C.2 presents the syntax for specifying the ColorVolumeTransform metadata group.

Table C.2 — Color volume transform syntax structure
smpte_st_2094_50_color_volume_transform() {	Type
has_custom_hdr_reference_white_flag	u(1)
has_adaptive_tone_map_flag	u(1)
reserved_zero	u(6)
if (has_custom_hdr_reference_white_flag == 1) {
hdr_reference_white	u(16)
}
if (has_adaptive_tone_map_flag == 1) {
smpte_st_2094_50_adaptive_tone_map()
}
}

C.2.3 Adaptive tone mapping syntax🔗

Table C.3 presents the syntax for specifying the HeadroomAdaptiveToneMap metadata group.

Table C.3 — Headroom-adaptive tone map structure syntax
smpte_st_2094_50_adaptive_tone_map() {	Type
baseline_hdr_headroom	u(16)
use_reference_white_tone_mapping_flag	u(1)
if (use_reference_white_tone_mapping_flag == 0) {
num_alternate_images	u(3)
gain_application_space_chromaticities_mode	u(2)
has_common_component_mix_params_flag	u(1)
has_common_curve_params_flag	u(1)
if (gain_application_space_chromaticities_mode == 3) {
for (r = 0; r < 8; r++) {
gain_application_space_chromaticities[r]	u(16)
}
}
for (a = 0; a < min(num_alternate_images, 4); a++) {
alternate_hdr_headrooms[a]	u(16)
smpte_st_2094_50_component_mixing(a)
smpte_st_2094_50_gain_curve(a)
}
} else {
reserved_zero	u(7)
}
}

C.2.4 Component mixing syntax🔗

Table C.4 presents the syntax for specifying a ComponentMix metadata group.

Table C.4 — Component mixing function structure syntax
smpte_st_2094_50_component_mixing(a) {	Type
if (a == 0 \|\| has_common_component_mix_params_flag == 0) {
component_mixing_type[a]	u(2)
if (component_mixing_type[a] != 3) {
reserved_zero	u(6)
} else {
for (k = 0; k < 6; k++) {
has_component_mixing_coefficient_flag[a][k]	u(1)
}
for (k = 0; k < 6; k++) {
if (has_component_mixing_coefficient_flag[a][k] == 1) {
component_mixing_coefficient[a][k]	u(16)
} else {
component_mixing_coefficient[a][k] = 0
}
}
}
} else {
component_mixing_type[a] = component_mixing_type[0]
if (component_mixing_type[a] == 3) {
for (k = 0; k < 6; k++) {
component_mixing_coefficient[a][k] = component_mixing_coefficient[0][k]
}
}
}
}

C.2.5 Gain curve syntax🔗

Table C.5 presents the syntax for specifying a GainCurve metadata group.

Table C.5 — Gain curve structure syntax
smpte_st_2094_50_gain_curve(a) {	Type
if (a == 0 \|\| has_common_curve_params_flag == 0) {
gain_curve_num_control_points_minus_1[a]	u(5)
gain_curve_use_pchip_slope_flag[a]	u(1)
reserved_zero	u(2)
for (c = 0; c < gain_curve_num_control_points_minus_1[a] + 1; c++) {
gain_curve_control_points_x[a][c]	u(16)
}
} else {
gain_curve_use_pchip_slope_flag[a] = gain_curve_use_pchip_slope_flag[0]
gain_curve_num_control_points_minus_1[a] = gain_curve_num_control_points_minus_1[0]
for (c = 0; c < gain_curve_num_control_points_minus_1[a] + 1; c++) {
gain_curve_control_points_x[a][c] = gain_curve_control_points_x[0][c]
}
}
for (c = 0; c < gain_curve_num_control_points_minus_1[a] + 1; c++) {
gain_curve_control_points_y[a][c]	u(16)
}
if (gain_curve_use_pchip_slope_flag[a] == 0) {
for (c = 0; c < gain_curve_num_control_points_minus_1[a] + 1; c++) {
gain_curve_control_points_theta[a][c]	u(16)
}
}
}

C.3 Semantics🔗

C.3.1 Introduction🔗

This clause describes how to assign values to the metadata items described in 7.1, given the syntax elements from Clause C.2.

C.3.2 Application semantics🔗

The ApplicationIdentifier metadata item shall be assigned the value 5.

The ApplicationVersion metadata item shall be assigned the value application_version.

The ProcessingWindow metadata group shall be assigned values as follows:

The WindowNumber metadadata item shall be assigned the value 0.
The UpperLeftCorner metadadata item shall be assigned the value $[0,0]$ .
The LowerRightCorner metadadata item shall be assigned the value of the size of the input image essence in pixels.

The ColorVolumeTransform metadata group shall be assigned values as specified in C.3.3.

C.3.3 Color volume transform semantics🔗

If has_custom_hdr_reference_white_flag==0, then:

The HdrReferenceWhite metadata item shall be assigned the value 203.

If has_custom_hdr_reference_white_flag==1, then:

The HdrReferenceWhite metadata item shall be assigned the value $clamp ($ hdr_reference_white $, 1, 50000) \times \frac{1}{5}$ .

If has_adaptive_tone_map_flag==0, then:

The HeadroomAdaptiveToneMap metadata group shall be absent.

If has_adaptive_tone_map_flag==1, then:

The HeadroomAdaptiveToneMap metadata group shall be present and shall have values assigned as specified in C.3.4.

C.3.4 Adaptive tone mapping semantics🔗

The BaselineHdrHeadroom metadata item shall be assigned the value $\min ($ baseline_hdr_headroom $, 60000) \times \frac{1}{10000}$ .

If use_reference_white_tone_mapping_flag==0, then:

The GainApplicationChromaticities metadata item shall be assigned values as specified in C.3.5.
The NumAlternateImages metadata item shall be assigned the value $\min ($ num_alternate_images $, 4)$ .
For each value $a \in {0, . . .,$ NumAlternateImages $- 1}$ :
- The AlternateHdrHeadroom[a] metadata item shall be assigned the value $\min ($ alternate_hdr_headrooms[a] $, 60000) \times \frac{1}{10000}$ .
- The ColorGainFunction[a] metadata group shall be assigned values as follows:
  - The ComponentMix[a] metadata group shall be assigned values as specified in C.3.6.
  - The GainCurve[a] metadata group shall be assigned values as specified in C.3.7.

If use_reference_white_tone_mapping_flag==1, then:

The remaining items in the HeadroomAdaptiveToneMap metadata group shall be assigned values as described in C.3.8.

C.3.5 Gain application color space chromaticity semantics🔗

The GainApplicationChromaticities, metadata item shall be assigned a value as follows:

If gain_application_space_chromaticities_mode==0, then:

The GainApplicationChromaticities metadata item shall be assigned the value $[0.64, 0.33, 0.3, 0.6, 0.15, 0.06, 0.3127, 0.329]$
This corresponds to the color primaries and white point specified in Section 1 of Recommendation ITU-R BT.709-6.

If gain_application_space_chromaticities_mode==1, then:

The GainApplicationChromaticities metadata item shall be assigned the value $[0.68, 0.32, 0.265, 0.69, 0.15, 0.06, 0.3127, 0.329]$
This corresponds to the color primaries specified in Table 1 of SMPTE ST 2113:2018 and the white point specified in Clause 6.2 of SMPTE ST 2113:2018.

If gain_application_space_chromaticities_mode==2, then

The GainApplicationChromaticities metadata item shall be assigned the value $[0.708, 0.292, 0.17, 0.797, 0.131, 0.046, 0.3127, 0.329]$
This corresponds to the color primaries and white point specified in Table 3 of Recommendation ITU-R BT.2020-2.

If gain_application_space_chromaticities_mode==3, then:

For each $r \in ℤ_{8}$ , the GainApplicationChromaticities[r] metadata item shall be assigned the value $χ_{r} = \min ($ gain_application_space_chromaticities[r] $, 50000) \times \frac{1}{50000}$ .

C.3.6 Component mixing semantics🔗

The ComponentMix[a] metadata group shall be assigned values as follows:

If component_mixing_type[a]==0 then:

The ComponentMixMax[a] metadata item shall be assigned the value 1.
The ComponentMixRed[a], ComponentMixGreen[a], ComponentMixBlue[a], ComponentMixMin[a], and ComponentMixComponent[a] metadata items shall be assigned the value 0.

If component_mixing_type[a]==1 then:

The ComponentMixComponent[a] metadata item shall be assigned the value 1.
The ComponentMixRed[a], ComponentMixGreen[a], ComponentMixBlue[a], ComponentMixMax[a], and ComponentMixMin[a] metadata items shall be assigned the value 0.

If component_mixing_type[a]==2 then:

The ComponentMixRed[a], ComponentMixGreen[a], and ComponentMixBlue[a] metadata items shall be assigned the value $\frac{1}{6}$ .
The ComponentMixMax[a] metadata item shall be assigned the value $\frac{1}{2}$ .
The ComponentMixMin[a] and ComponentMixComponent[a] metadata items shall be assigned the value 0.

If component_mixing_type[a]==3 then:

For $k \in {0, . . ., 5}$ , let $p_{k} = \min ($ component_mixing_coefficient[a][k] $, 50000) \times \frac{1}{50000}$ .
Let $p_{sum} = \sum_{k = 0}^{5} p_{k}$ be a normalization factor to ensure the coefficients sum to 1. It shall be the case that $p_{sum} \neq 0$ .
The ComponentMixRed[a], ComponentMixGreen[a], ComponentMixBlue[a], ComponentMixMax[a], ComponentMixMin[a], and ComponentMixComponent[a] metadata items shall be assigned the values $\frac{p_{0}}{p_{sum}}$ , $\frac{p_{1}}{p_{sum}}$ , $\frac{p_{2}}{p_{sum}}$ , $\frac{p_{3}}{p_{sum}}$ , $\frac{p_{4}}{p_{sum}}$ , and $\frac{p_{5}}{p_{sum}}$ respectively.

C.3.7 Gain curve semantics🔗

The GainCurve[a] metadata group shall be assigned values as follows:

The GainCurveNumControlPoints[a] metadata item shall be assigned the value gain_curve_num_control_points_minus_1[a] $+ 1$ .

Let $s$ be the sign of the gain curve control point values. If baseline_hdr_headroom is less than alternate_hdr_headrooms[a] then let $s = 1$ . Otherwise, let $s = - 1$ .

For each value $c \in {0, . . .,$ GainCurveNumControlPoints[a] $- 1)$ :

The GainCurveControlPointX[a][c] metadata item shall be assigned the value $\min ($ gain_curve_control_points_x[a][c] $, 64000) \times \frac{1}{1000}$ .
The GainCurveControlPointY[a][c] metadata item shall be assigned the value $s \times \min ($ gain_curve_control_points_y[a][c] $, 60000) \times \frac{1}{10000}$ .

If gain_curve_use_pchip_slope_flag[a]==0, then:

For each value $c \in {0, . . .,$ GainCurveNumControlPoints[a] $- 1)$ :
- Let $θ_{a, c} =$ gain_curve_control_points_theta[a][c].
- The GainCurveControlPointM[a][c] metadata item shall be assigned the value $\tan ((clamp (θ_{a, c}, 1, 35999) - 18000) \times \frac{π}{36000})$ .

If gain_curve_use_pchip_slope_flag[a]==1, then:

For each value $c \in {0, . . .,$ GainCurveNumControlPoints[a] $- 1)$ , the metadata item GainCurveControlPointM[a][c] shall be assigned a value following the computation specified in C.3.9.

C.3.8 Reference white adaptive tone mapping computation🔗

This clause specifies the metadata item values to assign in the HeadroomAdaptiveToneMap metadata group when the use_reference_white_tone_mapping_flag syntax element indicates that the parameters for headroom-adaptive tone mapping should be computed (as opposed to being specified).

Let $H_{baseline} =$ BaselineHdrHeadroom.

The GainApplicationChromaticities, metadata item shall be assigned the value $[0.708, 0.292, 0.17, 0.797, 0.131, 0.046, 0.3127, 0.329]$ . This corresponds to the color primaries and white point specified in Table 3 of Recommendation ITU-R BT.2020-2.

If $H_{baseline} = 0$ then:

The NumAlternateImages metadata item shall be assigned the value 0.

If $H_{baseline} > 0$ then:

The NumAlternateImages metadata item shall be assigned the value 2.
The AlternateHdrHeadroom[0] metadata item shall be assigned the value $H_{alt, 0} = 0$ .
The AlternateHdrHeadroom[1] metadata item shall be assigned the value $H_{alt, 1}$ as defined in Formula (C.1).

$H_{alt, 1} = \log_{2} (\frac{8}{3}) \times \min (\frac{H_{baseline}}{\log_{2} (1000 / 203)}, 1)$ (C.1)

For $a \in {0, . . .,$ NumAlternateImages $- 1}$ , the ColorGainFunction[a] metadata group shall be assigned values as follows:

The ComponentMix[a] metadata group shall be assigned values as follows:
- The ComponentMixMax[a] metadata item shall be assigned the value 1.
- The ComponentMixRed[a], ComponentMixGreen[a], ComponentMixBlue[a], ComponentMixMin[a], and ComponentMixComponent[a] metadata items shall be assigned the value 0.
The GainCurve[a] metadata group shall be assigned values as follows:
- Let $N_{cp} = 8$ .
  
  The GainCurveNumControlPoints[a] metadata item shall be assigned the value $N_{cp}$ .
- Let $y_{white, 0}$ be as defined in Formula (C.2).
  
  $y_{white, 0} = 1 - \frac{1}{2} \times \min (\frac{H_{baseline}}{\log_{2} (1000 / 203)}, 1)$ (C.2)
  
  Let $y_{white, 1} = 1$ .
  
  The control point values are be defined by the functions $G_{x}, G_{y}, G_{m} : [0,1] \times ℝ^{4} \times [0,1] \to ℝ$ , defined in Formula (C.6). These functions create a gain curve based on a knee in relative linear color space, which is be at the point $[1, y_{white, a}]$ .
  
  For each value $c \in ℤ_{N_{cp}}$ :
  - The GainCurveControlPointX[a][c] metadata item shall be assigned the value $G_{x} (\frac{c}{N_{cp} - 1}, 1, y_{white, a}, 2^{H_{baseline}}, 2^{H_{alt, a}}, 0.65)$ .
  - The GainCurveControlPointY[a][c] metadata item shall be assigned the value $G_{y} (\frac{c}{N_{cp} - 1}, 1, y_{white, a}, 2^{H_{baseline}}, 2^{H_{alt, a}}, 0.65)$ .
  - The GainCurveControlPointM[a][c] metadata item shall be assigned the value $G_{m} (\frac{c}{N_{cp} - 1}, 1, y_{white, a}, 2^{H_{baseline}}, 2^{H_{alt, a}}, 0.65)$ .

The functions $G_{x}, G_{y}, G_{m}$ define a parametric gain curve and its slope, given a knee point $[x_{knee}, y_{knee}] \in ℝ^{2}$ , a maximum point $[x_{max}, y_{max}] \in ℝ^{2}$ , and a highlight compression factor $κ \in [0,1]$ .

The gain curve is $\log_{2}$ of the gain of a tone curve defined by a 2D Bézier in relative linear color space, visualized on the left in Figure C.1. The control points of the Bézier curve are $[x_{knee}, y_{knee}]$ , $[x_{mid}, y_{mid}]$ , and $[x_{max}, y_{max}]$ . The middle Bézier control point $[x_{mid}, y_{mid}]$ is computed using the highlight compression factor $κ$ in Formula (C.3).

\begin{matrix} x_{mid} & = (1 - κ) \times x_{knee} + κ \times (\frac{x_{knee} \times y_{max}}{y_{knee}}) \\ y_{mid} & = (1 - κ) \times y_{knee} + κ \times y_{max} \end{matrix}

(C.3)

The parametric Bézier curve and its slope are given by the scalar functions $x, y, m : [0,1] \to ℝ$ defined in Formula (C.4).

\begin{matrix} x (t) & = a_{x} \times t^{2} + b_{x} \times t + c_{x} \\ y (t) & = a_{y} \times t^{2} + b_{y} \times t + c_{y} \\ m (t) & = \frac{2 \times a_{y} \times t + b_{y}}{2 \times a_{x} \times t + b_{x}} \end{matrix}

(C.4)

The quadratic parameters $a_{x}, b_{x}, c_{x} \in ℝ$ and $a_{y}, b_{y}, c_{y} \in ℝ$ in Formula (C.4) are defined in Formula (C.5).

\begin{matrix} a_{x} & = x_{knee} - 2 \times x_{mid} + x_{max} & b_{x} & = 2 \times x_{mid} - 2 \times x_{knee} & c_{x} & = x_{knee} \\ a_{y} & = y_{knee} - 2 \times y_{mid} + y_{max} & b_{y} & = 2 \times y_{mid} - 2 \times y_{knee} & c_{y} & = y_{knee} \end{matrix}

(C.5)

Finally, the functions $G_{x}, G_{y}, G_{m}$ are defined in Formula (C.6) by computing $\log_{2}$ of the gain of the tone curve defined by the functions $x, y, m$ .

\begin{matrix} G_{x} (t, x_{knee}, y_{knee}, x_{max}, y_{max}, κ) & = x (t) \\ G_{y} (t, x_{knee}, y_{knee}, x_{max}, y_{max}, κ) & = \log_{2} (\frac{y (t)}{x (t)}) \\ G_{m} (t, x_{knee}, y_{knee}, x_{max}, y_{max}, κ) & = \frac{x (t) \times m (t) - y (t)}{\log (2) \times x (t) \times y (t)} \end{matrix}

(C.6)

Figure C.1 illustrates the interpretation of the formulae in this clause. The Bézier control points in Formula (C.3) and the resulting Bézier curve from Formula (C.4) are displayed on the left. The resulting gain curve from Formula (C.6) is displayed on the right. The extrapolation behavior beyond the control points, specified by Formula (12), is indicated in both plots.

Figure C.1 — Illustration of Formula (C.6) and its components Formula (C.3) and Formula (C.4) with example parameters $x_{knee} = 1$ , $y_{knee} = 0.8$ , $x_{max} = 4$ , $y_{max} = 2$ , and $κ = 0.65$ .

C.3.9 Piecewise cubic Hermite interpolation package slope computation🔗

This clause specifies, for a given value of $a$ , the metadata item values to assign in the GainCurve[a] metadata group when the gain_curve_use_pchip_slope_flag syntax element indicates that the slopes of the $a$ th gain curve's control points should be computed (as opposed to being specified).

NOTE —⁠ The results of this computation are equivalent to the Piecewise Cubic Hermite Interpolation Package (PCHIP) algorithm described in DOI:10.1137/0905021.

Let $N_{cp} =$ GainCurveNumControlPoints[a]. For each $i \in ℤ_{N_{cp}}$ , let $x_{i} =$ GainCurveControlPointX[a][c] and let $y_{i} =$ GainCurveControlPointY[a][c].

For $i \in ℤ_{N_{cp} - 1}$ , let $h_{i} = x_{i + 1} - x_{i}$ be the length of the $i$ -th interval and let $s_{i} = \frac{y_{i + 1} - y_{i}}{x_{i + 1} - x_{i}}$ be the slope of the line connecting its control points.

Let $m_{0}$ be defined by Formula (C.7) if $N_{cp} \geq 3$ . Otherwise if $N_{cp} = 2$ then let $m_{0} = s_{0}$ and if $N_{cp} = 1$ then $m_{0}$ will not be used.

m_{0} = \frac{(2 \times h_{0} + h_{1}) \times s_{0} - h_{0} \times s_{1}}{h_{0} + h_{1}}

(C.7)

Let $m_{N_{cp} - 1}$ be defined by Formula (C.8) if $N_{cp} \geq 3$ . Otherwise if $N_{cp} = 2$ then let $m_{_{N_{cp} - 1}} = s_{0}$ .

m_{N_{cp} - 1} = \frac{(2 \times h_{N_{cp} - 2} + h_{N_{cp} - 3}) \times s_{N_{cp} - 2} - h_{N_{cp} - 2} \times s_{N_{cp} - 3}}{h_{N_{cp} - 2} + h_{N_{cp} - 3}}

(C.8)

For $i \in {1, . . ., N_{cp} - 2}$ , let $m_{i}$ be defined by Formula (C.9).

m_{i} = {\begin{matrix} 0 & : sign (s_{i - 1}) \neq sign (s_{i}) \\ \frac{3 \times (h_{i - 1} + h_{i}) \times s_{i - 1} \times s_{i}}{(2 \times h_{i - 1} + h_{i}) \times s_{i - 1} + (h_{i - 1} + 2 \times h_{i}) \times s_{i}} & : otherwise \end{matrix}

(C.9)

For each $c \in ℤ_{N_{cp}}$ , GainCurveControlPointM[a][c] metadata item shall be assigned the value $m_{c}$ .

Dynamic metadata for color volume transform — Application #5

Table of contents🔗

Foreword🔗

Introduction🔗

1 Scope🔗

2 Conformance🔗

3 Normative references🔗

4 Terms and definitions🔗

5 Mathematical notation🔗