High Dynamic Range D-Cinema Addendum

Front Matter🔗

Notice🔗

Digital Cinema Initiatives, LLC (DCI) is the author and creator of this specification for the purpose of copyright and other laws in all countries throughout the world. The DCI copyright notice must be included in all reproductions, whether in whole or in part, and may not be deleted or attributed to others. DCI hereby grants to its members and their suppliers a limited license to reproduce this specification for their own use, provided it is not sold. Others should obtain permission to reproduce this specification from Digital Cinema Initiatives, LLC.

This document is a specification developed and adopted by Digital Cinema Initiatives, LLC. This document may be revised by DCI. It is intended solely as a guide for companies interested in developing products, which can be compatible with other products, developed using this document. Each DCI member company shall decide independently the extent to which it will utilize, or require adherence to, these specifications. DCI shall not be liable for any exemplary, incidental, proximate or consequential damages or expenses arising from the use of this document. This document defines only one approach to compatibility, and other approaches may be available to the industry.

This document is an authorized and approved publication of DCI. Only DCI has the right and authority to revise or change the material contained in this document, and any revisions by any party other than DCI are unauthorized and prohibited.

Compliance with this document may require use of one or more features covered by proprietary rights (such as features which are the subject of a patent, patent application, copyright, mask work right or trade secret right). By publication of this document, no position is taken by DCI with respect to the validity or infringement of any patent or other proprietary right. DCI hereby expressly disclaims any liability for infringement of intellectual property rights of others by virtue of the use of this document. DCI has not and does not investigate any notices or allegations of infringement prompted by publication of any DCI document, nor does DCI undertake a duty to advise users or potential users of DCI documents of such notices or allegations. DCI hereby expressly advises all users or potential users of this document to investigate and analyze any potential infringement situation, seek the advice of intellectual property counsel, and, if indicated, obtain a license under any applicable intellectual property right or take the necessary steps to avoid infringement of any intellectual property right. DCI expressly disclaims any intent to promote infringement of any intellectual property right by virtue of the evolution, adoption, or publication of this document.

Table of Contents🔗

1 Introduction
2 Scope
3 Normative References
4 Terms and Definitions
5 Input Requirements
6 Standard Dynamic Range (SDR) Mode
7 Initial Conditions
8 Environment
1. 8.1 Ambient Luminance
2. 8.2 Reference Viewing Position for Color Grading
9 HDR Mode Image Parameters
Annex A Normative HDR Mode Tables
Annex B Subjective Parameters (informative)
1. B.1 Grayscale Tracking
2. B.2 Contouring
Annex C D65 Color Primaries, White Point and Color Conversions (Informative)
Bibliography (informative)

Table of Tables🔗

Table 1: Edit Units Per Second Requirements for HDR Reference Display
Table 2: Image Parameters & Tolerances for HDR Reference Display
Table 3: Black-To-White Gray Step-Scale Test Pattern Code Values, Luminance Values, & Chromaticity Coordinates.
Table 4: Black-To-Dark Gray Step-Scale Test Pattern Code Values, Luminance Values, & Chromaticity Coordinates
Table 5: Color Accuracy Color Patch Code Values, Luminance Values, & Chromaticity Coordinates

5 Input Requirements🔗

The HDR Reference Display shall support the HDR-DCDM, with full-range 12 bit image data formatted for [SMPTE ST 2084] EOTF with [ISO/CIE 11664] XYZ colorimetry at 2048x1080 or 4096x2160 image structures and frame rates as described in Table 1.

5.1 Signaling HDR in DCP Packaging🔗

HDR content shall be identified by the presence of an HDR flag in both [SMPTE ST 377:2004] MXF and CPL metadata, which indicates that the EOTF is [SMPTE ST 2084].

For MXF picture track files that carry HDR essence, this fact shall be signaled using the "Transfer Characteristic" property of the MXF "Generic Picture Essence Descriptor" to indicate the EOTF is [SMPTE ST 2084]. The UL value to be used shall be 06.0E.2B.34.04.01.01.0D.04.01.01.01.01.0A.00.00.

Composition Playlists containing picture track files that carry HDR essence shall signal this fact using [SMTPE ST 429-16] Metadata as follows:

Scope:	`http://www.dcimovies.com/schemas/2018/HDR-Metadata`
Name:	`Image Encoding Parameters`
Property Name:	`EOTF`
Property Value:	`ST 2084`

Below is an example excerpt from such a Composition:

<ExtensionMetadata scope="http://www.dcimovies.com/schemas/2018/HDR-Metadata">
   <Name>Image Encoding Parameters</Name>
      <PropertyList>
         <Property>
            <Name>EOTF</Name>
            <Value>ST 2084</Value>
         </Property>
   </PropertyList>
</ExtensionMetadata>

5.2 Device Behavior🔗

Devices shall display content in HDR mode when presented with a Composition Playlist and MXF Transfer Characteristic containing the signaling specified in Section 5.1.

5.3 Edit Unit🔗

The HDR Reference Display shall support the content frame rates in Table 1, expressed in Edit Units per second:

Table 1: Edit Units Per Second Requirements for HDR Reference Display🔗
Edit Unit/Sec.	2K 2D	2K 3D	4K 2D
24	Required	Required	Required
48	Required	Required	Required
60	Required	Required	Required
96	Required
120	Required

Support for HDR stereoscopic presentations is optional; “Required” in the 2K 3D category of Table 1 applies only to displays in which HDR stereoscopic exhibition is implemented.

Stereoscopic HDR implementations have yet to be sufficiently demonstrated to DCI. Therefore, parameters for stereoscopic HDR are reserved for this specification. Additional requirements for stereographic HDR may be specified by DCI in a future specification.

9 HDR Mode Image Parameters🔗

All image parameters shall be measured as light from the screen or display, with the measurements made from the reference viewing position in the Review Room, or from the center of the normal seating area in an Exhibition Theater.

9.1 Luminance Uniformity🔗

The variance in the measured luminance from the center to the sides and corners of the screen or display shall not exceed the specified tolerances in Table 2 as measured per [SMPTE RP 431-2].

9.2 Calibration White Points and Luminance🔗

When the HDR Reference Display is sent a full frame image with the code values 2060 X″, 2081 Y″, 2116 Z″, the chromaticity coordinates of the displayed image shall be x = 0.3127, y = 0.3291. These code values shall produce a displayed luminance of 100.1 cd/m² within the specified tolerances in Table 2.

When the HDR Reference Display is sent a full frame image with code values 2524 X″, 2546 Y″, 2583 Z″, the chromaticity coordinates of the displayed image shall be x = 0.3128, y = 0.3290. These code values shall produce a displayed luminance of 299.6 cd/m² within the specified tolerances in Table 2.

Behavior of code values representing output luminance exceeding 299.6 cd/m² is undefined.

Other creative white points are possible and can be accommodated, albeit with some marginal differences in peak luminance. Refer to Table 5 for examples of alternative creative white points.

In the event that display or projection technology is developed that is able to meet all provisions of this specification (e.g., peak luminance, screen black level, etc.) but is unable to meet the full-screen luminance requirements stated in this section, DCI leaves open the possibility of developing a new application profile to accommodate such technology.

9.3 Minimum Active Black Level🔗

Minimum Active Black Level shall be 0.005 cd/m² and shall not exceed the specified tolerances in Table 2. Behavior of code values representing output luminance below 0.005 cd/m² but greater than zero is undefined.

When the HDR Reference Display is sent a full frame images with the code values 60 X″, 62 Y″, 65 Z″, the chromaticity coordinates of the displayed image shall be x = 0.3095, y = 0.3296. These code values shall produce a displayed luminance of 0.005 cd/m² within the specified tolerances in Table 2.

Minimum active black level shall be measured in a manner that minimizes or eliminates the contribution of ambient light.

9.4 White Chromaticity Uniformity🔗

The variance in displayed chromaticity across the display shall not exceed the specified tolerances in Table 2.

9.5 Electro-Optical Transfer Function🔗

9.5.1 Encoding Function🔗

The encoding transfer function shall be defined in terms of output-referred [ISO 11664] XYZ tristimulus values produced by the HDR Reference Display unit. The HDR transfer functions are specified using 12bit [SMPTE ST 2084] XYZ Encoding Primaries and [SMPTE ST 2084] EOTF, as shown below:.

{C V}_{X^{″}} = f l o o r (\frac{1}{2} + k_{1} \cdot {(\frac{c_{1} + c_{2} {(\frac{X}{k_{0}})}^{m_{1}}}{1 + c_{3} {(\frac{X}{k_{0}})}^{m_{1}}})}^{m_{2}})

(1)🔗

{C V}_{Y^{″}} = f l o o r (\frac{1}{2} + k_{1} \cdot {(\frac{c_{1} + c_{2} {(\frac{Y}{k_{0}})}^{m_{1}}}{1 + c_{3} {(\frac{Y}{k_{0}})}^{m_{1}}})}^{m_{2}})

(2)🔗

{C V}_{Z^{″}} = f l o o r (\frac{1}{2} + k_{1} \cdot {(\frac{c_{1} + c_{2} {(\frac{Z}{k_{0}})}^{m_{1}}}{1 + c_{3} {(\frac{Z}{k_{0}})}^{m_{1}}})}^{m_{2}})

(3)🔗

where:

$k_{0} = 10, 000$ , $k_{1} = 4095$ , $m_{1} = \frac{2610}{4096} \cdot \frac{1}{4}$ , $m_{2} = \frac{2523}{4096} \cdot 128$ , $c_{1} = c_{3} - c_{2} + 1$ , $c_{2} = \frac{2413}{4096} \cdot 32$ and $c_{3} = \frac{2392}{4096} \cdot 32$

and the unary function $f l o o r ()$ yields the largest integer not greater than its argument.

If the data is transported over certain interfaces (like Serial Digital Interface), code values 0-15 and 4080-4095 are reserved (illegal) code values and these code values will be clipped (see [SMPTE ST 372]).

9.5.2 Decoding Function🔗

The following equations can be used to compute X, Y and Z from a set of code values:

X = k_{0} {(\frac{m a x [{(\frac{{C V}_{X^{″}}}{k_{1}})}^{\frac{1}{m_{2}}} - c_{1}, 0]}{c_{2} - c_{3} {(\frac{{C V}_{X^{″}}}{k_{1}})}^{\frac{1}{m_{2}}}})}^{\frac{1}{m_{1}}}

(4)🔗

Y = k_{0} {(\frac{m a x [{(\frac{{C V}_{Y^{″}}}{k_{1}})}^{\frac{1}{m_{2}}} - c_{1}, 0]}{c_{2} - c_{3} {(\frac{{C V}_{Y^{″}}}{k_{1}})}^{\frac{1}{m_{2}}}})}^{\frac{1}{m_{1}}}

(5)🔗

Z = k_{0} {(\frac{m a x [{(\frac{{C V}_{Z^{″}}}{k_{1}})}^{\frac{1}{m_{2}}} - c_{1}, 0]}{c_{2} - c_{3} {(\frac{{C V}_{Z^{″}}}{k_{1}})}^{\frac{1}{m_{2}}}})}^{\frac{1}{m_{1}}}

(6)🔗

9.5.3 Tracking Performance🔗

EOTF tracking performance shall be measured at the code-values described in Table 3 and Table 4 with the tolerances identified in Table 2.

9.6 Color Volume🔗

The HDR color volume is a cuboid with vertices determined by the XYZ coordinates of the three color primaries, the white point, and the black point. The color primaries and white point in Table 2 define the minimum color volume for an HDR Reference Display.

9.7 Color Accuracy🔗

Within the minimum color volume, all colors shall be accurately reproduced. Table 2 defines tolerances for the color primaries of the minimum color volume. Table 5 provides exact chromaticity and luminance values for a set of test code values that fall within these tolerances.

Annex A Normative HDR Mode Tables🔗

The HDR Reference Display image parameters and tolerances for the displayed image in Review Rooms and Exhibition Theaters, as measured from the display or screen, and including the room ambient light, are summarized in Table 2. Where the nominal parameters are specified as minimums, it is understood that these parameters shall not be constrained from future improvements as the technology progresses.

Tolerances for Electro-Optical Transfer Function distortion (measured as a percentage error) are calculated as follows:

Percentage error = 100*((measured luminance - target luminance) / target luminance)

where target luminance is derived by decoding the input code value using the decoding equation in Section 9.5.2, using the ranges and tolerances specified in Table 2.

Table 2: Image Parameters & Tolerances for HDR Reference Display🔗
Section	Parameter	Nominal	HDR Reference Projector		HDR Direct View Display
Section	Parameter	Nominal	Review Room Tolerance	Exhibition Theater Tolerance	Review Room Tolerance	Exhibition Theater Tolerance
9.1, 9.2	Luminance, center, Peak Luminance, White-1 D65	299.6 cd/m² (87.6 fL)	± 18.0 cd/m²	± 30.0 cd/m²	± 9.0 cd/m²	± 9.0 cd/m²
	Luminance, Screen Average, White-1 D65	299.6 cd/m² (87.6 fL)	N/A	N/A	± 9.0 cd/m²	± 9.0 cd/m²
	Luminance, sides	299.6 cd/m² (87.6 fL)	85% to 100% of center	75% to 100% of center	± 9.0 cd/m²	± 9.0 cd/m²
	Luminance, corners	299.6 cd/m² (87.6 fL)	85% to 100% of center	Not Specified	± 9.0 cd/m²	± 9.0 cd/m²
9.3	Minimum Active Black Level	0.005 cd/m² (0.0003 fL)	± 0.001 cd/m²	± 0.001 cd/m²	± 0.001 cd/m²	± 0.001 cd/m²
9.4	White chromaticity, center, Peak Luminance, White-1 D65	x = 0.3127 y = 0.3290	± 0.002 x ± 0.002 y	± 0.006 x ± 0.006 y	± 0.002 x ± 0.002 y	± 0.006 x ± 0.006 y
9.4	White chromaticity uniformity, corners (tolerance from center)	± 0.000 x ± 0.000 y	± 0.008 x ± 0.008 y	± 0.015 x ± 0.015 y	± 0.008 x ± 0.008 y	± 0.015 x ± 0.015 y
9.5	Electro-Optical Transfer Function	Per [SMPTE ST 2084]	Y≦0.02 cd/m² ± 20%; 0.02<Y≦1.0 cd/m² ± 5%; 1.0<Y≦299.6 cd/m² ± 3%	Y≦0.02 cd/m² ± 20%; 0.02<Y≦1.0 cd/m² ± 5%; 1.0<Y≦299.6 cd/m² ± 3%	Y≦0.02 cd/m² ± 20%; 0.02<Y≦1.0 cd/m² ± 5%; 1.0<Y≦299.6 cd/m² ± 3%	Y≦0.02 cd/m² ± 20%; 0.02<Y≦1.0 cd/m² ± 5%; 1.0<Y≦299.6 cd/m² ± 3%
9.6	Color Volume	Volume in XYZ space defined by the black point & the following points expressed in (Y,x,y), representing a 299.6 nits P3D65 color volume: Red (68.69, 0.6800, 0.3200), Green (207.52, 0.2650, 0.6900), Blue (23.79, 0.1500, 0.0600), Peak White (299.6, 0.3127, 0.3290)	N/A	N/A	N/A	N/A
9.7	Color Accuracy	The following points are expressed in (x,y): Red (0.6800, 0.3200), Green (0.2650, 0.6900), Blue (0.1500, 0.0600)	Red (0.6800 ± .01, 0.3200 ± .01), Green (0.2650 ± .02, 0.6900 ± .02), Blue (0.1500 + 0.01/- 0.03, 0.0600 + 0.02/- 0.04)	Red (0.6800 ± .01, 0.3200 ± .01), Green (0.2650 ± .02, 0.6900 ± .02), Blue (0.1500 + 0.01/- 0.03, 0.0600 + 0.02/- 0.04)	Red (0.6800 ± .01, 0.3200 ± .01), Green (0.2650 ± .02, 0.6900 ± .02), Blue (0.1500 + 0.01/- 0.03, 0.0600 + 0.02/- 0.04)	Red (0.6800 ± .01, 0.3200 ± .01), Green (0.2650 ± .02, 0.6900 ± .02), Blue (0.1500 + 0.01/- 0.03, 0.0600 + 0.02/- 0.04)

Table 3: Black-To-White Gray Step-Scale Test Pattern Code Values, Luminance Values, & Chromaticity Coordinates.🔗
	Input Code Values			Output Chromaticity Coordinates		Output Luminance
Step Number	X″	Y″	Z″	x	y	Y, cd/m²
1	472	481	496	0.3126	0.3292	0.50
2	603	614	632	0.3122	0.3292	1.00
3	758	771	792	0.3121	0.3293	2.00
4	1000	1015	1040	0.3124	0.3291	5.00
5	1211	1227	1255	0.3128	0.3288	10.00
6	1444	1462	1492	0.3128	0.3291	20.00
7	1783	1803	1836	0.3126	0.3292	50.01
8	2060	2081	2116	0.3127	0.3291	100.10
9	2350	2372	2408	0.3127	0.3292	200.21
10	2524	2546	2583	0.3128	0.3290	299.64
All measurements are made in the center of the Screen.

Table 4: Black-To-Dark Gray Step-Scale Test Pattern Code Values, Luminance Values, & Chromaticity Coordinates🔗
	Input Code Values			Output Chromaticity Coordinates		Output Luminance
Step Number	X″	Y″	Z″	x	y	Y, cd/m²
1	60	62	65	0.3095	0.3296	0.0050
2	74	76	79	0.3134	0.3302	0.0075
3	86	88	92	0.3133	0.3281	0.0100
4	105	108	112	0.3124	0.3309	0.0151
5	121	124	129	0.3129	0.3293	0.0202
6	157	161	167	0.3125	0.3300	0.0352
7	185	189	196	0.3138	0.3291	0.0501
8	221	226	234	0.3131	0.3296	0.0752
9	250	255	265	0.3129	0.3279	0.0998
10	332	339	351	0.3121	0.3289	0.1997
All measurements are made in the center of the Screen.

Table 5: Color Accuracy Color Patch Code Values, Luminance Values, & Chromaticity Coordinates🔗
	Input Code Values			Output Chromaticity Coordinates		Output Luminance
Patch	X″	Y″	Z″	x	y	Y, cd/m²
Red-1	2234	1925	68	0.6787	0.3202	68.13
Green-1	1988	2387	1327	0.2651	0.6899	207.35
Blue-1	1871	1525	2565	0.1501	0.0602	23.86
Cyan-1	2218	2434	2583	0.1998	0.3320	231.33
Magenta-1	2383	2049	2565	0.3362	0.1515	92.58
Yellow-1	2423	2510	1327	0.4380	0.5357	275.80
Red-2	2169	1899	1058	0.6401	0.3300	63.83
Green-2	2110	2402	1674	0.3001	0.6001	214.73
Blue-2	1834	1491	2524	0.1501	0.0602	21.70
Cyan-2	2280	2443	2576	0.2245	0.3288	236.21
Magenta-2	2322	2016	2533	0.3213	0.1541	85.39
Yellow-2	2432	2513	1731	0.4190	0.5054	277.72
White-1 D65	2524	2546	2583	0.3128	0.3290	299.64
White-2 D60	2509	2530	2534	0.3217	0.3376	288.81
White-3 D55	2493	2513	2478	0.3319	0.3476	277.72
The accuracy with which these colors shall be displayed is given in Table 2.

Annex B Subjective Parameters (informative)🔗

The following parameters are also important to picture quality, but because they are difficult to measure with today’s readily available instrumentation, they are generally assessed subjectively.

Instrumentation designers are encouraged to design and manufacture equipment that can be used to translate subjective parameters into objective performance characterization.

B.1 Grayscale Tracking🔗

Using the black-to-white gray step-scale test pattern, the entire step-scale appears neutral without any visible color non-uniformity. The black-to-white gray step-scale test pattern is centered on the display and occupies a rectangle sized 20% of the screen height by 80% of the screen width. The background is defined by code values [1000 1015 1040], which define a luminance of 5.0 cd/m2 and chromaticity coordinates x = 0.3124 y = 0.3291. Each step is 8% of the screen width and is defined by the code values in Table 3.

Using the black-to-dark gray step-scale test pattern, the entire step-scale appears neutral without any visible color non-uniformity. The black-to-dark gray step-scale test pattern is centered on the display and occupies a rectangle sized 20% of the screen height by 80% of the screen width. The background is defined by code values [122 124 129], which define a luminance of 0.020 cd/m² and chromaticity coordinates x = 0.3129 y = 0.3293. Each step is 8% of the screen width and is defined by the code values in Table 4.

B.2 Contouring🔗

Contouring is the appearance of steps or bands where only a continuous or smooth gradient is expected. Because contouring is a function of many variables, it is important to look at a series of test patterns with shallow gradations to simulate naturally occurring gradations in images.

Examples include horizons, particularly at sunset or sunrise, and the natural falloff around high intensity spotlights, particularly if diffused by atmosphere or lens filtration. These test pattern ramps have a step width of no less than 4 pixels with an increment of one code value per step and are placed on a background equal to the minimum value in the ramp, so that the eye is adapted for maximum sensitivity.

Since dynamic fades to black are widely used in real-world content, a dynamic test pattern that fades slowly to black is another useful approach.

Each image is viewed in the proper environment as defined in Section 7, and ought not to exhibit any contouring (step in luminance), or color deviation from the neutral gray.

Annex C D65 Color Primaries, White Point and Color Conversions (Informative)🔗

The color image encoding parameters for today’s HDR Reference Displays and the corresponding color conversion steps to convert from P3D65 R′G′B′ to X″Y″Z″ and from X″Y″Z″ to P3D65 RGB are shown here as an example for implementation. P3D65 is defined in [SMPTE ST 2113].

C.1 Color Primaries🔗

Table 6: Chromaticity Coordinates of Primaries.
Encoding Primaries
R (x, y) = (0.6800, 0.3200)
G (x, y) = (0.2650, 0.6900)
B (x, y) = (0.1500, 0.0600)

C.2 White Reference🔗

Table 7: Chromaticity Coordinates of Primaries. x, y refers to the chromaticity coordinates defined by [ISO 11664].
White Reference
(x, y) = (0.3127,0.3290)

C.3 Luminance🔗

The Reference White Luminance is 299.6 cd/m².

C.4 Color Conversion R′G′B′ to X″Y″Z″🔗

Color conversion from R′G′B′ to X″Y″Z″ typically involves the following five-step process:

To the R′G′B′ code values, apply the inverse-quantization process to convert the image’s integer code values to a non-linear R′G′B′ signal in the range [0.0,1.0] from the code value’s integer range, 12bit full-range code values range from [0,4095] and 16 bit full-range code values range from [0,65535].
To the non-linear R′G′B′ signal, apply [SMPTE ST 2084] EOTF to convert non-linear R′G′B′ signal to linear RGB signal.
To the linear RGB signal, apply the RGB to XYZ primary conversion matrix to convert linear RGB to linear XYZ.
To the linear XYZ signal, apply the [SMPTE ST 2084] Inverse-EOTF to convert from linear XYZ to non-linear X″Y″Z″.
To the non-linear X″Y″Z″ signal, apply the 12 bit full-range quantization process to convert non-linear X″Y″Z″ to 12 bit X″Y″Z″ code values.

The transfer function of the HDR Reference Display is explicitly specified by [SMPTE ST 2084]. The actual coefficients of the color transform matrices depend on the color primaries of the Mastering HDR Reference Display (encoding side) and the Cinema HDR Display (decoding side), and their respective white points.

[SMPTE ST 2084] is a defined standard, and 12-bit quantization is sufficient, so a normalized PQ is not needed. Using a normalized PQ might impede the cross-utilization of assets in other formats.

The processing steps for converting 12 bit R′G′B′ code values (which range from 0 to 4095) of the color-graded master to device-independent X″Y″Z″ are shown below.

This color space conversion can be implemented within the color corrector or applied in a separate batch process. The equations below combine step #1 (inverse quantization) and step #2 ([SMPTE ST 2084] EOTF):

R = k_{0} {(\frac{m a x [{(\frac{{C V}_{R^{'}}}{k_{1}})}^{\frac{1}{m_{2}}} - c_{1}, 0]}{c_{2} - c_{3} {(\frac{{C V}_{R^{'}}}{k_{1}})}^{\frac{1}{m_{2}}}})}^{\frac{1}{m_{1}}}

(7)🔗

G = k_{0} {(\frac{m a x [{(\frac{{C V}_{G^{'}}}{k_{1}})}^{\frac{1}{m_{2}}} - c_{1}, 0]}{c_{2} - c_{3} {(\frac{{C V}_{G^{'}}}{k_{1}})}^{\frac{1}{m_{2}}}})}^{\frac{1}{m_{1}}}

(8)🔗

B = k_{0} {(\frac{m a x [{(\frac{{C V}_{B^{'}}}{k_{1}})}^{\frac{1}{m_{2}}} - c_{1}, 0]}{c_{2} - c_{3} {(\frac{{C V}_{B^{'}}}{k_{1}})}^{\frac{1}{m_{2}}}})}^{\frac{1}{m_{1}}}

(9)🔗

where:

The output (RGB) of this linearization is a floating point number that ranges from 0.0 to 10000.0. The 3x3 linear matrix is then applied to this signal, resulting in a linear XYZ signal with floating point values that range from 0.0 to 10000.0. To minimize quantization errors, this matrix should be implemented as a floating point calculation. The matrix is shown here to 14 significant digits.

[\begin{matrix} X \\ Y \\ Z \end{matrix}] = (\begin{matrix} 0.48657094864822 & 0.26566769316910 & 0.19821728523436 \\ 0.22897456406975 & 0.69173852183651 & 0.07928691409375 \\ 0 & 0.04511338185890 & 1.04394436890098 \end{matrix}) * [\begin{matrix} R \\ G \\ B \end{matrix}]

(10)🔗

Finally, the X″Y″Z″ encoding transfer function is defined by the following expression which performs both step #4 (Inverse-EOTF) and step #5 (12bit Quantization). This equation does not compensate for the screen black level, so it represents an absolute encoding of the light levels independent of the screen black level.

{C V}_{X^{″}} = f l o o r (\frac{1}{2} + k_{1} \cdot {(\frac{c_{1} + c_{2} {(\frac{X}{k_{0}})}^{m_{1}}}{1 + c_{3} {(\frac{X}{k_{0}})}^{m_{1}}})}^{m_{2}})

(11)🔗

{C V}_{Y^{″}} = f l o o r (\frac{1}{2} + k_{1} \cdot {(\frac{c_{1} + c_{2} {(\frac{Y}{k_{0}})}^{m_{1}}}{1 + c_{3} {(\frac{Y}{k_{0}})}^{m_{1}}})}^{m_{2}})

(12)🔗

{C V}_{Z^{″}} = f l o o r (\frac{1}{2} + k_{1} \cdot {(\frac{c_{1} + c_{2} {(\frac{Z}{k_{0}})}^{m_{1}}}{1 + c_{3} {(\frac{Z}{k_{0}})}^{m_{1}}})}^{m_{2}})

(13)🔗

where:

The unary function $f l o o r ()$ yields the largest integer not greater than its argument.

C.5 Color Conversion X″Y″Z″ to P3D65 RGB🔗

The X″Y″Z″-to-P3D65 RGB processing steps for a Cinema HDR Display with the same color primaries as the HDR Reference Display are shown below and defined by the following steps:

Apply Inverse Quantization to the 12 bit X″Y″Z″ code values, converting 12 bit X″Y″Z″ code values to non-linear X″Y″Z″ in the range [0.0,1.0]
Apply [SMPTE ST 2084] EOTF to non-linear X″Y″Z″ values, converting non-linear X″Y″Z″ to linear XYZ
Apply XYZ to RGB conversion to linear XYZ values

The equations below show step #1 (inverse quantization) and step #2 ([SMPTE ST 2084] EOTF) combined:

X = k_{0} {(\frac{m a x [{(\frac{{C V}_{X^{″}}}{k_{1}})}^{\frac{1}{m_{2}}} - c_{1}, 0]}{c_{2} - c_{3} {(\frac{{C V}_{X^{″}}}{k_{1}})}^{\frac{1}{m_{2}}}})}^{\frac{1}{m_{1}}}

(14)🔗

Y = k_{0} {(\frac{m a x [{(\frac{{C V}_{Y^{″}}}{k_{1}})}^{\frac{1}{m_{2}}} - c_{1}, 0]}{c_{2} - c_{3} {(\frac{{C V}_{Y^{″}}}{k_{1}})}^{\frac{1}{m_{2}}}})}^{\frac{1}{m_{1}}}

(15)🔗

Z = k_{0} {(\frac{m a x [{(\frac{{C V}_{Z^{″}}}{k_{1}})}^{\frac{1}{m_{2}}} - c_{1}, 0]}{c_{2} - c_{3} {(\frac{{C V}_{Z^{″}}}{k_{1}})}^{\frac{1}{m_{2}}}})}^{\frac{1}{m_{1}}}

(16)🔗

where:

Apply XYZ to P3D65 color encoding primaries transformation:

[\begin{matrix} R \\ G \\ B \end{matrix}] = (\begin{matrix} 2.49349691194143 & - 0.93138361791912 & - 0.40271078445072 \\ - 0.82948896956157 & 1.76266406031835 & 0.02362468584194 \\ 0.03584583024378 & - 0.07617238926804 & 0.95688452400769 \end{matrix}) * [\begin{matrix} X \\ Y \\ Z \end{matrix}]

(17)🔗

The resulting linear RGB light levels may end up being converted to other formats as the image data flows through the image/display processing operations involved in ultimately displaying the image to the viewer via the HDR display.

If other formats within the HDR display that may have a limited precision, it is important to preserve the visual fidelity/accuracy that is achievable with the 12 bit X″Y″Z″ [SMPTE ST 2084] distribution format across the minimum gamut (luminance range and color volume) specified elsewhere in this document to ensure that additional fidelity isn’t loss.

High Dynamic Range D-Cinema Addendum

Front Matter🔗

Notice🔗

Table of Contents🔗

Table of Tables🔗

1 Introduction🔗

2 Scope🔗

3 Normative References🔗

4 Terms and Definitions🔗

4.1 Edit Unit🔗

4.2 Minimum Active Black Level🔗

4.3 Double Prime Notation🔗

4.4 HDR Digital Cinema Distribution Master (HDR-DCDM)🔗

4.5 HDR Digital Cinema Package (HDR-DCP)🔗

5 Input Requirements🔗

5.1 Signaling HDR in DCP Packaging🔗

5.2 Device Behavior🔗

5.3 Edit Unit🔗

6 Standard Dynamic Range (SDR) Mode🔗

7 Initial Conditions🔗

8 Environment🔗

8.1 Ambient Luminance🔗

8.2 Reference Viewing Position for Color Grading🔗

9 HDR Mode Image Parameters🔗

9.1 Luminance Uniformity🔗

9.2 Calibration White Points and Luminance🔗

9.3 Minimum Active Black Level🔗

9.4 White Chromaticity Uniformity🔗

9.5 Electro-Optical Transfer Function🔗

9.5.1 Encoding Function🔗

9.5.2 Decoding Function🔗

9.5.3 Tracking Performance🔗

9.6 Color Volume🔗

9.7 Color Accuracy🔗

Annex A Normative HDR Mode Tables🔗

Annex B Subjective Parameters (informative)🔗

B.1 Grayscale Tracking🔗

B.2 Contouring🔗

Annex C D65 Color Primaries, White Point and Color Conversions (Informative)🔗

C.1 Color Primaries🔗

C.2 White Reference🔗

C.3 Luminance🔗

C.4 Color Conversion R′G′B′ to X″Y″Z″🔗

C.5 Color Conversion X″Y″Z″ to P3D65 RGB🔗

Bibliography (informative)🔗