CSS Color HDR Module Level 1

1. Introduction

This section is not normative.

CSS Color 4 adds Wide Color Gamut (WCG) color spaces to the Open Web Platform. By design, these are all Standard Dynamic Range (SDR) color spaces. This specification defines additions to support High Dynamic Range (HDR).

While WCG specifications have been broadly stable for some decades, HDR standards are less mature and have undergone frequent revision in the last decade.

1.1. Value Definitions

This specification follows the CSS property definition conventions from [CSS2] using the value definition syntax from [CSS-VALUES-3]. Value types not defined in this specification are defined in CSS Values & Units [CSS-VALUES-3]. Combination with other CSS modules may expand the definitions of these value types.

In addition to the property-specific values listed in their definitions, all properties defined in this specification also accept the CSS-wide keywords as their property value. For readability they have not been repeated explicitly.

2. HDR Terminology

2.1. Defining Dynamic Range

Dynamic range is the difference in luminance between the lightest and the darkest colors. Dynamic range is measured in photographic stops. One stop is a doubling of luminance.

function DynamicRange (high, low) {
  return Math.log2(high) - Math.log2(low);
  } 

Media white, also called HDR Reference White, is the color of a normal white background, or of white text on a dark background. It can be comfortably viewed, over the whole screen.

In Standard Dynamic Range (SDR), media white is also lightest possible color, produced by full-intensity red, green, and blue.

It is common to adjust the overall brighness of the screen to acommodate user preference or viewing conditions which are different to the standard ones.

For SDR, making the screen brighter does not change the dynamic range, because the darkest color also gets brighter.

In High Dynamic Range (HDR), brighter colors than media white can be displayed. For example, if media white on an HDR display is set to 203 cd/m² it might be possible to display small highlights at 1000 cd/m². Typically, the brightest colors can only be displayed on a small part of the display, and for a limited time. This is because of energy usage and heating considerations.

For HDR, using a brighter screen increases the dynamic range, while the luminance of media white remains constant.

add a diagram showing SDR and HDR dynamic ranges on a log scale

When § 7 Compositing SDR and HDR content, and for color space conversion, the media white for SDR content should be anchored at 203 cd/m² [Rpt_BT.2408] so that that the media white level of the inputs to compositing will end up at the media white level of the combined signal.

When displaying HDR (or mixed SDR and HDR) content, for displays which are less capable than the reference mastering display, and for viewing conditions different to the standard ones, a color re-rendering step ((OOTF) will be performed. This may result in a media white being displayed at a value lower or higher than 203 cd/m².

2.2. Introducing Headroom

The peak luminance level which an HDR display can produce varies greatly.

The amount by which peak white is greater than media white is termed the HDR headroom, and depends on the level of media white, user preference, and viewing conditions.

It is typically expressed in photographic stops. Thus, standard dynamic range (SDR) by definition has an HDR headroom of 0 stops, because the brightest white is media white.

The Web platform does not currently directly expose the level of headroom of a display, because it depends on viewing conditions and real-time, unquantized headroom information would be a tracking vector (for example, detecting that a user moved outside and that it is a sunny day).

It is not always desirable to use the maximum available level of HDR headroom. CSS provides a way to control, in broad terms, how much headroom is desired; and this level can vary by element and over time.

3. Controlling Dynamic Range

3.1. The dynamic-range-limit property

standard

The highest luminance color that is displayed is the same as media white, i.e. the CSS color white.

no-limit

The highest peak luminance that is displayed is much greater than media white, i.e. the CSS color white; the precise level is not specified.

constrained-high

The highest peak luminance that is displayed is somewhat greater than media white, i.e. the CSS color white, such that a mix of SDR and HDR content can be comfortably viewed together.

body { dynamic-range-limit: standard; }
div.photogrid img { dynamic-range-limit: constrained-high }

3.2. Mixing Dynamic Range Limits: the dynamic-range-limit-mix() function

This function takes two or more dynamic-range-limit values, converts them internally to a value in stops above media white, and alters the display to the result of mixing them by the specified amount. The actual calculated result is not exposed.

dynamic-range-limit-mix() = dynamic-range-limit-mix( [ <'dynamic-range-limit'> && <percentage [0,100]> ]#{2,} )

If the sum of all percentages is 0%, then the function is invalid.

3.3. Computed Value for dynamic-range-limit

If the specified value is standard, constrained-high, or no-limit, then the computed value is the specified value.

If the specified value is dynamic-range-limit-mix(), then the computed value is determined by the following algorithm:

1. Let v1, ..., vN be the computed values for the parameters to be mixed.

2. Let p1, ..., pN be the mixing percentages, normalized to sum to 100%.

3. Define the contributing percentages as:

   • Let p1_standard,...,pN_standard be the percentages for standard in v1,...,vN

   • Let p1_constrained_high,...,pN_constrained_high be the percentages for constrained-high in v1,...,vN

   • Let p1_no_limit,...,pN_no_limit be the percentages for no-limit in v1,...,vN

4. Compute the weighted sums as:

   • p_standard=(p1_standard*p1+...+pN_standard*pN)/100.

   • p_constrained_high=(p1_constrained_high*p1+...+pN_constrained_high*pN)/100.

   • p_no_limit=(p1_no_limit*p1+...+pN_no_limit*pN)/100.

5. If p_standard, p_constrained_high, or p_no_limit equals 100%, then the computed value is standard, constrained-high, or no-limit, respectively.

6. Otherwise, the computed value is dynamic-range-limit-mix(), with parameters standard, constrained-high, and no-limit, in that order, and percentages p_standard, p_constrained_high, and p_no_limit, omitting parameters with a percentage equal to 0%.

dynamic-range-limit-mix(
    high 10%,
    dynamic-range-limit-mix(standard 25%, constrained-high 75%) 20%,
    dynamic-range-limit-mix(constrained-high 10%, no-limit 30%) 20%)

dynamic-range-limit-mix(standard 10%, constrained-high 40%, no-limit 50%)

4. HDR colors parameterized by headroom: the hdr-color() function

The hdr-color() function allows a range of colors to be specified, whose value is automatically calculated based on the HDR headroom.

It does this by specifying two <color> values, each with an associated level of HDR headroom. The actual value is computed by interpolating between these two colors, based on the current amount of HDR headroom, as described in § 4.1 Interpolating colors based on headroom.

The actual calculated color is not exposed, nor is the actual HDR headroom, as this is a fingerprinting vector.

Its syntax is as follows:

hdr-color() = color-hdr([ <color> && <number [0,∞]>? ]#{2})

color-hdr(
  color(rec2100-linear 0.9 1.0 0.8) 0,
  color(rec2100-linear 1.8 2.0 1.5) 2);

color(rec2100-linear 0.9 1.0 0.8)

color(rec2100-linear 1.8 2.0 1.5) 2);

4.1. Interpolating colors based on headroom

To interpolate between a color c1 at headroom H1 and a color c2 at headroom H2, giving result color cxyz, when the target headroom is H:

1. Let c1xyz be c1 converted to D65 CIE XYZ

2. Let c2xyz be c2 converted to D65 CIE XYZ

3. Let w1 = clamp((log(H) - log(H2)) / (log(H1) - log(H2)), 0, 1)

4. Let w2 = clamp((log(H) - log(H1)) / (log(H2) - log(H1)), 0, 1) Note that w2 = 1 - w1

5. Let eps = 0.001 (one JND in linear-light space)

6. Let cxyz = pow(c1xyz + eps, w1) * pow(c2xyz + eps, w2) - eps

c1xyz = color(xyz-d65 0.853 0.9619 0.8769)
c2xyz = color(xyz-d65 1.689 1.918 1.648)
w1 = 
w2 =

5. Specifying Predefined and Custom Color Spaces: the color() Function

The color() function allows a color to be specified in a particular, given color space (rather than the implicit sRGB color space that most of the other color functions operate in).

In this specification the color() function is extended to allow predefined color spaces for HDR, in addition to the predefined SDR spaces from CSS Color 4 §  10. Predefined Color Spaces and the relative color syntax from CSS Color 5 § 4 Relative Colors.

Its syntax is now as follows:

color() = color( [from <color>]? <colorspace-params> [ / [ <alpha-value> | none ] ]? )
<colorspace-params> = [<custom-params> | <predefined-rgb-params> | 
  <predefined-polar-params> | <predefined-rectangular-params> | <xyz-params>]
<custom-params> = <dashed-ident> [ <number> | <percentage> | none ]+
<predefined-rgb-params> = <predefined-rgb> [ <number> | <percentage> | none ]{3}
<predefined-polar-params> = jzczhz [ <number> | <percentage> | none ]{2} [ <hue> | none]
<predefined-rectangular-params> = <predefined-rectangular> [ <number> | <percentage> | none ]{3}
<predefined-rgb> = srgb | srgb-linear | display-p3 | a98-rgb | prophoto-rgb | rec2020 | 
  rec2100-pq | rec2100-hlg | rec2100-linear
<predefined-rectangular> = jzazbz | ictcp
<xyz-params> = <xyz> [ <number> | <percentage> | none ]{3}
<xyz> = xyz | xyz-d50 | xyz-d65

6. Predefined color spaces for HDR:

In addition to the SDR color spaces defined by CSS Color 4, the following HDR color spaces are defined for use in the color function.

Serialization of values in these new color spaces is identical to the description in CSS Color 4 §  15. Serializing <color> Values.

6.1. rec2100-pq

The rec2100-pq [Rec_BT.2100] color space accepts three numeric parameters, representing the red, green, and blue channels of the color, with each having a valid range of [0, 1] regardless of the actual bit depth (10 or 12 bits per component).

The Perceptual Quantizer (PQ) electro-optical transfer function is used [SMPTE-ST-2084],[Rec_BT.2100]. PQ assumes a reference viewing condition where the screen surround is at 5 cd/m².

ITU Reference 2100 is used for HDR 4k and 8k television.

It has the following characteristics: (The display primaries are the same as [Rec.2020]):

For narrow-range PQ video in a non-reference viewing environment, or for HLG (in any viewing environment), the black level should be adjusted using the PLUGE test signal and procedure specified in [Rec_BT.814] Annex . For PQ values in CSS, which uses wide-range, the black corresponds to code point 0.

 color(rec2100-pq 1.0 1.0 1.0);

 color(rec2100-pq 0.58 0.58 0.58);

 color(rec2100-pq 0.34 0.34 0.34)

add other examples, including encoding of sRGB red, green, blue and P3 red, green, blue.

Linear-light RGB signals are converted to PQ encoded as follows. The maximum encodable value (peak, small-area white) in PQ is 10,000 cd/m². Media white is 203 cd/m² [Rpt_BT.2408].

var Er;      // the red, green or blue component, [0, 1] for SDR, [0, 70ish] for HDR
var Yw = 203;  // the luminance of diffuse white, cd/m²
var x = Er * Yw / 10000;   // luminance of peak white is 10,000 cd/m².
const n = 2610 / (2 ** 14);
const m = 2523 / (2 ** 5);
const c1 = 3424 / (2 ** 12);
const c2 = 2413 / (2 ** 7);
const c3 = 2392 / (2 ** 7);
xPQ = (((c1 + (c2 * (x ** n))) / (1 + (c3 * (x ** n)))) ** m);

xPQ is the "gamma-corrected" (OETF-adjusted) signal [0, 1].

PQ encoded values are converted to linear-light as follows:

var xPQ;      // the red, green or blue PQ-encoded component, [0, 1]
const ninv = (2 ** 14) / 2610;
const minv = (2 ** 5) / 2523;
const c1 = 3424 / (2 ** 12);
const c2 = 2413 / (2 ** 7);
const c3 = 2392 / (2 ** 7);
var x = (((Math.max(((xPQ ** minv) - c1), 0) / (c2 - (c3 * (xPQ ** minv)))) ** ninv);
var Yw = 203;      // the luminance of diffuse white, cd/m²
var Ea = x * 10000;   // luminance, [0, 10,000].
var Er = x * 10000 / Yw;   // luminance relative to diffuse white, [0, 70 or so].

6.2. rec2100-hlg

The rec2100-hlg [Rec_BT.2100] color space accepts three numeric parameters, representing the red, green, and blue channels of the color, with each having a valid range of [0, 1] regardless of the actual bit depth (10 or 12 bits per component).

The Hybrid Log-Gamma (HLG) electro-optical transfer function is used [ARIB_STD-B67],[Rec_BT.2100]. HLG can be used with displays of different brightness in a wide range of viewing environments, with user control of the overall brightness level. A value of 0.75 represents "diffuse" or "media" white while an "18% reflectance grey" card has a value of 0.38. [Rec_BT.2390].

It has the following characteristics: (The display primaries are the same as [Rec.2020]):

For narrow-range HLG video (in any viewing environment), the black level should be adjusted using the PLUGE test signal and procedure specified in [Rec_BT.814] Annex 4.

For HLG values in CSS, which uses wide-range, the black corresponds to code point 0.

add other examples

 color(rec2100-hlg 0.75 0.75 0.75);

 color(rec2100-hlg 0.38 0.38 0.38)

Linear-light RGB signals are converted to HLG encoded as follows [Rec_BT.2390]:

var E;      // the red, green or blue component, [0, 1]
const a = 0.17883277;
const b = 0.28466892;   // 1 - (4 * a)
const c = 0.55991073;   // 0.5 - a * Math.log(4 *a)
// handle negative values
var sign = E < 0? -1 : 1;
var abs = Math.abs(E);
if (abs <= 1/12) {
  Edash = sign * Math.sqrt( 3 * abs);
}
else {
  Edash = a * Math.log(12 * E - b) + c;
}

Edash is the "gamma-corrected" (OETF-adjusted) signal.

The reverse conversion (HLG encoded to linear light) is as follows [Rec_BT.2390]::

var Edash;      // the red, green or blue encoded component, [0, 1]
const a = 0.17883277;
const b = 0.28466892;   // 1 - (4 * a)
const c = 0.55991073;   // 0.5 - a * Math.log(4 *a)
if (Edash <= 0.5) {
  E = (Edash ** 2) / 3;
}
else {
  E = (Math.exp((Edash - c) / a) + b) / 12;
}

add black level lift Β as defined on same page?

6.3. rec2100-linear

The rec2100-linear [Rec_BT.2100] color space accepts three numeric parameters, representing the red, green, and blue channels of the color, with each having a nominal range of [0, 1] regardless of the actual bit depth (10 or 12 bits per component).

The color with red, green and blue all at 1.0 represents media white with a luminance of 203 cd/m².

color(rec2100-linear 1 1 1)

color(rec2100-linear 9.852 9.852 9.852)

 color(rec2100-linear 1 1 1)

A linear-light electro-optical transfer function is used.

It has the following characteristics: (The display primaries are the same as [Rec.2020]):

6.4. Jzazbz

The Jzazbz color space [Safdar-PUCS] accepts three numeric parameters, with J_z representing the Lightness (similar to L in Lab) while a_z and b_z represent the redness-greenness and yellowness-blueness opponent-color axes (similar to a and b in Lab).

CIE Lab uses a lightness scale with a [0%, 100%] range, relative to media white, and has been experimentally extended to L=400%. In contrast, the J_z axis in Jzazbz, which has a [0, 1.0] range, uses an encoding similar to Perceptual Quantizer, and can represent a dynamic range of more than 13 stops.

It has the following characteristics:

Note that unlike Lab, a D65 whitepoint is used. Thus, for most RGB spaces (which also use a D65 whitepoint) no chromatic adaptation step need be performed.

 color(jzazbz 0.22207 -0.00016 -0.00012)

6.5. JzCzHz

Similar to LCH, which is the polar representation of Lab, JzCzHz is the polar form of Jzazbz. J_z is identical to the value in JzCzHz and represents the Lightness, while C_z represents the Chroma or colorfulness and H_z represents a hue angle, measured from the positive a_z axis, towards the positive b_z axis.

 color(jzazbz 0.17542 -0.1179 0.1092)

 color(jzczhz 0.17542 0.1614 132.50)

6.5.1. Converting Jzazbz colors to JzCzHz colors

Conversion to JzCzHz is trivial:

1. Hz = atan2(bz, az) // but convert to degrees!
2. Cz = sqrt(az^2 + bz^2)
3. Jz is the same

6.5.2. Converting JzCzHz colors to Jzazbz colors

Conversion to Jzazbz is trivial:

1. az = Cz cos(H) // convert to radians first!
2. bz = Cz sin(H) // convert to radians first!
3. Jz is the same

6.6. ICtCp

The ICtCp color space [Perrin] is defined as Constant Intensity IC_TC_P signal format in [Rec_BT.2100] and accepts three numeric parameters, with I representing the Intensity (similar to L in Lab, but covering a luminance range up to 10,000 cd/m²) while C_T and C_P represent the yellowness-blueness (tritanope) and redness-greenness (protanope) opponent-color axes (similar to b and a, respectively, in Lab).

It is based on human visual system LMS cone primaries; the Hunt-Pointer-Estevez (HPE) XYZ to LMS transform is used, normalized to a D65 whitepoint. A 4% crosstalk matrix is then applied [What_is_ICtCp], to reduce the gamut hull concavities of BT.2020 RGB, thus reducing interpolation errors. The crosstalk also provides improved lines of constant hue and improved uniformity of Just Noticeable Difference (JND) MacAdam ellipses.

It has the following characteristics:

Although [Rec_BT.2100] defines IC_TC_P by a conversion from linear-light BT.2100 RGB [Rec_BT.2100], this conversion proceeds via LMS and thus, any other color space can also be represented by applying an XYZ to LMS transform as shown in [What_is_ICtCp].

Note that unlike CIE Lab, a D65 whitepoint is used.

Also unlike Lab, which has primarily been tested with lower-intensity reflective colors, IC_TC_P has been tested with high-chroma, self-luminous, and high intensity (HDR) colors. This makes it suitable for color difference measurement (deltaE ITP) and for gamut mapping of SDR and HDR colors.

 color(ictcp 0.5393 -0.2643 -0.0625)

 color(ictcp 0.58069 0 0)

7. Compositing SDR and HDR content

Compositing should take place in CIE XYZ, as it is a linear-light space without gamut limitations. Implementations may chose to composite in a linear-light RGB space instead, which will give the same result provided out-of-gamut values (negative, or greater than 100%) are correctly handled and not clipped or gamut mapped until the final transfer to the device color space.

HDR using the HLG transfer function, must map SDR media white to the same luminance as is used to display the 75% HLG value. [SMPTE-ST-2084]

For further details, see also tables 3 and 4 in ITU Rpt_BT.2408-0 [Rpt_BT.2408]

HDR using the PQ transfer function, should map SDR media white to 203 cd/m², the same luminance as is used to display the 58% PQ value. [SMPTE-ST-2084].

However, implementations may chose to incorporate a color re-rendering step to account for non-reference viewing conditions.

8. Serializing <color> Values

8.1. Serializing values of the color() function

This section extends CSS Color 4 § 15.5 Serializing values of the color() function

The serialized form of color() values is derived from the computed value and uses the color() form, with ASCII lowercase letters for the function name and the color space name.

The component values are serialized in base 10, as <number>. A single ASCII space character " " must be used as the separator between the component values, and also between the color space name and the first color component.

For the predefined HDR color spaces, the minimum precision for round-tripping is as follows:

(16bit, half-float, or float per component is recommended for internal storage). Values must be rounded towards +∞, not truncated.

9. Sample code for Color Conversions

This section is not normative.

For clarity, a library is used for matrix multiplication. (This is more readable than inlining all the multiplies and adds). The matrices are in column-major order.

This code also assumes all of the conversion code from CSS Color 4 §  17. Sample code for Color Conversions is available.

The LMS used in Jzazbz are not the same as the ones used in ICtCp, take care to use the right ones!

9.1. Sample code for rec2100-linear

The BT.2020 and BT.2100 color spaces use the same RGB primaries and white point, and both place media white at a component value of 1.0.

// These functions use the color conversion functions from CSS Color 4

function XYZ_to_lin_2100(XYZ) {
    // convert an array of D65 XYZ to linear-light BT.2100 RGB
    // such that [0,0,0] is black and [1,1,1] is media white.
    // component values greater than 1 indicate HDR colors

    return  XYZ_to_lin_2020(XYZ);
}

function lin_2100_to_XYZ(RGB) {
    // convert an array of linear-light BT.2100 RGB values
    // to D65 XYZ

    return lin_2020_to_XYZ(RGB);
}

9.2. Sample code for rec2100-pq

function XYZ_to_pq_2100(XYZ) {
    // convert an array of D65 XYZ to PQ-encoded BT.2100 RGB
    // such that [0,0,0] is black and [1,1,1] is 10,000 cd/m^2 white;
    // media white is at [0.5807,0.5807,0.5807] (to four significant figures).

    let linRGB = XYZ_to_lin_2100(XYZ);
    return pq_encode(linRGB);
}

function pq_2100_to_XYZ(RGB) {
    // convert an array of PQ-encoded BT.2100 RGB values
    // to D65 XYZ

    let linRGB = pq_decode(RGB);
    return lin_2100_to_XYZ(linRGB);
}

function pq_encode(RGB) {

    const Yw = 203;    // absolute luminance of media white, cd/m²
    const n = 2610 / (2 ** 14);
    const m = 2523 / (2 ** 5);
    const c1 = 3424 / (2 ** 12);
    const c2 = 2413 / (2 ** 7);
    const c3 = 2392 / (2 ** 7);

    // given PQ encoded component in range [0, 1]
    // return media-white relative linear-light
    return RGB.map(function (val) {
        let x = Math.max(val * Yw / 10000, 0);     // absolute luminance of peak white is 10,000 cd/m².
        let num = (c1 + (c2 * (x ** n)));
        let denom = (1 + (c3 * (x ** n)));

        return ((num / denom)  ** m);
    });
}

function pq_decode(RGB) {

    const Yw = 203;    // absolute luminance of media white, cd/m²
    const ninv = (2 ** 14) / 2610;
    const minv = (2 ** 5) / 2523;
    const c1 = 3424 / (2 ** 12);
    const c2 = 2413 / (2 ** 7);
    const c3 = 2392 / (2 ** 7);

    // given PQ encoded component in range [0, 1]
    // return media-white relative linear-light
    return RGB.map(function (val) {
        let x = ((Math.max(((val ** minv) - c1), 0) / (c2 - (c3 * (val ** minv)))) ** ninv);
        return (x * 10000 / Yw);     // luminance relative to diffuse white, [0, 70 or so].
    });
}

9.3. Sample code for rec2100-hlg

function XYZ_to_hlg_2100(XYZ) {
    // convert an array of D65 XYZ to HLG-encoded BT.2100 RGB
    // such that [0,0,0] is black and [0.75,0.75,0.75] is media white

    let linRGB = XYZ_to_lin_2100(XYZ);
    return hlg_encode(linRGB);
}

function hlg_2100_to_XYZ(RGB) {
    // convert an array of PQ-encoded BT.2100 RGB values
    // to D65 XYZ

    let linRGB = hlg_decode(RGB);
    return lin_2100_to_XYZ(linRGB);
}

function hlg_encode(RGB) {

    const a = 0.17883277;
    const b = 0.28466892; // 1 - (4 * a)
    const c = 0.55991073; // 0.5 - a * Math.log(4 *a)
    const scale = 3.7743;    // Place 18% grey at HLG 0.38, so media white at 0.75

    return RGB.map(function (val) {
        // first scale to put linear-light media white at 1/3
        val /= scale;
        // now the HLG OETF
        // ITU-R BT.2390-10 p.23
        // 6.1 The hybrid log-gamma opto-electronic transfer function (OETF)
        if (val <= 1 / 12) {
            return spow(3 * val, 0.5);
        }
        return a * Math.log(12 * val - b) + c;
    });
}

function hlg_decode(RGB) {

    const a = 0.17883277;
    const b = 0.28466892; // 1 - (4 * a)
    const c = 0.55991073; // 0.5 - a * Math.log(4 *a)
    const scale = 3.7743;    // Place 18% grey at HLG 0.38, so media white at 0.75

    return RGB.map(function (val) {
        // first the HLG EOTF
        // ITU-R BT.2390-10 p.30 section
        // 6.3 The hybrid log-gamma electro-optical transfer function (EOTF)
        // Then scale by 3 so media white is 1.0
        if (val <= 0.5) {
            return (val ** 2) / 3 * scale;
        }
        return ((Math.exp((val - c) / a) + b) / 12) * scale;
    });
}

function spow (base, exp) {
    let sign = base < 0? -1 : 1;
    return sign * (Math.abs(base) ** exp);
}

9.4. Sample code for jzazbz

This uses the same signed power (spow) function defined above.

function XYZ_to_Jzazbz (XYZ) {
    // convert an array of D65 XYZ toJzAzBz
    // such that [0,0,0] is black and
    // media white is [0.2220, -0.00016, -0.0001]

    const Yw = 203; // absolute luminance of media white
    const M = [
        [  0.41478972, 0.579999,  0.0146480 ],
        [ -0.2015100,  1.120649,  0.0531008 ],
        [ -0.0166008,  0.264800,  0.6684799 ],
    ];
    const b = 1.15;
    const g = 0.66;

    // First make XYZ absolute, not relative to media white
    // Maximum luminance in PQ is 10,000 cd/m²
    // BT.2048 says media white Y=203  cd/m²
    let [Xa, Ya, Za] = XYZ.map(v => v * Yw);

    // then modify X and Y, to minimize blue curvature
    let Xm = b * Xa - (b - 1) * Za;
    let Ym = g * Ya - (g - 1) * Xa;

    // now move to LMS cone domain
    let LMS = multiplyMatrices(M, [Xm, Ym, Za]);
    return LMStoJzazbz(LMS);
}

function LMStoJzazbz(LMS) {

    const M = [
        [  0.5,       0.5,       0        ],
        [  3.524000, -4.066708,  0.542708 ],
        [  0.199076,  1.096799, -1.295875 ],
    ];
    const c1 = 3424 / 2 ** 12;
    const c2 = 2413 / 2 ** 7;
    const c3 = 2392 / 2 ** 7;
    const n = 2610 / 2 ** 14;
    const p = (1.7 * 2523) / 2 ** 5;    // compared to usual PQ, 1.7 scale
    const d = -0.56;
    const d0 = 1.6295499532821566e-11;  // tiny shift to move black back to 0


    // PQ-encode LMS
    let PQLMS = (
        LMS.map(function (val) {
            let num = c1 + c2 * spow((val / 10000), n);
            let denom = 1 + c3 * spow((val / 10000), n);

            return spow((num / denom), p);
        })
    );

    // calculate Iz az bz
    let [Iz, az, bz] = multiplyMatrices(M, PQLMS);
    // now Jz from Iz
    let Jz = ((1 + d) * Iz) / (1 + d * Iz) - d0;
    return [Jz, az, bz];
}

9.5. Sample code for ICtCp

Rather than first requiring conversion to rec2100-linear, which is how the conversion is defined in [Rec_BT.2100], this sample code proceeds directly from absolute CIE XYZ for compatibility with the other color conversion code.

The 4% crosstalk matrix, and the hue rotation, are also built into the XYZ to LMS step, rather than being applied as three separate steps.

The end result is identical, this just takes fewer steps.

function XYZ_to_ICtCp (XYZ) {
    // convert an array of D65 XYZ to ICtCp

    // The matrix below includes the 4% crosstalk components
    // and is from the procedure in the Dolby "What is ICtCp" paper"
    const M = [
        [  0.3592832590121217,  0.6976051147779502, -0.0358915932320290 ],
        [ -0.1920808463704993,  1.1004767970374321,  0.0753748658519118 ],
        [  0.0070797844607479,  0.0748396662186362,  0.8433265453898765 ],
    ];

    let LMS = multiplyMatrices(M, XYZ.map(v => v * Yw));
    return LMStoICtCp(LMS);
}

function LMStoICtCp (LMS) {

    const c1 = 3424 / 4096;
    const c2 = 2413 / 128;
    const c3 = 2392 / 128;
    const m1 = 2610 / 16384;
    const m2 = 2523 / 32;

    // This matrix includes the Ebner LMS coefficients,
    // the rotation, and the scaling to [-0.5,0.5] range
    // rational terms are from Fröhlich p.97
    // and ITU-R BT.2124-0 pp.2-3
    const M = [
        [  2048 / 4096,   2048 / 4096,       0      ],
        [  6610 / 4096, -13613 / 4096,  7003 / 4096 ],
        [ 17933 / 4096, -17390 / 4096,  -543 / 4096 ],
    ];

    // apply the PQ EOTF
    // values scaled so [0, 10,000] maps to [0, 1]
    // we can't ever be dividing by zero because of the "1 +" in the denominator
    let PQLMS = LMS.map (function (val) {
        let num = c1 + (c2 * ((val / 10000) ** m1));
        let denom = 1 + (c3 * ((val / 10000) ** m1));

        return (num / denom)  ** m2;
    });

    // LMS to IPT, with rotation for Y'C'bC'r compatibility
    return multiplyMatrices(M, PQLMS);
}

function ICtCp_to_XYZ (ICtCp) {
    // convert ICtCp to an array of absolute, D65 XYZ

    const M = [
        [  2.0701522183894223, -1.3263473389671563,  0.2066510476294053 ],
        [  0.3647385209748072,  0.6805660249472273, -0.0453045459220347 ],
        [ -0.0497472075358123, -0.0492609666966131,  1.1880659249923042 ],
    ];

    let LMS = ICtCptoLMS(ICtCp);
    return multiplyMatrices(M, LMS);
}

function ICtCptoLMS (ICtCp) {

    const c1 = 3424 / 4096;
    const c2 = 2413 / 128;
    const c3 = 2392 / 128;
    const im1 = 16384 / 2610;
    const im2 = 32 / 2523;

    const M = [
        [ 0.9999999999999998,  0.0086090370379328,  0.1110296250030260 ],
        [ 0.9999999999999998, -0.0086090370379328, -0.1110296250030259 ],
        [ 0.9999999999999998,  0.5600313357106791, -0.3206271749873188 ],
    ];

    let PQLMS = multiplyMatrices(M, ICtCp);

    // Undo PQ encoding, From BT.2124-0 Annex 2 Conversion 3
    let LMS = PQLMS.map (function (val) {
        let num  = Math.max((val ** im2) - c1, 0);
        let denom = (c2 - (c3 * (val ** im2)));
        return 10000 * ((num / denom) ** im1);
    });

    return LMS;
}

10. Sample code for ΔEITP Color Differences

This section is not normative.

The ΔEITP [Rec_BT.2124] color difference metric may be used to measure the perceptual color difference between two display-referred colors in an HDR or mixed SDR/HDR context, for example in display calibration or gamut and tone mapping.

It is a Euclideam distance in ICtCp color space, scaled such that a ΔEITP of 1.0 represents one just-noticeable difference.

// Calculate deltaE ITP
// scaled root sum of squares
// ITU-R BT.2124-0 Annex 1
/**
 * @param {number[]} reference - Array of ICtCp: I as 0..1, Ct and Cp as -1..1
 * @param {number[]} sample -    Array of ICtCp: I as 0..1, Ct and Cp as -1..1
 * @return {number} How different a color sample is from reference
 */
function deltaEITP (reference, sample) {
    let [I1, Ct1, Cp1] = reference;
	let [I2, Ct2, Cp2] = sample;
	let ΔI = I1 - I2;
	let ΔT = 0.5 * (Ct1 - Ct2);
	let ΔP = Cp1 - Cp2;
	return 720 * Math.sqrt(ΔI ** 2 + ΔT ** 2 + ΔP ** 2);
}

Privacy Considerations

The reason that numerical values of HDR headroom are not directly exposed by the Web platform is because doing so would expose the current viewing conditions, which would be a privacy violation.

Security Considerations

No Security concerns have been raised on this document

Accessibility Considerations

Some individuals may have a sensitivity to very bright colors, so user agents should provide a mechanism to limit the maximum luminance at user option. The toe and knee procedure in section 5.4.1 Mapping to display with limited brightness range of [Rec_BT.2390] is suggested as suitable.

The dynamic-range-limit property could also be set to standard or constrained-high in a user stylesheet.