View source for ICtCp

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'''''IC<sub>T</sub>C<sub>P</sub>''''', '''''ICtCp''''', or '''''ITP''''' is a [[color representation format]] specified in the [[Rec. 2100|Rec. ITU-R BT.2100]] standard that is used as a part of the [[color image pipeline]] in [[video]] and [[digital photography]] systems for [[high dynamic range]] (HDR) and [[wide color gamut]] (WCG) imagery.<ref name="Recommendation2100">{{cite web|url=https://www.itu.int/rec/R-REC-BT.2100/|title=BT.2100-2: Image parameter values for high dynamic range television for use in production and international programme exchange|date=July 2018|website=[[ITU-R]]}}</ref> It was developed by [[Dolby Laboratories]]<ref name="DolbyICtCpPaperApril2016Dolby" /> from the '''''IPT''''' color space by Ebner and Fairchild.<ref name=":0">{{Cite journal|last=Ebner|first=Fritz|date=1998-07-01|title=Derivation and modelling hue uniformity and development of the IPT color space|url=https://scholarworks.rit.edu/theses/2858|journal=Theses}}</ref><ref name=":1">F.Ebner, M.D.Fairchild, Development and testing of a color space (IPT) with improved hue uniformity. In: Proceedings of The Sixth Color Imaging Conference, 8-13, 1998 </ref>  The format is derived from an associated ''[[RGB]]'' [[color space]] by a [[coordinate transformation]] that includes two matrix transformations and an intermediate nonlinear transfer function that is informally known as [[gamma correction|gamma pre-correction]]. The transformation produces three signals called ''I'', ''C<sub>T</sub>'', and ''C<sub>P</sub>''. The ''IC<sub>T</sub>C<sub>P</sub>'' transformation can be used with ''RGB'' signals derived from either the [[Perceptual Quantizer|perceptual quantizer]] (PQ) or [[hybrid log–gamma]] (HLG) nonlinearity functions, but is most commonly associated with the PQ function (which was also developed by Dolby).

The ''I'' ("intensity") component is a [[Luma (video)|luma]] component that represents the brightness of the video, and ''C<sub>T</sub>'' and ''C<sub>P</sub>'' are blue-yellow (named from [[Color blindness|tritanopia]]) and red-green (named from [[Color blindness|protanopia]]) [[chrominance|chroma]] components.<ref name="DolbyICtCpPaperApril2016Dolby">{{cite news|url=https://www.dolby.com/us/en/technologies/dolby-vision/ICtCp-white-paper.pdf|title=What Is ICtCp – Introduction?|access-date=2016-04-20|publisher=Dolby}}</ref> Ebner also used IPT as short for "Image Processing Transform".<ref name=":0" />

The ''IC<sub>T</sub>C<sub>P</sub>'' color representation scheme is conceptually related to the [[LMS color space|''LMS'' color space]], as the color transformation from ''RGB'' to ''IC<sub>T</sub>C<sub>P</sub>'' is defined by first converting ''RGB'' to ''LMS'' with a 3×3 matrix transformation, then applying the nonlinearity function, and then converting the nonlinear signals to ''IC<sub>T</sub>C<sub>P</sub>'' using another 3×3 matrix transformation.<ref name="SMPTE2084HDR2014">{{cite web|title=ST 2084:2014|url=https://www.smpte.org/standards/document-index/st|publisher=[[Society of Motion Picture and Television Engineers]]}}</ref> IC<sub>T</sub>C<sub>P</sub> was defined as a [[YCbCr|YCC]] digital format with support for 4:4:4, 4:2:2 and 4:2:0 [[chroma subsampling]] in [[Extended Display Identification Data|CTA-861]]-H (that means that in limited range 10 bit mode 0, 1, 2, 3, 1020, 1021, 1022, 1023 values are reserved).<ref>{{Cite web|title=A DTV Profile for Uncompressed High Speed Digital Interfaces (ANSI/CTA-861-H)|url=https://shop.cta.tech/products/a-dtv-profile-for-uncompressed-high-speed-digital-interfaces-cta-861-h|access-date=2021-03-11|website=Consumer Technology Association®|language=en}}</ref>
[[File:ICtCp top view.png|500x500px|frameless|right]]

==Derivation==
''IC<sub>T</sub>C<sub>P</sub>'' is defined by [[Rec. 2100]] as being derived from linear ''RGB'' as follows:<ref name=Recommendation2100 />

# Calculate [[LMS color space|''LMS'']] from BT.2100 RGB:<math>
\begin{bmatrix}
L\\M\\S
\end{bmatrix}
=
\frac{1}{4096}
\begin{bmatrix}
1688 & 2146 & 262\\
683 & 2951 & 462\\
99 & 309 & 3688
\end{bmatrix}
\begin{bmatrix}
R\\G\\B
\end{bmatrix}
</math>
# Normalize the LMS by a non-linearity:
#* If the [[Perceptual quantizer|PQ transfer function]] is used:<math>
\begin{bmatrix}
L'\\M'\\S'
\end{bmatrix}
=
EOTF_{PQ}^{-1}
\left(
\begin{bmatrix}
L\\M\\S
\end{bmatrix}
\right)
</math>
#* If the [[Hybrid log–gamma|HLG transfer function]] is used:<math>
\begin{bmatrix}
L'\\M'\\S'
\end{bmatrix}
=
OETF_{HLG}
\left(
\begin{bmatrix}
L\\M\\S
\end{bmatrix}
\right)
</math>
#Calculate ''IC<sub>T</sub>C<sub>P</sub>'': 
#*for PQ:<math>
\begin{bmatrix}
I\\C_T\\C_P
\end{bmatrix}
=
\frac{1}{4096}
\begin{bmatrix}
2048 & 2048 & 0\\
6610 & -13613 & 7003\\
17933 & -17390 & -543
\end{bmatrix}
\begin{bmatrix}
L'\\M'\\S'
\end{bmatrix}
</math>
#*for [[opto-electronic transfer function|HLG]]: <math>
\begin{bmatrix}
I\\C_T\\C_P
\end{bmatrix}
=
\frac{1}{4096}
\begin{bmatrix}
2048 & 2048 & 0\\
3625 & -7465 & 3840\\
9500 & -9212 & -288
\end{bmatrix}
\begin{bmatrix}
L'\\M'\\S'
\end{bmatrix}
</math>
All three above mentioned matrixes were derived (only the first 2 are documented derivations<ref name="DolbyICtCpPaperApril2016Dolby" />) from the matrixes in IPT. The HLG matrix can be derived the same way as the PQ matrix, with the only difference being the scaling of the chroma rows. The inverted decoding ''IC<sub>T</sub>C<sub>P</sub>'' matrixes are specified in ITU-T Series H Supplement 18.<ref>{{Cite web|title=ITU-T Recommendation database|url=https://www.itu.int/ITU-T/recommendations/rec.aspx?id=13441&lang=en|access-date=2020-11-14|website=ITU|language=en|hdl-access=free|hdl=11.1002/1000/13441}}</ref>

IC<sub>T</sub>C<sub>P</sub> is defined such that the entire BT.2020 space fits into the range [0, 1] for I and [-0.5, +0.5] for the two chroma components. The related [[uniform color space]] ITP used in ΔE<sub>ITP</sub> (Rec. 2124) scales C<sub>T</sub> by 0.5 to restore uniformity.<ref name=bt2124>{{cite web |title=BT.2124: Objective metric for the assessment of the potential visibility of colour differences in television |url=https://www.itu.int/rec/R-REC-BT.2124/en |website=www.itu.int |access-date=24 June 2020}}</ref> There is support for ICtCp in zimg (including zimg as part of FFmpeg) and color-science, for both HLG and PQ.

=== In IPT ===
The preceder to ''IC<sub>T</sub>C<sub>P</sub>'', Ebner & Fairchild '''IPT''' [[color appearance model]] (1998), has a mostly similar transformation pipeline of input &rarr; LMS &rarr; nonlinearity &rarr; IPT.<ref name=":0" /><ref>{{Cite journal |last1=Ebner |first1=Fritz |last2=Fairchild |first2=Mark D. |date=1998-01-01 |title=Development and Testing of a Color Space (IPT) with Improved Hue Uniformity |url=https://www.ingentaconnect.com/content/ist/cic/1998/00001998/00000001/art00003#expand/collapse |journal=Color and Imaging Conference |volume=1998 |issue=1 |pages=8–13|doi=10.2352/CIC.1998.6.1.art00003 |s2cid=46137693 }}{{Closed access}}</ref> The differences are that it defines its input to the more general [[CIEXYZ]] tristimulus color space and as a result has a more conventional Hunt-Pointer-Estevez (for D65) matrix for LMS. The nonlinearity is a [[Gamma correction#Power law for video display|fixed gamma of 0.43]], quite close to the one used by RLAB. The second matrix here is slightly different from the ''IC<sub>T</sub>C<sub>P</sub>'' matrix, mainly in that is also considers S (blue cone) for intensity, but ''IC<sub>T</sub>C<sub>P</sub>'' has also Rotation matrix (to align skin tones) and Scalar matrix (scaled to fit the full BT.2020 gamut inside the -0.5 to 0.5 region) multiplied with this matrix:<ref name="DolbyICtCpPaperApril2016Dolby" /><ref>{{cite journal |last1=Xue |first1=Yang |title=Uniform color spaces based on CIECAM02 and IPT color difference equations |journal=RITTheses |date=1 November 2008 |url=https://scholarworks.rit.edu/theses/2866/ |page=7}}</ref>

# Calculate LMS (see {{section link|LMS color space|Hunt, RLAB}} for D65, slightly different<ref name=":0" />): <math>
\begin{bmatrix}
L\\M\\S
\end{bmatrix}
=
\begin{bmatrix}
0.4002 & 0.7075 & -0.0807 \\ -0.2280 & 1.1500 & 0.0612 \\ 0 & 0 & 0.9184
\end{bmatrix}
\begin{bmatrix}
X\\Y\\Z
\end{bmatrix} </math>
# Nonlinearity (L'M'S'): For each of L, M, S components [[Gamma correction|apply a power function]]: <math>X' = \begin{cases}
X^{0.43} &\text{for } X \ge 0\\
-(-X)^{0.43} &\text{for } X < 0
\end{cases}
</math>
# <math>
\begin{bmatrix}
I\\P\\T
\end{bmatrix}
=
\begin{bmatrix}
0.4000 & 0.4000  & 0.2000\\
4.4550 & -4.8510 & 0.3960\\
0.8056 &  0.3572 & -1.1628
\end{bmatrix}
\begin{bmatrix}
L'\\M'\\S'
\end{bmatrix}
</math>

=== IPTPQc2 ===



'''IPTPQc2''' is another related colorspace used by [[Dolby Vision]] profile 5 BL+RPU (without EL).<ref name=":3322">{{Cite web|last=Dolby|date=|title=Dolby Vision Profiles and Levels Version 1.3.2 - Specification|url=https://professional.dolby.com/siteassets/content-creation/dolby-vision-for-content-creators/dolbyvisionprofileslevels_v1_3_2_2019_09_16.pdf|url-status=dead|archive-url=https://web.archive.org/web/20200929014520/https://professional.dolby.com/siteassets/content-creation/dolby-vision-for-content-creators/dolbyvisionprofileslevels_v1_3_2_2019_09_16.pdf|archive-date=29 September 2020|access-date=27 April 2021|website=}}</ref> The "c2" in the name means a cross talk matrix is used with c = 2%. It uses full range quantization (0-1023 for 10 bit video, no values reserved). It is also often referred to as '''IPTPQc2/IPT''', as the matrix is in fact the same as in the 1998 IPT paper, just in inverse representation.<ref>{{cite web|url=https://github.com/mpv-player/mpv/issues/7326#issuecomment-592221831|title=Dolby Vision with wrong colors · Issue #7326 · mpv-player/mpv|website=GitHub|language=en}}</ref> Documentation on this format is scarce due to its proprietary nature, but a patent<ref>{{Cite patent|title=Signal reshaping and coding in the ipt-pq color space|country=US|number=20180131938A1|pubdate=2018-05-10|gdate=2019-11-19|assign1=Dolby Laboratories Licensing Corp|invent1=Lu, Taoran|invent2=Pu, Fangjun|invent3=Yin, Peng|invent4=Chen, Tao|status=patent}}</ref> on the "IPT-PQ" (perceptually quantized IPT) color space {{speculation inline |text=seems to describe how Dolby changed the domain to PQ by changing the traditional power function from 1998 IPT paper to PQ function for each of LMS components.| reason=It either describes this or it doesn't.  Someone fluent in patent-ese (aka obfuscated over-broad claims on 200 variants of the same thing) needs to read this and provide a definitive "describes" vs. a "seems to"|date=December 2023}}  The matrix is as follows:

<math>
\begin{bmatrix}
I\\P\\T
\end{bmatrix}_{PQC2}
=
\left(
\frac{1}{8192}
\begin{bmatrix}
8192 & 799 & 1681\\
8192 & -933 & 1091\\
8192 & 267 & -5545
\end{bmatrix}
\right)^{-1}
\begin{bmatrix}
L'\\M'\\S'
\end{bmatrix}
</math>

Note the matrix inversion used and an error was made in patent in 1091 number{{Clarify| reason=What does this mean?|date=September 2021}} of the matrix (the matrix after inversion is correct in patent). In addition, this format has no nonlinearity, and is assumed to be BT.2020-based.<ref>{{cite web |title=testing-av/testing-video: IPTPQc2.java |url=https://github.com/testing-av/testing-video/blob/9256b779f7721bd3dbdceedab7c65b6f64bbab79/core/src/main/java/band/full/video/dolby/IPTPQc2.java |website=GitHub |language=en}}</ref>

The second step, the dynamic range adjustment modeling (reshaping<ref>{{Cite web|title=Description of the reshaper parameters derivation process in ETM reference software|url=http://phenix.it-sudparis.eu/jct/doc_end_user/current_document.php?id=10318|access-date=2020-11-14|website=phenix.it-sudparis.eu}}</ref>), is also defined in the patent. 

It is used by [[Disney+]], [[Apple TV+]] and [[Netflix]].{{Citation needed|date=September 2021}}

Decoder of IPTPQc2 with reshaping and MMR (but no NLQ and dynamic metadata) is available in libplacebo.<ref>{{Cite web|title=colorspace: add support for Dolby Vision (!207) · Merge requests · VideoLAN / libplacebo|url=https://code.videolan.org/videolan/libplacebo/-/merge_requests/207|access-date=2021-12-11|website=GitLab|date=29 November 2021 |language=en}}</ref>

Support for decoding all stages was added in [[Mpv (media player)|mpv]].

==Characteristics==
''IC<sub>T</sub>C<sub>P</sub>'' has near constant luminance.<ref name="chromaSub">{{cite web|title=Subsampling in ICtCp vs YCbCr|url=https://www.dolby.com/us/en/technologies/dolby-vision/ictcp_vs_ycbcr-subsampling.pdf|url-status=dead|archive-url=https://web.archive.org/web/20181013172410/https://www.dolby.com/us/en/technologies/dolby-vision/ictcp_vs_ycbcr-subsampling.pdf|archive-date=13 October 2018|publisher=Dolby Laboratories, Inc.}}</ref> The [[Pearson correlation coefficient|correlation coefficient]] between encoded ''I'' and true luminance is 0.998, much higher than the 0.819 for ''YC<sub>B</sub>C<sub>R</sub>''. An improved constant luminance versus ''YC<sub>B</sub>C<sub>R</sub>'' is an advantage for color processing operations such as [[chroma subsampling]] and [[gamut mapping]] where only the color difference information is changed.<ref name=DolbyICtCpPaperApril2016Dolby/>

''IC<sub>T</sub>C<sub>P</sub>'' also improves hue linearity compared with ''YC<sub>B</sub>C<sub>R</sub>'', which helps with compression performance and color volume mapping.<ref name="compression">{{cite web|url=https://www.zte.com.cn/global/about/magazine/zte-communications/2016/1/en_214/448972|title=ITP Colour Space and Its Compression Performance for High Dynamic Range and Wide Colour Gamut Video Distribution|publisher=ZTE}}</ref><ref>{{cite book|last1=Cotton|first1=Andrew|title=SMPTE 2018|last2=Thompson|first2=Simon|year=2018|isbn=978-1-61482-960-7|pages=10–11|chapter=Scene-light conversions: the key to enabling live HDR production|doi=10.5594/M001822|s2cid=188363770 }}</ref> Adaptive reshaping can further provide a 10% improvement on compression performance.<ref name="EPFL">{{cite journal |last1=Perrin |first1=Anne-Flore |last2=Rerabek |first2=Martin |last3=Husak |first3=Walt |last4=Ebrahimi |first4=Touradj |title=ICtCp Versus Y'CbCr: Evaluation of ICtCp Color Space and an Adaptive Reshaper for HDR and WCG |journal=IEEE Consumer Electronics Magazine |date=May 2018 |volume=7 |issue=3 |pages=38–47 |url=https://infoscience.epfl.ch/record/222897#record-files-collapse-header |url-access=subscription |doi=10.1109/MCE.2017.2714696|s2cid=4800923 }}</ref>

Improvement in luminance and hue uniformity make scaled ''IC<sub>T</sub>C<sub>P</sub>'' a practical color space for calculating color differences ([[Color difference#Rec. ITU-R BT.2124 or ΔEITP|ΔE<sub>ITP</sub>]]), as introduced by ITU-R Rec. BT.2124.<ref name=bt2124/>

In terms of [[CIEDE2000]] color quantization error, 10-bit ''IC<sub>T</sub>C<sub>P</sub>'' would be equivalent to 11.5 bit ''YC<sub>B</sub>C<sub>R</sub>''.<ref name=DolbyICtCpPaperApril2016Dolby/>

==Uses==
''IC<sub>T</sub>C<sub>P</sub>'' is supported in the [[HEVC]] video coding standard.<ref name=HEVCFebruary2016JCTVC-W1003>{{cite news |title=Draft text for ICtCp support in HEVC (Draft 1) |author=Peng Yin |author2=Chad Fogg |author3=Gary J. Sullivan |author4=Alexis Michael Tourapis |publisher=JCT-VC |url=http://phenix.it-sudparis.eu/jct/doc_end_user/current_document.php?id=10478 |date=2016-03-19 |access-date=2016-04-20}}</ref> It is also a digital YCC format and can be signaled in [[Extended Display Identification Data|EDID]]'s Colorimetry block as part of CTA-861-H.

==References==
{{reflist}}

{{Color space}}

[[Category:Color space]]
[[Category:High dynamic range]]
[[Category:Ultra-high-definition television]]