ICtCp

IC_TC_P,ICtCp,orITPis acolor representation formatspecified in theRec. ITU-R BT.2100standard that is used as a part of thecolor image pipelineinvideoanddigital photographysystems forhigh dynamic range(HDR) andwide color gamut(WCG) imagery.It was developed byDolby Laboratoriesfrom theIPTcolor space by Ebner and Fairchild.The format is derived from an associatedRGBcolor spaceby acoordinate transformationthat includes two matrix transformations and an intermediate nonlinear transfer function that is informally known asgamma pre-correction.The transformation produces three signals calledI,C_T,andC_P.TheIC_TC_Ptransformation can be used withRGBsignals derived from either theperceptual quantizer(PQ) orhybrid log–gamma(HLG) nonlinearity functions, but is most commonly associated with the PQ function (which was also developed by Dolby).

TheI( "intensity" ) component is alumacomponent that represents the brightness of the video, andC_TandC_Pare blue-yellow (named fromtritanopia) and red-green (named fromprotanopia)chromacomponents.Ebner also used IPT as short for "Image Processing Transform".

TheIC_TC_Pcolor representation scheme is conceptually related to theLMScolor space,as the color transformation fromRGBtoIC_TC_Pis defined by first convertingRGBtoLMSwith a 3×3 matrix transformation, then applying the nonlinearity function, and then converting the nonlinear signals toIC_TC_Pusing another 3×3 matrix transformation.IC_TC_Pwas defined as aYCCdigital format with support for 4:4:4, 4:2:2 and 4:2:0chroma subsamplinginCTA-861-H (that means that in limited range 10 bit mode 0, 1, 2, 3, 1020, 1021, 1022, 1023 values are reserved).

Derivation

IC_TC_Pis defined by Rec. 2100 as being derived from linearRGBas follows:

1. CalculateLMSfrom BT.2100 RGB:${\begin{bmatrix}L\\M\\S\end{bmatrix}}={\frac {1}{4096}}{\begin{bmatrix}1688&2146&262\\683&2951&462\\99&309&3688\end{bmatrix}}{\begin{bmatrix}R\\G\\B\end{bmatrix}}$
2. Normalize the LMS by a non-linearity:
   • If thePQ transfer functionis used:${\begin{bmatrix}L'\\M'\\S'\end{bmatrix}}=EOTF_{PQ}^{-1}\left({\begin{bmatrix}L\\M\\S\end{bmatrix}}\right)$
   • If theHLG transfer functionis used:${\begin{bmatrix}L'\\M'\\S'\end{bmatrix}}=OETF_{HLG}\left({\begin{bmatrix}L\\M\\S\end{bmatrix}}\right)$
3. CalculateIC_TC_P:
   • for PQ:${\begin{bmatrix}I\\C_{T}\\C_{P}\end{bmatrix}}={\frac {1}{4096}}{\begin{bmatrix}2048&2048&0\\6610&-13613&7003\\17933&-17390&-543\end{bmatrix}}{\begin{bmatrix}L'\\M'\\S'\end{bmatrix}}$
   • forHLG:${\begin{bmatrix}I\\C_{T}\\C_{P}\end{bmatrix}}={\frac {1}{4096}}{\begin{bmatrix}2048&2048&0\\3625&-7465&3840\\9500&-9212&-288\end{bmatrix}}{\begin{bmatrix}L'\\M'\\S'\end{bmatrix}}$

All three above mentioned matrixes were derived (only the first 2 are documented derivations) 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 decodingIC_TC_Pmatrixes are specified in ITU-T Series H Supplement 18.

IC_TC_Pis 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 relateduniform color spaceITP used in ΔE_ITP(Rec. 2124) scales C_Tby 0.5 to restore uniformity.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 toIC_TC_P,Ebner & FairchildIPTcolor appearance model(1998), has a mostly similar transformation pipeline of input → LMS → nonlinearity → IPT.The differences are that it defines its input to the more generalCIEXYZtristimulus color space and as a result has a more conventional Hunt-Pointer-Estevez (for D65) matrix for LMS. The nonlinearity is afixed gamma of 0.43,quite close to the one used by RLAB. The second matrix here is slightly different from theIC_TC_Pmatrix, mainly in that is also considers S (blue cone) for intensity, butIC_TC_Phas 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:

1. Calculate LMS (seeLMS color space § Hunt, RLABfor D65, slightly different):${\begin{bmatrix}L\\M\\S\end{bmatrix}}={\begin{bmatrix}0.4002&0.7075&-0.0807\\-0.2280&1.1500&0.0612\\0&0&0.9184\end{bmatrix}}{\begin{bmatrix}X\\Y\\Z\end{bmatrix}}$
2. Nonlinearity (L'M'S'): For each of L, M, S componentsapply a power function:$X'={\begin{cases}X^{0.43}&{\text{for }}X\geq 0\\-(-X)^{0.43}&{\text{for }}X<0\end{cases}}$
3. ${\begin{bmatrix}I\\P\\T\end{bmatrix}}={\begin{bmatrix}0.4000&0.4000&0.2000\\4.4550&-4.8510&0.3960\\0.8056&0.3572&-1.1628\end{bmatrix}}{\begin{bmatrix}L'\\M'\\S'\end{bmatrix}}$

IPTPQc2

IPTPQc2is another related colorspace used byDolby Visionprofile 5 BL+RPU (without EL).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 asIPTPQc2/IPT,as the matrix is in fact the same as in the 1998 IPT paper, just in inverse representation.Documentation on this format is scarce due to its proprietary nature, but a patenton the "IPT-PQ" (perceptually quantized IPT) color spaceseems 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.The matrix is as follows:

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

Note the matrix inversion used and an error was made in patent in 1091 numberof 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.

The second step, the dynamic range adjustment modeling (reshaping), is also defined in the patent.

It is used byDisney+,Apple TV+andNetflix.

Decoder of IPTPQc2 with reshaping and MMR (but no NLQ and dynamic metadata) is available in libplacebo.

Support for decoding all stages was added inmpv.

Characteristics

IC_TC_Phas near constant luminance.Thecorrelation coefficientbetween encodedIand true luminance is 0.998, much higher than the 0.819 forYC_BC_R.An improved constant luminance versusYC_BC_Ris an advantage for color processing operations such aschroma subsamplingandgamut mappingwhere only the color difference information is changed.

IC_TC_Palso improves hue linearity compared withYC_BC_R,which helps with compression performance and color volume mapping.Adaptive reshaping can further provide a 10% improvement on compression performance.

Improvement in luminance and hue uniformity make scaledIC_TC_Pa practical color space for calculating color differences (ΔE_ITP), as introduced by ITU-R Rec. BT.2124.

In terms ofCIEDE2000color quantization error, 10-bitIC_TC_Pwould be equivalent to 11.5 bitYC_BC_R.

Uses

IC_TC_Pis supported in theHEVCvideo coding standard.It is also a digital YCC format and can be signaled inEDID's Colorimetry block as part of CTA-861-H.