Perceptual quantizer

The perceptual quantizer (PQ), published by SMPTE as SMPTE ST 2084,^[1] is a transfer function that allows for HDR display by replacing the gamma curve used in SDR.^[2][3][4][5] It is capable of representing luminance level up to 10000 cd/m² (nits) and down to 0.0001 nits.^[2] It was developed by Dolby^[6] and standardized in 2014 by SMPTE^[1] and also in 2016 by ITU in Rec. 2100.^[7][8] ITU specifies the use of PQ or HLG as transfer functions for HDR-TV.^[7] PQ is the basis of HDR video formats (such as Dolby Vision,^[2][9] HDR10^[10] and HDR10+^[11]) and is also used for HDR still picture formats.^[12][13] PQ is not backward compatible with the BT.1886 EOTF (i.e. the gamma curve of SDR), while HLG is compatible.

Chart showing the PQ electro-optical transfer function.

PQ is a non-linear transfer function based on the human visual perception of banding and is able to produce no visible banding in 12 bits.^[14] A power function (used as EOTFs in standard dynamic range applications) extended to 10000 cd/m² would have required 15 bits.^[14]

Technical details

The PQ EOTF (electro-optical transfer function) is as follows:^[7][15]

${\displaystyle F_{D}=EOTF[E']=10000\left({\frac {\max[(E'^{1/m_{2}}-c_{1}),0]}{c_{2}-c_{3}\cdot E'^{1/m_{2}}}}\right)^{1/m_{1}}}$

The PQ inverse EOTF is as follows:

${\displaystyle E'=EOTF^{-1}[F_{D}]=\left({\frac {c_{1}+c_{2}\cdot Y^{m_{1}}}{1+c_{3}\cdot Y^{m_{1}}}}\right)^{m_{2}}}$

where

• ${\displaystyle E'}$ is the non-linear signal value, in the range ${\displaystyle \left[0,1\right]}$.
• ${\displaystyle F_{D}}$ is the displayed luminance in cd/m²
• ${\displaystyle Y=F_{D}/10000}$ is the normalized linear displayed value, in the range [0:1] (with ${\displaystyle Y=1}$ representing the peak luminance of 10000 cd/m²)
• ${\displaystyle m_{1}={\frac {2610}{16384}}={\frac {1305}{8192}}=0.1593017578125}$
• ${\displaystyle m_{2}=128{\frac {2523}{4096}}={\frac {2523}{32}}=78.84375}$

• ${\displaystyle c_{1}={\frac {3424}{4096}}={\frac {107}{128}}=0.8359375=c_{3}-c_{2}+1}$
• ${\displaystyle c_{2}=32{\frac {2413}{4096}}={\frac {2413}{128}}=18.8515625}$
• ${\displaystyle c_{3}=32{\frac {2392}{4096}}={\frac {2392}{128}}=18.6875}$

See also

• Transfer functions in imaging
• High-dynamic-range television