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 has been 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.

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

References

1. "ST 2084:2014". IEEE Xplore. doi:10.5594/SMPTE.ST2084.2014. ISBN 978-1-61482-829-7. from the original on 24 July 2020. Retrieved 24 July 2020.
2. Dolby Laboratories. "Dolby Vision Whitepaper" (PDF). (PDF) from the original on 4 June 2016. Retrieved 24 August 2016.
3. Eilertsen, Gabriel (2018). The high dynamic range imaging pipeline. Linköping University Electronic Press. pp. 30–31. ISBN 9789176853023. from the original on 23 January 2021. Retrieved 22 August 2020.
4. Chris Tribbey (10 July 2015). . MESA. Archived from the original on 13 September 2015. Retrieved 21 September 2015.
5. Bryant Frazer (9 June 2015). "Colorist Stephen Nakamura on Grading Tomorrowland in HDR". studiodaily. from the original on 13 September 2015. Retrieved 21 September 2015.
6. Dolby. "Dolby Vision Whitepaper - An introduction to Dolby Vision" (PDF). Retrieved 14 February 2021.
7. "BT.2100 : Image parameter values for high dynamic range television for use in production and international programme exchange". International Telecommunication Union. 4 July 2016. from the original on 27 April 2019. Retrieved 25 January 2021.
8. "ITU announces BT.2100 HDR TV standard". Rasmus Larsen. 5 July 2016. from the original on 10 July 2016. Retrieved 26 July 2016.
9. Dolby. (PDF). Archived from the original (PDF) on 29 September 2020. Retrieved 12 February 2021.
10. Consumer Technology Association (27 August 2015). "CEA Defines 'HDR Compatible' Displays". from the original on 11 June 2019. Retrieved 12 February 2021.
11. HDR10+ Technologies, LLC (4 September 2019). "HDR10+ System Whitepaper" (PDF). Retrieved 12 February 2021.
12. "AV1 Image File Format (AVIF)". aomediacodec.github.io. Retrieved 2021-01-31.
13. "Canon EOS-1D X Mark III Review". The-Digital-Picture.com. Retrieved 2021-02-15.
14. Adam Wilt (20 February 2014). "HPA Tech Retreat 2014 – Day 4". DV Info Net. from the original on 1 November 2014. Retrieved 5 November 2014.
15. "BT.2124 : Objective metric for the assessment of the potential visibility of colour differences in television". www.itu.int. Retrieved 2021-04-29.