# Perceptual quantizer

(Redirected from 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.

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)
• ${\displaystyle m_{1}={\frac {2610}{16384}}={\frac {1305}{8192}}=0.1593017578125}$
• ${\displaystyle m_{2}=128{\frac {2523}{4096}}={\frac {2523}{32}}=78.84375}$
• ${\displaystyle c_{1}={\frac {3424}{4096}}={\frac {107}{128}}=0.8359375=c_{3}-c_{2}+1}$
• ${\displaystyle c_{2}=32{\frac {2413}{4096}}={\frac {2413}{128}}=18.8515625}$
• ${\displaystyle c_{3}=32{\frac {2392}{4096}}={\frac {2392}{128}}=18.6875}$

## References

1. ^ a b "ST 2084:2014". IEEE Xplore. doi:10.5594/SMPTE.ST2084.2014. ISBN 978-1-61482-829-7. Archived from the original on 24 July 2020. Retrieved 24 July 2020.
2. ^ a b c Dolby Laboratories. "Dolby Vision Whitepaper" (PDF). Archived (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. Archived from the original on 23 January 2021. Retrieved 22 August 2020.
4. ^ Chris Tribbey (10 July 2015). "HDR Special Report: SMPTE Standards Director: No HDR Format War, Yet". 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. Archived 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. ^ a b c "BT.2100 : Image parameter values for high dynamic range television for use in production and international programme exchange". International Telecommunication Union. 4 July 2016. Archived from the original on 27 April 2019. Retrieved 25 January 2021.
8. ^ "ITU announces BT.2100 HDR TV standard". Rasmus Larsen. 5 July 2016. Archived from the original on 10 July 2016. Retrieved 26 July 2016.
9. ^ Dolby. "Dolby Vision Profiles and Levels Version 1.3.2 - Specification" (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". Archived 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.{{cite web}}: CS1 maint: numeric names: authors list (link)
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. ^ a b Adam Wilt (20 February 2014). "HPA Tech Retreat 2014 – Day 4". DV Info Net. Archived 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.