Perceptual quantizer explained

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. It was developed by Dolby^[6] and standardized in 2014 by SMPTE 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. PQ is the basis of HDR video formats (such as Dolby Vision,^[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.

Technical details

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

F _{D} = EOTF[E'] = 10000 \left( (max [ (E' ^{1 /m _{2}} - c _{1),} 0 ])/(c _{2} - c _{3} ⋅ E' ^{1 /m _{2}}) \right) ^{1 / m _{1}}

The PQ inverse EOTF is as follows:

E' = EOTF ^{-1} [F _{D]} = \left( (c _{1} + c _{2} ⋅ Y ^{m _{1}})/(1 + c _{3} ⋅ Y ^{m _{1}}) \right) ^{m _{2}}

where

E' is the non-linear signal value, in the range \left[ 0 , 1 \right] .F _{D} is the displayed luminance in cd/m²Y = F _{D/10000} is the normalized linear displayed value, in the range [0:1] (with Y = 1 representing the peak luminance of 10000 cd/m²)m _{1} = (2610)/(16384) = (1305)/(8192) = 0 . 1593017578125 m _{2} = 128 (2523)/(4096) = (2523)/(32) = 78 . 84375 c _{1} = (3424)/(4096) = (107)/(128) = 0 . 8359375 = c _{3} - c _{2} + 1 c _{2} = 32 (2413)/(4096) = (2413)/(128) = 18 . 8515625 c _{3} = 32 (2392)/(4096) = (2392)/(128) = 18 . 6875

See also

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

Notes and References

1. News: ST 2084:2014. IEEE Xplore. dead. 24 July 2020. https://web.archive.org/web/20200724211453/https://ieeexplore.ieee.org/document/7291452. 24 July 2020. 10.5594/SMPTE.ST2084.2014. 978-1-61482-829-7 .
2. Web site: Dolby Laboratories. Dolby Vision Whitepaper. live. https://web.archive.org/web/20160604120415/http://www.dolby.com/us/en/technologies/dolby-vision/dolby-vision-white-paper.pdf. 4 June 2016. 24 August 2016.
3. Book: Eilertsen. Gabriel. The high dynamic range imaging pipeline. 2018. Linköping University Electronic Press. 9789176853023. 30–31. 22 August 2020. https://web.archive.org/web/20210123115652/https://books.google.com/books?id=LCtbDwAAQBAJ&pg=PA30. 23 January 2021. live.
4. News: Chris Tribbey. 10 July 2015. HDR Special Report: SMPTE Standards Director: No HDR Format War, Yet. MESA. dead. 21 September 2015. https://web.archive.org/web/20150913044219/http://mesalliance.org/blog/me-daily/2015/07/10/smpte-standards-director-no-hdr-format-war-yet/. 13 September 2015.
5. News: Bryant Frazer. 9 June 2015. Colorist Stephen Nakamura on Grading Tomorrowland in HDR. studiodaily. live. 21 September 2015. https://web.archive.org/web/20150913064202/http://www.studiodaily.com/2015/06/colorist-stephen-nakamura-grading-tomorrowland-dolby-vision/. 13 September 2015.
6. Web site: Dolby. Dolby Vision Whitepaper - An introduction to Dolby Vision. 14 February 2021.
7. News: 4 July 2016. BT.2100 : Image parameter values for high dynamic range television for use in production and international programme exchange. International Telecommunication Union. live. 25 January 2021. https://web.archive.org/web/20190427004028/https://www.itu.int/rec/R-REC-BT.2100. 27 April 2019.
8. News: 5 July 2016. ITU announces BT.2100 HDR TV standard. Rasmus Larsen. live. 26 July 2016. https://web.archive.org/web/20160710015254/http://www.flatpanelshd.com/news.php?subaction=showfull&id=1467719709. 10 July 2016.
9. Web site: Dolby. Dolby Vision Profiles and Levels Version 1.3.2 - Specification. dead. 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. 29 September 2020. 12 February 2021.
10. Web site: Consumer Technology Association. 27 August 2015. CEA Defines 'HDR Compatible' Displays. live. https://web.archive.org/web/20190611151620/https://www.cta.tech/News/Press-Releases/2015/August/CEA-Defines-%E2%80%98HDR-Compatible%E2%80%99-Displays.aspx. 11 June 2019. 12 February 2021.
11. Web site: HDR10+ Technologies, LLC. 4 September 2019. HDR10+ System Whitepaper. 12 February 2021.
12. Web site: AV1 Image File Format (AVIF). 2021-01-31. aomediacodec.github.io.
13. Web site: Canon EOS-1D X Mark III Review. 2021-02-15. The-Digital-Picture.com.
14. News: Adam Wilt. 20 February 2014. HPA Tech Retreat 2014 – Day 4. DV Info Net. live. 5 November 2014. https://web.archive.org/web/20141101213814/http://www.dvinfo.net/article/trip_reports/hpa-tech-retreat-2014-day-4.html. 1 November 2014.
15. Web site: BT.2124 : Objective metric for the assessment of the potential visibility of colour differences in television. 2021-04-29. www.itu.int.