perceptual quantizer

The perceptual quantizer (PQ), published by SMPTE as SMPTE ST 2084,{{cite news|title=ST 2084:2014|publisher=IEEE Xplore|url=https://ieeexplore.ieee.org/document/7291452|url-status=dead|access-date=24 July 2020|archive-url=https://web.archive.org/web/20200724211453/https://ieeexplore.ieee.org/document/7291452|archive-date=24 July 2020|doi=10.5594/SMPTE.ST2084.2014|isbn=978-1-61482-829-7 }} is a transfer function that allows for HDR display by replacing the gamma curve used in SDR.{{cite web|author=Dolby Laboratories|title=Dolby Vision Whitepaper|url=http://www.dolby.com/us/en/technologies/dolby-vision/dolby-vision-white-paper.pdf|url-status=live|archive-url=https://web.archive.org/web/20160604120415/http://www.dolby.com/us/en/technologies/dolby-vision/dolby-vision-white-paper.pdf|archive-date=4 June 2016|access-date=24 August 2016}}{{cite book|last1=Eilertsen|first1=Gabriel|url=https://books.google.com/books?id=LCtbDwAAQBAJ&pg=PA30|title=The high dynamic range imaging pipeline|date=2018|publisher=Linköping University Electronic Press|isbn=9789176853023|pages=30–31|access-date=22 August 2020|archive-url=https://web.archive.org/web/20210123115652/https://books.google.com/books?id=LCtbDwAAQBAJ&pg=PA30|archive-date=23 January 2021|url-status=live}}{{cite news|author=Chris Tribbey|date=10 July 2015|title=HDR Special Report: SMPTE Standards Director: No HDR Format War, Yet|publisher=MESA|url=http://mesalliance.org/blog/me-daily/2015/07/10/smpte-standards-director-no-hdr-format-war-yet/|url-status=dead|access-date=21 September 2015|archive-url=https://web.archive.org/web/20150913044219/http://mesalliance.org/blog/me-daily/2015/07/10/smpte-standards-director-no-hdr-format-war-yet/|archive-date=13 September 2015}}{{cite news|author=Bryant Frazer|date=9 June 2015|title=Colorist Stephen Nakamura on Grading Tomorrowland in HDR|publisher=studiodaily|url=http://www.studiodaily.com/2015/06/colorist-stephen-nakamura-grading-tomorrowland-dolby-vision/|url-status=live|access-date=21 September 2015|archive-url=https://web.archive.org/web/20150913064202/http://www.studiodaily.com/2015/06/colorist-stephen-nakamura-grading-tomorrowland-dolby-vision/|archive-date=13 September 2015}} It is capable of representing luminance level up to 10000 cd/m² (nits) and down to 0.0001 nits. It was developed by Dolby{{Cite web|last=Dolby|date=|title=Dolby Vision Whitepaper - An introduction to Dolby Vision|url=https://professional.dolby.com/siteassets/pdfs/dolby-vision-whitepaper_an-introduction-to-dolby-vision_0916.pdf|access-date=14 February 2021|website=}} and standardized in 2014 by SMPTE and also in 2016 by ITU in Rec. 2100.{{cite news|last=|first=|date=4 July 2016|title=BT.2100 : Image parameter values for high dynamic range television for use in production and international programme exchange|work=|publisher=International Telecommunication Union|url=https://www.itu.int/rec/R-REC-BT.2100|url-status=live|access-date=25 January 2021|archive-url=https://web.archive.org/web/20190427004028/https://www.itu.int/rec/R-REC-BT.2100|archive-date=27 April 2019}}{{cite news|date=5 July 2016|title=ITU announces BT.2100 HDR TV standard|publisher=Rasmus Larsen|url=https://www.flatpanelshd.com/news.php?subaction=showfull&id=1467719709|url-status=live|access-date=26 July 2016|archive-url=https://web.archive.org/web/20160710015254/http://www.flatpanelshd.com/news.php?subaction=showfull&id=1467719709|archive-date=10 July 2016}} 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,{{Cite web|last=Dolby|date=|title=Dolby Vision Profiles and Levels Version 1.3.2 - Specification|url=https://professional.dolby.com/siteassets/content-creation/dolby-vision-for-content-creators/dolbyvisionprofileslevels_v1_3_2_2019_09_16.pdf|url-status=dead|archive-url=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|archive-date=29 September 2020|access-date=12 February 2021|website=}} HDR10{{Cite web|last=Consumer Technology Association|date=27 August 2015|title=CEA Defines 'HDR Compatible' Displays|url=https://www.cta.tech/News/Press-Releases/2015/August/CEA-Defines-‘HDR-Compatible’-Displays.aspx|url-status=live|archive-url=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|archive-date=11 June 2019|access-date=12 February 2021|website=}} and HDR10+{{Cite web|last=HDR10+ Technologies, LLC|date=4 September 2019|title=HDR10+ System Whitepaper|url=https://hdr10plus.org/wp-content/uploads/2019/08/HDR10_WhitePaper.pdf|access-date=12 February 2021|website=}}) and is also used for HDR still picture formats.{{Cite web|title=AV1 Image File Format (AVIF)|url=https://aomediacodec.github.io/av1-avif/|access-date=2021-01-31|website=aomediacodec.github.io}}{{Cite web|title=Canon EOS-1D X Mark III Review|url=https://www.the-digital-picture.com/Reviews/Canon-EOS-1D-X-Mark-III.aspx|access-date=2021-02-15|website=The-Digital-Picture.com}} PQ is not backward compatible with the BT.1886 EOTF (i.e. the gamma curve of SDR), while HLG is compatible.

File:PQ EOTF (SMPTE2084).png

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.{{cite news|author=Adam Wilt|date=20 February 2014|title=HPA Tech Retreat 2014 – Day 4|publisher=DV Info Net|url=http://www.dvinfo.net/article/trip_reports/hpa-tech-retreat-2014-day-4.html|url-status=live|access-date=5 November 2014|archive-url=https://web.archive.org/web/20141101213814/http://www.dvinfo.net/article/trip_reports/hpa-tech-retreat-2014-day-4.html|archive-date=1 November 2014}} 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:{{Cite web|title=BT.2124 : Objective metric for the assessment of the potential visibility of colour differences in television|url=https://www.itu.int/rec/R-REC-BT.2124/en|access-date=2021-04-29|website=www.itu.int}}

$F_D = EOTF[E'] = 10000 \left( \frac{\max[ (E'^{1/m_2} - c_1), 0]} {c_2 - c_3 \cdot E' ^ {1/m_2} } \right) ^ {1/ m_1}$

The PQ inverse EOTF is as follows:

$E' = EOTF^{-1}[F_D] = \left( \frac{c_1 + c_2 \cdot Y^{m_1}}{1 + c_3 \cdot Y^{m_1} } \right)^{m_2}$

where

$E'$ is the non-linear signal value, in the range $\left[0, 1 \right]$ .
$F_D$ is the displayed luminance in cd/m²
$Y = F_D/10000$ is the normalized linear displayed value, in the range [0:1] (with $Y = 1$ representing the peak luminance of 10000 cd/m²)
$m_1 = \frac{2610}{16384} = \frac{1305}{8192} = 0.1593017578125$
$m_2 = 128 \frac{2523}{4096} = \frac{2523}{32} = 78.84375$

$c_1 = \frac{3424}{4096} = \frac{107}{128} = 0.8359375 = c_3 - c_2 + 1$
$c_2 = 32 \frac{2413}{4096} = \frac{2413}{128} = 18.8515625$
$c_3 = 32 \frac{2392}{4096} = \frac{2392}{128} = 18.6875$

References

Category:Transfer functions

perceptual quantizer

Technical details

See also

References