Perceptual quantizer

The '''perceptual quantizer''' ('''PQ'''), published by SMPTE as '''SMPTE ST 2084,<ref name="SMPTE2084HDR2014">{{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 }}</ref>''' is a transfer function that allows for HDR display by replacing the gamma curve used in SDR.<ref name="DolbyVisionWhitePaper">{{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}}</ref><ref name="Eilertsen">{{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}}</ref><ref name="HDRReportSMPTE2015MESA">{{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}}</ref><ref name="GradingHDR2015studiodaily">{{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}}</ref> Its 0–1 value range represents luminance levels from 0 to 10,000 cd/m2 (nits).<ref name="DolbyVisionWhitePaper" /> It was developed by Dolby<ref name=":52">{{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=}}</ref> and standardized in 2014 by SMPTE<ref name="SMPTE2084HDR2014" /> and also in 2016 by ITU in Rec. 2100.<ref name="Recommendation2100">{{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}}</ref><ref name="ITUAnnouncesHDRJuly2016">{{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}}</ref> ITU specifies the use of PQ or HLG as transfer functions for HDR-TV.<ref name="Recommendation2100" /> PQ is the basis of HDR video formats (such as Dolby Vision,<ref name="DolbyVisionWhitePaper" /><ref name=":332">{{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=}}</ref> HDR10<ref name=":02">{{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=}}</ref> and HDR10+<ref name=":22">{{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=|archive-date=4 September 2019|archive-url=https://web.archive.org/web/20190904110551/https://hdr10plus.org/wp-content/uploads/2019/08/HDR10_WhitePaper.pdf|url-status=dead}}</ref>) and is also used for HDR still picture formats.<ref name=":15">{{Cite web|title=AV1 Image File Format (AVIF)|url=https://aomediacodec.github.io/av1-avif/|access-date=2021-01-31|website=aomediacodec.github.io}}</ref><ref name=":16">{{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}}</ref> PQ is not backward compatible with the BT.1886 EOTF (i.e. the gamma curve of SDR), while HLG is compatible.

480px|right|thumb|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.<ref name="HPATechFebruary2014">{{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}}</ref> A power function (used as EOTFs in standard dynamic range applications) extended to 10000 cd/m2 would have required 15 bits.<ref name="HPATechFebruary2014" />

== Technical details == The '''PQ EOTF''' (electro-optical transfer function) is as follows:<ref name="Recommendation2100" /><ref>{{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}}</ref>

<math>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} </math>

The '''PQ inverse EOTF''' is as follows:

<math>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}</math>

where

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

* <math>c_1 = \frac{3424}{4096} = \frac{107}{128} = 0.8359375 = c_3 - c_2 + 1 </math> * <math>c_2 = 32 \frac{2413}{4096} = \frac{2413}{128} = 18.8515625</math> * <math>c_3 = 32 \frac{2392}{4096} = \frac{2392}{128} = 18.6875</math>

== References == {{Reflist}}

Category:Transfer functions