Perceptual quantizer

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Short description: Transfer function for HDR displays

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]

[math]\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} }[/math]

The PQ inverse EOTF is as follows:

[math]\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} }[/math]

where

  • [math]\displaystyle{ E' }[/math] is the non-linear signal value, in the range [math]\displaystyle{ \left[0, 1 \right] }[/math].
  • [math]\displaystyle{ F_D }[/math] is the displayed luminance in cd/m2
  • [math]\displaystyle{ Y = F_D/10000 }[/math] is the normalized linear displayed value, in the range [0:1] (with [math]\displaystyle{ Y = 1 }[/math] representing the peak luminance of 10000 cd/m2)
  • [math]\displaystyle{ m_1 = \frac{2610}{16384} = \frac{1305}{8192} = 0.1593017578125 }[/math]
  • [math]\displaystyle{ m_2 = 128 \frac{2523}{4096} = \frac{2523}{32} = 78.84375 }[/math]
  • [math]\displaystyle{ c_1 = \frac{3424}{4096} = \frac{107}{128} = 0.8359375 = c_3 - c_2 + 1 }[/math]
  • [math]\displaystyle{ c_2 = 32 \frac{2413}{4096} = \frac{2413}{128} = 18.8515625 }[/math]
  • [math]\displaystyle{ c_3 = 32 \frac{2392}{4096} = \frac{2392}{128} = 18.6875 }[/math]

See also

References

  1. ↑ 1.0 1.1 "ST 2084:2014". IEEE Xplore. doi:10.5594/SMPTE.ST2084.2014. ISBN 978-1-61482-829-7. https://ieeexplore.ieee.org/document/7291452. 
  2. ↑ 2.0 2.1 2.2 Dolby Laboratories. "Dolby Vision Whitepaper". http://www.dolby.com/us/en/technologies/dolby-vision/dolby-vision-white-paper.pdf. 
  3. ↑ Eilertsen, Gabriel (2018). The high dynamic range imaging pipeline. Linköping University Electronic Press. pp. 30–31. ISBN 9789176853023. https://books.google.com/books?id=LCtbDwAAQBAJ&pg=PA30. Retrieved 22 August 2020. 
  4. ↑ Chris Tribbey (10 July 2015). "HDR Special Report: SMPTE Standards Director: No HDR Format War, Yet". MESA. http://mesalliance.org/blog/me-daily/2015/07/10/smpte-standards-director-no-hdr-format-war-yet/. 
  5. ↑ Bryant Frazer (9 June 2015). "Colorist Stephen Nakamura on Grading Tomorrowland in HDR". studiodaily. http://www.studiodaily.com/2015/06/colorist-stephen-nakamura-grading-tomorrowland-dolby-vision/. 
  6. ↑ Dolby. "Dolby Vision Whitepaper - An introduction to Dolby Vision". https://professional.dolby.com/siteassets/pdfs/dolby-vision-whitepaper_an-introduction-to-dolby-vision_0916.pdf. 
  7. ↑ 7.0 7.1 7.2 "BT.2100 : Image parameter values for high dynamic range television for use in production and international programme exchange". International Telecommunication Union. 4 July 2016. https://www.itu.int/rec/R-REC-BT.2100. 
  8. ↑ "ITU announces BT.2100 HDR TV standard". Rasmus Larsen. 5 July 2016. https://www.flatpanelshd.com/news.php?subaction=showfull&id=1467719709. 
  9. ↑ Dolby. "Dolby Vision Profiles and Levels Version 1.3.2 - Specification". https://professional.dolby.com/siteassets/content-creation/dolby-vision-for-content-creators/dolbyvisionprofileslevels_v1_3_2_2019_09_16.pdf. 
  10. ↑ Consumer Technology Association (27 August 2015). "CEA Defines 'HDR Compatible' Displays". https://www.cta.tech/News/Press-Releases/2015/August/CEA-Defines-‘HDR-Compatible’-Displays.aspx. 
  11. ↑ HDR10+ Technologies, LLC (4 September 2019). "HDR10+ System Whitepaper". https://hdr10plus.org/wp-content/uploads/2019/08/HDR10_WhitePaper.pdf. 
  12. ↑ "AV1 Image File Format (AVIF)". https://aomediacodec.github.io/av1-avif/. 
  13. ↑ "Canon EOS-1D X Mark III Review". https://www.the-digital-picture.com/Reviews/Canon-EOS-1D-X-Mark-III.aspx. 
  14. ↑ 14.0 14.1 Adam Wilt (20 February 2014). "HPA Tech Retreat 2014 – Day 4". DV Info Net. http://www.dvinfo.net/article/trip_reports/hpa-tech-retreat-2014-day-4.html. 
  15. ↑ "BT.2124 : Objective metric for the assessment of the potential visibility of colour differences in television". https://www.itu.int/rec/R-REC-BT.2124/en. 



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