Perceptual quantizer

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]

F D = E O T F [ E ′ ] = 10000 ( max [ ( E ′ 1 / m 2 − c 1 ) , 0 ] c 2 − c 3 ⋅ E ′ 1 / m 2 ) 1 / m 1 {\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:

E ′ = E O T F − 1 [ F D ] = ( c 1 + c 2 ⋅ Y m 1 1 + c 3 ⋅ Y m 1 ) m 2 {\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

  • E ′ {\displaystyle E'} is the non-linear signal value, in the range [ 0 , 1 ] {\displaystyle \left[0,1\right]} .
  • F D {\displaystyle F_{D}} is the displayed luminance in cd/m2
  • Y = F D / 10000 {\displaystyle Y=F_{D}/10000} is the normalized linear displayed value, in the range [0:1] (with Y = 1 {\displaystyle Y=1} representing the peak luminance of 10000 cd/m2)
  • m 1 = 2610 16384 = 1305 8192 = 0.1593017578125 {\displaystyle m_{1}={\frac {2610}{16384}}={\frac {1305}{8192}}=0.1593017578125}
  • m 2 = 128 2523 4096 = 2523 32 = 78.84375 {\displaystyle m_{2}=128{\frac {2523}{4096}}={\frac {2523}{32}}=78.84375}
  • c 1 = 3424 4096 = 107 128 = 0.8359375 = c 3 − c 2 + 1 {\displaystyle c_{1}={\frac {3424}{4096}}={\frac {107}{128}}=0.8359375=c_{3}-c_{2}+1}
  • c 2 = 32 2413 4096 = 2413 128 = 18.8515625 {\displaystyle c_{2}=32{\frac {2413}{4096}}={\frac {2413}{128}}=18.8515625}
  • c 3 = 32 2392 4096 = 2392 128 = 18.6875 {\displaystyle c_{3}=32{\frac {2392}{4096}}={\frac {2392}{128}}=18.6875}

See also

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.
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