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] cd/m2 (nits).[ 2] Dolby [ 6] SMPTE [ 1] ITU in Rec. 2100 .[ 7] [ 8] HLG as transfer functions for HDR-TV.[ 7] Dolby Vision ,[ 2] [ 9] HDR10 [ 10] HDR10+ [ 11] [ 12] [ 13] BT.1886 EOTF (i.e. the gamma curve of SDR ), while HLG is compatible.
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.[ 14] 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'}
[
0
,
1
]
{\displaystyle \left[0,1\right]}
F
D
{\displaystyle F_{D}}
2
Y
=
F
D
/
10000
{\displaystyle Y=F_{D}/10000}
Y
=
1
{\displaystyle Y=1}
2 )
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
Standard- and high-dynamic-range color representation
Formats Standards Technology
Compatible codecs
Other
SDR (standard dynamic range)
Standards Technology
.png)
![{\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}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/725527ff67c0fd8d2daa4340826d7b78414951b5)
![{\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}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2ce3c6160b3566f183899b47b1c00e33e6ad54b8)
![{\displaystyle \left[0,1\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c57121c2b6c63c0b2f38eb96b1f7a543b5d1c522)
