Hybrid log–gamma

HLG is designed to be better-suited for television broadcasting, where the metadata required for other HDR formats is not backward compatible with non-HDR displays, consumes additional bandwidth, and may also become out-of-sync or damaged in transmission. HLG defines a non-linear optical-electro transfer function, in which the lower half of the signal values use a gamma curve and the upper half of the signal values use a logarithmic curve.[20][21] In practice, the signal is interpreted as normal by standard-dynamic-range displays (albeit capable of displaying more detail in highlights), but HLG-compatible displays can correctly interpret the logarithmic portion of the signal curve to provide a wider dynamic range.[22][23][24] In contrast with the other HDR formats it does not use metadata.[25]

The HLG transfer function is backward compatible with SDR's gamma curve. However, HLG is commonly used with Rec. 2020 color primaries which produce a de-saturated image with visible hue shifts on non-compatible devices.[26] HLG is therefore backward compatible with SDR-UHDTV and will show color distortion on common SDR devices that only support Rec. 709 color primaries.[26]

HLG defines a nonlinear transfer function in which the lower half of the signal values use a gamma curve and the upper half of the signal values use a logarithmic curve.[4][27]

HLG reference OETF is as follows (as defined in ARIB STD-B67):

$${\displaystyle E'={\begin{cases}r\,{\sqrt {E}}\ &0\leq E\leq 1,\!\\a\ln(E-b)+c&1<E\end{cases}}}$$

or as follows (as defined in Rec. 2100):[5]

$${\displaystyle E'={\begin{cases}{\sqrt {3E}}\ &0\leq E\leq {\frac {1}{12}},\!\\a\ln(12E-b)+c&{\frac {1}{12}}<E\leq 1\end{cases}}}$$

where

• E is the linear light signal normalized by the reference white level in the range ${\displaystyle \left[0,12\right]}$ in ARIB STD-B67 and in the range ${\displaystyle \left[0,1\right]}$ in Rec. 2100.
• E' is the resulting nonlinear signal
• r is the reference white level and has a signal value of 0.5
• and the constants a, b, and c are defined as a = 0.17883277, b = 1 - 4a = 0.28466892, and c = 0.5 - a ln(4a) = 0.55991073

The signal value is 0.5 for the reference white level while the signal value for 1 has a relative luminance that is 12 times higher than the reference white level.[27] ARIB STD-B67 has a nominal range of 0 to 12.[28] HLG uses a logarithmic curve for the upper half of the signal values due to Weber's law.[27]

HLG reference OOTF is as follows:[5]

$${\displaystyle {\begin{cases}F_{D}=OOTF[E]=\alpha Y_{S}^{\gamma -1}E\!\\R_{D}=\alpha Y_{S}^{\gamma -1}R_{S}\!\\G_{D}=\alpha Y_{S}^{\gamma -1}G_{S}\!\\B_{D}=\alpha Y_{S}^{\gamma -1}B_{S}\!\\Y_{S}=0.2627R_{S}+0.6780G_{S}+0.0593B_{S}\end{cases}}}$$

where

• ${\displaystyle F_{D}}$ is the luminance of a displayed linear component ${\displaystyle R_{D},G_{D},B_{D}}$ in cd/m².
• ${\displaystyle E}$ is a signal for each colour component {Rs, Gs, Bs} proportional to scene linear light normalized to the range ${\displaystyle \left[0,1\right]}$.
• ${\displaystyle Y_{S}}$ is the normalized linear scene luminance.
• ${\displaystyle \alpha }$ is the variable for user gain in cd/m². It represents LW, the nominal peak luminance of a display for achromatic pixels.
• ${\displaystyle \gamma }$ is the system gamma. ${\displaystyle \gamma }$ = 1.2 at the nominal display peak luminance of 1000 cd/m².

HLG reference EOTF is as follows:[5]

${\displaystyle F_{D}=OOTF[OETF^{-1}[max(0,(1-\beta )E'+\beta )]]}$

where

• ${\displaystyle F_{D}}$ is the luminance of a displayed linear component ${\displaystyle R_{D},G_{D},B_{D}}$ in cd/m².
• ${\displaystyle E'}$ is the non-linear electrical signal ${\displaystyle R',G',B'}$ in the range ${\displaystyle \left[0,1\right]}$.
• ${\displaystyle \beta ={\sqrt {3(L_{B}/L_{W})^{1/\gamma }}}}$ is the variable for user black level lift.
• ${\displaystyle L_{W}}$ is nominal peak luminance of the display in cd/m² for achromatic pixels.
• ${\displaystyle L_{B}}$ is the display luminance for black in cd/m².

HLG does not need to use metadata since it is compatible with both SDR displays and HDR displays.[1][3] HLG can be used with displays of different brightness in a wide range of viewing environments.[3]

The dynamic range that can be perceived by the human eye in a single image is around 14 stops.[27] An SDR video display with a 2.4 gamma curve and a bit depth of 8-bits per sample can display a range of about 6 stops without visible banding.[27] Professional SDR video displays with a bit depth of 10-bits per sample extend that range to about 10 stops.[27] When HLG is displayed on a 2,000 cd/m² display with a bit depth of 10-bits per sample it can display a range of 200,000:1 or 17.6 stops without visible banding.[27]

HLG increases the dynamic range of the video compared to a conventional gamma curve by using a logarithmic curve for the upper half of the signal values.[27] HLG also increases the dynamic range by not including the linear part of the conventional gamma curve used by Rec. 601 and Rec. 709.[29] The linear part of the conventional gamma curve was used to limit camera noise in low light video but is no longer needed with HDR cameras.[29]

HLG is supported in Rec. 2100 with a nominal peak luminance of 1,000 cd/m² and a system gamma value that can be adjusted depending on background luminance.[5][30]

HLG is supported in HEVC with a formula that is mathematically equivalent to ARIB STD-B67 but has a nominal range of 0 to 1 instead of 0 to 12:[28]

$${\displaystyle V={\begin{cases}{\sqrt {3}}\cdot L_{c}^{0.5}&{\frac {1}{12}}\geq L_{c}\geq 0,\!\\a\cdot \ln(12L_{c}-b)+c&1\geq L_{c}>{\frac {1}{12}}\end{cases}}}$$

where

• L_c has a nominal range of 0 to 1 and V is the resulting nonlinear signal
• the constants a, b, and c are defined as a = 0.17883277, b = 1 - 4a = 0.28466892, and c = 0.5 - a ln(4a) = 0.55991073

• Dynamic range
• Gamma correction
• High-dynamic-range rendering
• High-dynamic-range imaging
• High-dynamic-range video

• ARIB STD-B67
• T. Borer and A. Cotton, A "Display Independent" High Dynamic Range Television System, BBC Research & Development White Paper WHP 309, September 2015