HLGcurves

HLGcurves refer to the transfer curves used by Hybrid Log-Gamma (HLG), an HDR standard developed by BBC and NHK and specified in ITU-R BT.2100. The curves describe how scene luminance is mapped to encoded video values (the opto-electronic transfer function, OETF) and how displays revert those values back to luminance (the electro-optical transfer function, EOTF). HLG is designed to deliver backward compatibility with standard dynamic range (SDR) displays without requiring metadata, while still providing improved dynamic range on HDR televisions and devices.

The HLG transfer function is implemented as a piecewise curve that blends a gamma-like response at low to mid luminance with a logarithmic response at higher luminance. This dual nature helps preserve SDR compatibility when content is viewed on SDR displays and provides a controlled roll-off for bright highlights on HDR displays. A small, common parameter throughout implementations is a 0.178 constant that shapes the logarithmic portion, along with a white level reference Lw that sets the transition point between the two regions. In normalized form, and with Lw as the reference white level, the forward OETF and its inverse EOTF are typically described as:

- For L <= Lw: OETF C = 0.5 * sqrt(L / Lw)

- For L > Lw: OETF C = 0.5 + a * ln(L / Lw), with a ≈ 0.178

- Inverse (display side): L = Lw * (2C)^2 for C <= 0.5, and L = Lw * exp((C - 0.5) / a) for C > 0.5

HLGcurves are widely used in broadcast and streaming workflows, enabling HDR viewing with broad compatibility across devices without the need for metadata. See also HDR, ITU-R BT.2100, and ST 2084 (PQ).