Hybrid log–gamma

Key takeaways

Hybrid log–gamma belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Hybrid log–gamma to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Hybrid log–gamma from memory before moving on to harder problems.

Reference excerpt

Hybrid log–gamma (HLG) is a transfer function jointly developed by the BBC and NHK for high dynamic range (HDR) display. It is backward compatible with the transfer function of SDR (the gamma curve). It was approved as ARIB STD-B67 by the Association of Radio Industries and Businesses (ARIB). It is also defined in ATSC 3.0, Digital Video Broadcasting (DVB) UHD-1 Phase 2, and International Telecommunication Union (ITU) Rec. 2100.

HLG is an HDR format that uses the HLG transfer function, BT.2020 color primaries and a bitdepth of 10-bit. HLG was designed to be backward compatible with SDR UHDTV. However, HLG is not intended to be fully backward compatible with traditional SDR displays that cannot interpret BT.2020 colorimetry. Both HLG transfer function and the HLG format are royalty-free. The backward compatibility allows them to be used with existing transmission standards when the receiver is compatible with the BT.2020 colour container, reducing complexity and cost for both equipment manufacturers and content distributors. They are supported by HDMI 2.0b, HEVC, VP9, and H.264/MPEG-4 AVC, and are used by video services such as BBC iPlayer, DirecTV, Freeview Play, and YouTube.

Description 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. 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. In contrast with the other HDR formats it does not use metadata. 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. HLG is therefore backward compatible with SDR-UHDTV and will show color distortion on common SDR devices that only support Rec. 709 color primaries.

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

E ′ = { r E 0 ≤ E ≤ 1 , a ln ⁡ ( E − b ) + c 1 < E {\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):

E ′ = { 3 E 0 ≤ E ≤ 1 12 , a ln ⁡ ( 12 E − b ) + c 1 12 < E ≤ 1 {\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 [ 0 , 12 ] {\displaystyle \left[0,12\right]} in ARIB STD-B67 and in the range [ 0 , 1 ] {\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. ARIB STD-B67 has a nominal range of 0 to 12. HLG uses a logarithmic curve for the upper half of the signal values due to Weber's law. HLG reference OOTF is as follows:

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Hybrid log–gamma

Start with the simplest possible case. Write down what Hybrid log–gamma claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Hybrid log–gamma before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Hybrid log–gamma ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Hybrid log–gamma

In research: Hybrid log–gamma appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Hybrid log–gamma in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Hybrid log–gamma is common in secondary-school and first-year university syllabi. It links to neighbouring topics High dynamic range, Television technology, Ultra-high-definition television, so understanding it makes those chapters shorter.
In everyday life: Look for Hybrid log–gamma outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Hybrid log–gamma in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Hybrid log–gamma means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Hybrid log–gamma out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hybrid log–gamma in simple terms?

Hybrid log–gamma (HLG) is a transfer function jointly developed by the BBC and NHK for high dynamic range (HDR) display. It is backward compatible with the transfer function of SDR (the gamma curve).

Why does Hybrid log–gamma matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Hybrid log–gamma?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Hybrid log–gamma.