Perceptual quantizer

Key takeaways

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

Reference excerpt

The perceptual quantizer (PQ), published by SMPTE as SMPTE ST 2084, is a transfer function that allows for HDR display by replacing the gamma curve used in SDR. Its 0–1 value range represents luminance levels from 0 to 10,000 cd/m2 (nits). It was developed by Dolby and standardized in 2014 by SMPTE and also in 2016 by ITU in Rec. 2100. ITU specifies the use of PQ or HLG as transfer functions for HDR-TV. PQ is the basis of HDR video formats (such as Dolby Vision, HDR10 and HDR10+) and is also used for HDR still picture formats. 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. A power function (used as EOTFs in standard dynamic range applications) extended to 10000 cd/m2 would have required 15 bits.

Technical details The PQ EOTF (electro-optical transfer function) is as follows:

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}

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Perceptual quantizer

Start with the simplest possible case. Write down what Perceptual quantizer claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, 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 Perceptual quantizer 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 Perceptual quantizer 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 Perceptual quantizer

In research: Perceptual quantizer appears in mathematics 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 Perceptual quantizer 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: Perceptual quantizer is common in secondary-school and first-year university syllabi. It links to neighbouring topics Transfer functions, so understanding it makes those chapters shorter.
In everyday life: Look for Perceptual quantizer 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 Perceptual quantizer in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Perceptual quantizer 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 Perceptual quantizer out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Perceptual quantizer in simple terms?

The perceptual quantizer (PQ), published by SMPTE as SMPTE ST 2084, is a transfer function that allows for HDR display by replacing the gamma curve used in SDR. Its 0–1 value range represents luminance levels from 0 to 10,000 cd/m2 (nits).

Why does Perceptual quantizer matter?

Because it connects several mathematics 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 Perceptual quantizer?

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 Perceptual quantizer.