HDR Tone Mapping

The Dynamic Range Problem

Scene vs Display

Source	Luminance Range
Real world	$10^{-6}$ to $10^6$ cd/m² (12+ orders)
Human vision (adapted)	~10,000:1
SDR display	~100:1 to 1,000:1
HDR display	~1,000:1 to 10,000:1

The challenge: How to represent full scene brightness on a limited display?

Scene-Referred vs Display-Referred

Term	Meaning
Scene-referred	Linear colours representing actual scene luminance (HDR)
Display-referred	Colours ready for a specific display (SDR)

Tone mapping bridges these two domains.

What is Tone Mapping?

Tone mapping transforms image colours from scene-referred to display-referred:

• Reduces dynamic range to fit the display
• Preserves important visual details
• Often combined with display encoding (gamma correction)

Why Do We Need It?

1. Reduce dynamic range for limited displays
2. Customise look (colour grading, artistic intent)
3. Simulate human vision (dark adaptation for night scenes)
4. Adapt to viewing conditions (ambient light)
5. Make rendered images look more realistic

Basic Tone Mapping

Simple Exposure Adjustment

$R_d = \frac{R_s}{L_s \cdot \text{exposure}}$

Problems:

• No contrast compression
• Only works for moderate dynamic range
• Clipping occurs if range too large

Tone Curves

A tone curve maps input luminance to output:

Region	Purpose
Linear (slope 1)	Preserves midtones
Shoulder	Compresses highlights
Toe	Lifts shadows (optional)

The ideal tone curve has slope 1 everywhere—but display limitations require compression.

Global vs Local Tone Mapping

Global Tone Mapping

Same curve applied to every pixel:

Advantages	Disadvantages
Simple, fast	May lose local detail
Consistent
Reproducible

Local Tone Mapping

Different curves for different image regions:

Advantages	Disadvantages
Preserves local contrast	Can cause halos at edges
More detail preservation	More complex

HDR vs SDR Standards

SDR (Standard Dynamic Range)

Property	Value
Colour space	ITU-R BT.709 (sRGB)
Dynamic range	~6 stops
Bit depth	8-10 bits
Transfer function	Gamma ≈ 2.2

HDR (High Dynamic Range)

Property	Value
Colour space	ITU-R BT.2020 (wider gamut)
Transfer function	PQ or HLG
Bit depth	10-12 bits
Peak brightness	Up to 10,000 cd/m²

PQ (Perceptual Quantiser)

Designed for HDR:

• Based on human contrast sensitivity
• Peak luminance: 10,000 cd/m²
• Approximates perceptual uniformity

HLG (Hybrid Log-Gamma)

Backwards compatible with SDR:

• Relative brightness (no absolute reference)
• SDR displays show reasonable image
• HDR displays show full range

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Summary

• Tone mapping compresses HDR scene values to display range
• Scene-referred (HDR) → Tone mapping → Display-referred (SDR)
• Global methods apply one curve; local methods vary by region
• HDR standards (PQ, HLG) support higher brightness ranges

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Past Paper Questions

2024 Paper 3 Question 3: Explain the difference between scene-referred and display-referred colour. When is each used?

2023 Paper 3 Question 3: Compare global and local tone mapping approaches.

2022 Paper 3 Question 3: What is the dynamic range problem in graphics?