RGB Colour Spaces

RGB Triangle

An RGB colour space is defined by:

• Primaries: The chromaticity coordinates (x, y) of red, green, and blue
• White point: The chromaticity of “white” (usually D65)

All colours within the RGB triangle on the chromaticity diagram can be reproduced.

Linear vs Display-Encoded RGB

Linear RGB

Property	Description
Values	Proportional to light intensity
Use	Physical calculations, rendering
Format	Floating point (0.0 to 1.0, or HDR > 1.0)

Display-Encoded RGB (sRGB)

Property	Description
Values	Perceptually uniform (roughly)
Use	Storage and display
Format	Integer (0-255)

Conversion: Linear to Display-Encoded

For sRGB with γ ≈ 2.2:

$R_{\text{linear}} = (R' / 255)^\gamma$

$R' = 255 \cdot R_{\text{linear}}^{1/\gamma}$

Prime notation ($R'$) indicates display-encoded values.

sRGB Standard

Properties

Property	Value
Primaries	ITU-R BT.709
White point	D65
Gamma	≈ 2.2 (piecewise function)
Bit depth	8 bits/channel typical

Piecewise sRGB Transfer Function

Linear segment near zero, gamma for the rest:

$V_{\text{out}} = \begin{cases} 12.92 \cdot V_{\text{linear}} & V_{\text{linear}} \leq 0.00313 \\ 1.055 \cdot V_{\text{linear}}^{1/2.4} - 0.055 & V_{\text{linear}} > 0.00313 \end{cases}$

Major RGB Colour Spaces

ITU-R BT.709 (sRGB)

Primary	x	y
Red	0.64	0.33
Green	0.30	0.60
Blue	0.15	0.06

Standard for HD video and web.

ITU-R BT.2020

Primary	x	y
Red	0.708	0.292
Green	0.170	0.797
Blue	0.131	0.046

Standard for UHD/HDR. Larger gamut than BT.709.

Adobe RGB

Extends green primary compared to sRGB:

• Useful for photography
• Better gamut for natural greens
• Requires colour-managed workflow

CMYK Colour Space

Subtractive Model

Printers use cyan, magenta, yellow inks that absorb light:

Ink	Absorbs	Reflects
Cyan	Red	Green + Blue
Magenta	Green	Red + Blue
Yellow	Blue	Green + Red

Why Black (K)?

Pure CMY mixing gives muddy grey, not true black:

• Inks are not perfect absorbers
• Black ink provides true black
• Black ink is cheaper than CMY overlay
• Text needs crisp black edges

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Summary

• RGB spaces are defined by three primaries and a white point
• Linear RGB for physics; display-encoded for storage
• sRGB (BT.709) is the standard for web and HD
• CMYK is subtractive, used for printing

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Past Paper Questions

2024 Paper 3 Question 3: Explain the difference between linear RGB and sRGB. When would you use each?

2023 Paper 3 Question 4: What are the primaries of sRGB? Why do different RGB spaces have different primaries?

2022 Paper 3 Question 3: Why does CMYK need a black (K) channel?