CIE XYZ Colour Space

Design Goals

CIE XYZ (1931) was designed with specific objectives:

1. Abstract from specific display primaries
2. All colour matching functions positive (no negative light)
3. The Y value approximates luminance

XYZ Values

Given a light spectrum $L(\lambda)$, compute XYZ:

$X = \int L(\lambda) \bar{x}(\lambda) d\lambda$

$Y = \int L(\lambda) \bar{y}(\lambda) d\lambda$

$Z = \int L(\lambda) \bar{z}(\lambda) d\lambda$

where $\bar{x}$, $\bar{y}$, $\bar{z}$ are the CIE colour matching functions.

Properties of XYZ

Property	Description
All positive	All physically realisable colours have X, Y, Z ≥ 0
Y = Luminance	The Y value approximates perceived brightness
Device-independent	Not tied to any specific display technology
Imaginary primaries	The X, Y, Z primaries cannot be physically realised

Chromaticity Coordinates

To separate colour from intensity, normalise XYZ:

$x = \frac{X}{X + Y + Z}, \quad y = \frac{Y}{X + Y + Z}, \quad z = \frac{Z}{X + Y + Z}$

Note: $x + y + z = 1$, so we only need $(x, y)$ to specify chromaticity.

Why Chromaticity?

• Removes luminance information
• Describes “colour” independent of brightness
• Useful for comparing colours at different intensities

The Chromaticity Diagram

Regions

Region	Description
Curved edge	Pure wavelengths (spectral colours)
Straight line (bottom)	Non-spectral purples (red + blue mixtures)
Interior	Mixtures of wavelengths
Points outside	Not physically realisable

Reading the Diagram

• White point: Near the centre (depends on illuminant)
• Saturation: Colours near the edge are more saturated
• Hue: Position around the diagram

Colour Gamuts

A gamut is the range of colours a device can reproduce, shown as a triangle on the chromaticity diagram.

Common Gamuts

Gamut	Use	Size
sRGB	Standard displays, web	Small
Adobe RGB	Photography, printing	Larger green region
DCI-P3	Digital cinema	Medium-large
Rec. 2020	HDR, ultra-HD	Very large

Why XYZ Matters

Standard Reference

• XYZ is the “lingua franca” of colour science
• All other RGB spaces are defined by transforms to/from XYZ
• Enables colour communication between different devices

Advantages

• No single RGB gamut covers all colours
• XYZ captures all visible colours
• Transformations preserve the physical meaning

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Summary

• CIE XYZ is a device-independent colour space designed in 1931
• Y approximates luminance; X and Z describe chromaticity
• Chromaticity coordinates (x, y) separate colour from intensity
• All visible colours fall within the chromaticity diagram

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Past Paper Questions

2024 Paper 3 Question 3: What is the CIE XYZ colour space? Why were specific design goals chosen for X, Y, and Z?

2023 Paper 3 Question 4: Explain the purpose of chromaticity coordinates.

2022 Paper 3 Question 3: What does the curved edge of the chromaticity diagram represent?