Perceptually Uniform Colour Spaces

The Problem with RGB and XYZ

Distance in RGB or XYZ space does not correspond to perceived colour difference.

MacAdam Ellipses

Experiments showed that colours within an ellipse appear indistinguishable. Ellipses are:

• Different sizes in different regions of the chromaticity diagram
• Not circular (distance varies with direction)
• Much larger in green region than in blue

This means equal distances in XYZ do not correspond to equal perceptual differences.

CIE Lab* (Lab)

Design

Lab was designed to be approximately perceptually uniform:

Channel	Meaning	Range
L*	Lightness	0 (black) to 100 (white)
a*	Green (−) to Red (+)	Approximately −128 to +128
b*	Blue (−) to Yellow (+)	Approximately −128 to +128

Conversion from XYZ

$L^* = 116 f(Y/Y_n) - 16$

$a^* = 500 [f(X/X_n) - f(Y/Y_n)]$

$b^* = 200 [f(Y/Y_n) - f(Z/Z_n)]$

where:

$f(t) = \begin{cases} t^{1/3} & t > \delta^3 \\ \frac{t}{3\delta^2} + \frac{4}{29} & t \leq \delta^3 \end{cases}$

and $\delta = 6/29$, $X_n$, $Y_n$, $Z_n$ are the white point values.

Properties

• Euclidean distance ≈ perceptual colour difference
• Lightness separated from chromaticity
• Device-independent

CIE Luv* (Luv)

Design

Another approximately perceptually uniform space:

Channel	Meaning
L*	Lightness (same formula as Lab)
u’	Chromaticity coordinate
v’	Chromaticity coordinate

Advantages over Lab

• Uses u’v’ chromaticity (improved uniformity)
• Better for additive colour mixing
• Simpler chromaticity diagram projection

Colour Difference Formulas

ΔE (Delta E)

Measures perceptual difference between two colours:

$\Delta E_{ab}^* = \sqrt{(L_1^* - L_2^*)^2 + (a_1^* - a_2^*)^2 + (b_1^* - b_2^*)^2}$

ΔE Value	Perceptibility
< 1.0	Not perceptible
1-2	Perceptible through close observation
2-10	Perceptible at a glance
> 10	Definitely different colours

Use Cases

Space	Best For
Lab/Luv	Colour difference calculations, colour picker interfaces
RGB	Displays, rendering
XYZ	Device-independent specification, conversions

Munsell System

Historical Context

Albert H. Munsell (1905) created a perceptually organised system:

Coordinate	Meaning
Hue	Colour type (R, Y, G, B, P)
Value	Lightness (0-10)
Chroma	Saturation (0 to maximum)

Properties

• Perceptually uniform spacing between samples
• Highly irregular shape (not spherical)
• Basis for HSV/HSL models

HSV and HLS

User-friendly spaces derived from RGB:

Space	Coordinates
HSV	Hue (0-360°), Saturation (0-100%), Value (0-100%)
HLS	Hue (0-360°), Lightness (0-100%), Saturation (0-100%)

Not perceptually uniform, but intuitive for colour selection interfaces.

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Summary

• RGB and XYZ distances don’t match perceived differences
• Lab and Luv are approximately perceptually uniform
• ΔE measures perceptual colour difference
• Munsell system inspired modern colour picker interfaces

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Past Paper Questions

2024 Paper 3 Question 3: Why is RGB not perceptually uniform? What problem does this cause?

2023 Paper 3 Question 4: Explain the purpose of the Lab colour space. What do L*, a*, and b* represent?

2022 Paper 3 Question 3: What is ΔE and how is it used?