CIELAB and CIELUV: Uniformity in Color Measurement (Part 3)

CIELAB and CIELUV were introduced by the CIE in 1976 as approximately uniform color spaces. This means that equal numerical distances approximately correspond to equal visual color differences. These models thus represented an improvement over the non-uniform x,y-space in which MacAdam ellipses vary greatly in size and shape.

Purpose of CIELAB and CIELUV

• Reduction of non-uniformity in perception
• Simplification of color difference calculations
• Standardization of color measurement in industry and science

Although both models are usable, CIELAB is most commonly applied in technical and industrial color measurement.

CIELAB: Structure of the Space

CIELAB defines three axes:

• L* – lightness (0 = black, 100 = white)
• a* – red–green axis (positive = red, negative = green)
• b* – yellow–blue axis (positive = yellow, negative = blue)

The axis cross-section (a*, b*) is always centered around a* = 0, b* = 0, which corresponds to the chosen white reference.

Conversion from XYZ to CIELAB

Conditions for the standard formulas: X/Xₙ > 0.008856, Y/Yₙ > 0.008856, Z/Zₙ > 0.008856 (below this threshold, adapted linear formulas apply).

Formulas:

• L* = 116 × f(Y/Yₙ) - 16
• a* = 500 × [f(X/Xₙ) - f(Y/Yₙ)]
• b* = 200 × [f(Y/Yₙ) - f(Z/Zₙ)]

where f(t) = t^(1/3) for t > 0.008856

Here Xₙ, Yₙ, Zₙ are the tristimulus values of the white reference (e.g., D65 or another light source). The white reference thus determines the orientation of the entire CIELAB space.

CIELAB in Polar Coordinates (C*ab and hab)

Many applications prefer saturation and hue over a* and b*. Therefore, polar coordinates are defined:

Chroma (Saturation)

C*ab = √(a*² + b*²)

Hue Angle

hab = arctan(b*/a*)

Characteristics of the hue angle:

• 0° lies on the positive a*-axis
• The angle runs up to 360° (= back to 0°)
• The angle direction is mathematically positive (counterclockwise)

CIELUV: When to Use It?

Although less commonly applied than CIELAB, CIELUV is particularly useful for:

• Lighting technology applications
• Emissive color sources
• Situations where additive color mixing relationships are important

CIELUV works with L*, u* and v* and is designed to ensure uniform steps in chromaticity under specific conditions.

Application of CIELAB in Color Measurement

With CIELAB, it is possible to:

• Numerically specify colors
• Calculate color differences (ΔE*ab, ΔE00 etc.)
• Establish color quality and tolerance limits
• Consistently compare measurements between instruments, light sources, and materials

This makes CIELAB the standard model in:

• Coatings industry
• Plastics production
• Textile
• Graphic industry
• Quality control processes

The next article will further elaborate on color differences in CIELAB and the development of ΔE methods.

---

👉 Want to learn more about CIELAB and color differences? View the courses at kleurenschool.nl

---

Questions about CIELAB or application in quality control? Contact us via info@kleurinstituut.nl or call +31 (0)70 364 98 02.