CIELAB and LCH Explained

Lab is more than a coordinate transform. It is a working model for perceptual spacing, gamut boundaries, palette ramps, tolerancing, and the practical handoff between legacy CIE workflows and modern Oklab/OKLCh tools. This workbench exposes those tradeoffs in one place.

CIE XYZ is rigorous, but it is not perceptually uniform. Two XYZ points the same Euclidean distance apart can look very different in perceived color difference. Worse, the non-uniformity is itself non-uniform - dense regions sit near the green edge of the chromaticity diagram while the entire blue corner is spread across a small visual interval.

Designers, paint companies, and quality-control engineers needed a coordinate system where equal numerical distance meant equal perceived difference. In 1976 the CIE published two candidates: CIELAB (often written CIE L*a*b*) and CIELUV. CIELAB became the workhorse for surface color; CIELUV survived in television and some video applications. This article focuses on CIELAB.

The Lab transform works in two steps. First, divide X, Y, and Z by the corresponding values of the reference white, normalizing the input. Second, apply a non-linear cube-root function (with a small linear segment near zero), then combine to produce three coordinates.

Applied to each channel:

Read these three lines carefully. L* depends only on the Y channel - it is a perceptually scaled lightness function. a* compares the cube-rooted X to the cube-rooted Y - effectively a red-green opponent signal. b* compares Y to Z - effectively a yellow-blue opponent signal. The structure deliberately echoes Hering's three opponent channels.

CIELAB is a three-dimensional Cartesian space with three orthogonal axes. Knowing what each axis means is the entry ticket to reading Lab values fluently.

Why a cube root? The simple answer is empirical: human lightness perception scales approximately as the cube root of luminance over a wide range. This relationship was established through psychophysical experiments long before CIELAB - it shows up in the Munsell value scale, Stevens's power law for brightness, and the Weber-Fechner approximations that preceded it.

Applying the cube root makes the L* coordinate match perceived lightness. A patch at L* = 50 looks halfway between black and white. A patch at Y = 18 (the famous "18% gray") sits very close to L* = 50, which is why mid-gray cards have that counter-intuitive value.

CIELAB's Cartesian a*/b* layout is mathematically convenient but psychologically awkward. People don't think in terms of "+20 red and +15 yellow"; they think "orangish, medium-saturated." The polar form LCh (also written L*C*h°) keeps L* but replaces a*, b* with chroma and hue angle.

Lab is defined relative to a reference white. The same physical sample, described against D65, gets different Lab numbers than against D50. ICC color management uses Lab at D50; most digital imaging uses D65. Mismatching the assumed white point is one of the most common (and silent) sources of color management bugs.

The whole point of building a perceptually uniform space was to make color difference calculable as a simple distance. In CIELAB the original formula was just Euclidean:

Two stimuli with ΔE = 1 are at the "just noticeable difference" threshold for most observers. ΔE = 2-3 looks like a slight but clear shift; ΔE = 5 is a definite color step; ΔE = 10 is dramatic. The 1976 formula is the simplest in a family that has grown over time - CIE94 and CIEDE2000 weight the components to fix known non-uniformities.

CIELAB is much better than XYZ for uniform spacing, but not perfect. The well-known MacAdam ellipses - small regions in chromaticity space within which observers cannot tell colors apart - vary in size by an order of magnitude across the gamut. In Lab, the variation is smaller, but blues remain compressed and the saturated reds stretched. ΔE = 1 means different things in different parts of the gamut.

Two main fixes evolved. CIEDE2000 stays in CIELAB but applies location-dependent weights to the lightness, chroma, and hue terms so that "equal ΔE" maps more consistently to "equal perceived difference." CAM16-UCS works in a different space derived from the CIECAM16 appearance model and is even closer to uniform - but it is computationally heavier and not yet standard in design tools.

In 2020 Björn Ottosson published Oklab, a perceptually scaled color space designed to be even closer to uniform than CIELAB while remaining computationally cheap. It is based on a different LMS-style cone basis followed by a cube root and a final matrix transform. The space comes in Oklab (Cartesian) and OKLCh (polar) forms, mirroring CIELAB.

Oklab fixes several of CIELAB's local distortions - especially the saturated blue and red regions - without giving up the speed needed for live color picking and interactive design. The CSS Color Module Level 4 specifies OKLCh as a first-class color syntax for the web. As of 2024, browser support is universal.

LCh's biggest practical win is palette design. By fixing one or two of L*, C*, h° and varying the third, you produce families of colors with controlled perceptual relationships. This is the basis of every credible "design system color ramp" - where Material Design, Tailwind, and Radix all use LCh-aware curves rather than raw HSL.

Six questions on CIELAB, LCh, and color difference. Wrong answers come with brief explanations.