LAB

LAB spaces color so that equal steps in numbers look like equal steps to your eyes. Lightness gets its own axis, so measuring color distance finally matches what people actually see.

CIELAB puts lightness on its own vertical axis and opponent colors on two flat axes, so a ruler step anywhere equals one visible step.

Why Does This Exist?

RGB steps lie. Twenty units between two greens can look identical while twenty units between two reds look like different colors, so "nearest color" searches in RGB return answers humans disagree with. CIELAB, drawn up by the International Commission on Illumination in 1976, was engineered the other way around: warp the coordinates until Euclidean distance tracks perceived difference.

Use it when the question is "how different do these look": print inspection, paint matching, grading segmentation quality, picking visibly distinct label colors. For finding one color under changing light, HSV is usually simpler; the tradeoff map is in color spaces.

Think of It Like This

A surveyed map versus a stretched tourist map

A tourist map stretches the center: one centimeter downtown covers two blocks while one centimeter in the suburbs covers ten. Measuring with a ruler on that map lies about real walking distance.

CIELAB is the surveyed map. Cartographers stretched and squeezed the color territory until one ruler centimeter means one "just noticeable difference" everywhere. RGB is the tourist map: ruler-true nowhere in particular.

The analogy stops here: the survey assumed one standard daylight (D65) and average viewing conditions, so under exotic lighting the ruler drifts.

How It Actually Works

CIELAB has three axes. $L^*$ (lightness) runs $0$ (black) to $100$ (white). $a^*$ runs green (negative) to red (positive) and $b^*$ runs blue (negative) to yellow (positive), each roughly spanning $-127$ to $+127$ . The star marks that these are the 1976 revision, not Hunter's older Lab.

Conversion goes RGB to XYZ tristimulus values first (a linear remix fixed by the standard), then each XYZ ratio against the D65 reference white $X_n, Y_n, Z_n$ passes through a cube-root-ish curve $f$ . Lightness is $L^* = 116\, f(Y / Y_n) - 16$ . The cube root mimics human vision: we resolve shadows finely and highlights coarsely, so dark-end steps get stretched apart.

Worked example: mid-gray is not halfway down

Take a surface reflecting half the reference light, $Y / Y_n = 0.5$ . Then $f(0.5) = 0.5^{1/3} \approx 0.794$ , and $L^* = 116 \times 0.794 - 16 \approx 76.1$ . Half the physical light reads as lightness $76$ , not $50$ : the scale spends most of its numbers where eyes see best. Full white ( $Y / Y_n = 1$ ) gives exactly $L^* = 100$ .

Color distance is just Euclidean distance

Because the space is near-uniform, the plain distance $\Delta E = \sqrt{(\Delta L^*)^2 + (\Delta a^*)^2 + (\Delta b^*)^2}$ approximates visible difference. A $\Delta E$ near $1$ is barely noticeable; past $5$ nobody argues the colors match. No lookup tables, no weights: that single property is the whole point of the space.

Code

1def lightness(yn):2    # yn: luminance relative to the D65 reference white, 0..13    f = yn ** (1 / 3) if yn > 0.008856 else 7.787 * yn + 16 / 1164    return 116 * f - 165
6print(round(lightness(0.5), 1))  # half the light, not half the lightness7print(round(lightness(1.0), 1))  # reference white pins the top8# -> 76.19# -> 100.0

Watch Out For

OpenCV's 8-bit LAB is rescaled, not the textbook range

In 8-bit OpenCV images $L^*$ is squeezed from $0$ – $100$ into $0$ – $255$ and $a^*, b^*$ are shifted by $+128$ so negatives fit a byte. Reading channel values as textbook $L^*a^*b^*$ numbers (or thresholding with literature bounds) misses every target. Convert to float for real units, or rescale the bounds to match.

Forgetting the white point invalidates comparisons

$L^*a^*b^*$ values are ratios against the D65 reference white. Two LAB triples computed under different assumed illuminants are not comparable, and their $\Delta E$ is meaningless. Fix one white point for the whole pipeline before comparing across cameras or datasets.

The Quick Version

CIELAB warps color coordinates so Euclidean distance tracks visible difference.
$L^*$ is lightness from 0 to 100; $a^*$ and $b^*$ are green-red and blue-yellow opponent axes.
Half the physical light reads as lightness 76, because the cube-root curve favors shadow detail.
A delta-E near 1 is barely visible; past 5 the colors clearly differ.
OpenCV rescales 8-bit LAB, so use float images when you need true textbook units.