# Is CIE Lab color space separating color and lightness?

When one wants to do manipulation with the “color part of an image” separately from the “brighness” part, many people think that the suitable color space to proceed is the CIE Lab color space. They think that

• the L direction of this color space is pure brightness, and has no relation to the “color components” of the image;
• the a,b directions of this color space are “pure color”, and have no relation to the “brightness component” of the image.
(People more versed in colors may think that these properties hold only approximately, and CIE CAM is what provides a better approximation.)

In facts, the ideas expressed above are more than 50% bogus. While the first part is indeed valid (at least approximately, see Helmholtz—Kohlrausch effect), the second part has no relation to reality whatsover. Essentially, the coordinates a,b depend on brightness in exactly the same way as coordinates R,G,B! (Likewise for CIE CAM.)

The “true” (as far as anything may be called “true” when discussing the color perception!) correlates of the “color part of the image” are coordinates a/L, b/L of the L a/L b/L color space. Unfortunately, this is (AFAIK) never written explicitly — but if one reads carefully, this may be deduced from the CIE CAM document.

On one hand, this may be “more or less common sense” for anyone with photography background and an ability to read math formulas: indeed, increasing exposure 1 step multiplies all of the coordinates L, a, b by the same amount — at least when the image is bright enough so that the tone curve of Lab is close to cubic root — while one expects that “just increasing exposure” should not change “the perceived color”. On the other hand, since such “theoretical considerations” often have little relationship to the actual work of human vision system, we provide simple tools for anyone to see what happens.

Below we provide 2 images; for best results, load them into an application which may show details of colors under the mouse. Both images have 3 strips: Lightness of the top strip is 35, the middle is 50, and the bottom is 65. The whole picture is of hue=90° (in other words, a=0 everywhere); the middle strip is is just a color patch with a=0, b=29. The other strips are gradients with b changing gradually. Your task: In the top and bottom strips, find the best match for the color of the middle strip.

Here the b changes as: the top strip: from 15 to 43; the bottom strip: 48 to 10.
If a,b would correlate well with the “color part”, then the “best match” would be near the middle of the top strip (likewise for bottom stip).

Here the b changes as: the top strip: from 10 to 30; the bottom strip: 56 to 20. The middles are close to b=20.3, b=37.7 which have the same ratio b/L as in the middle strip.
If a/L,b/L would correlate well with the “color part”, then the “best match” would be near the middle of the top strip (likewise for bottom stip).

Judge for yourself which of the matches is better!

For me, the best matches on the second picture are a tiny bit to the right of the middle. This means that for best result, one should “mix 85% of L, a/L, b/L with 15% of Lab”. In other words, use L, a/L0.85, b/L0.85

We choose hue=90° since it is lest succeptible to the Bezold-Brücke Effect, which may have brought in another muddling contribution to the already overwhelming mess of “eye-brain interaction”.

The gradients above are calculated in sRGB, but on the bottom picture, they interpolate between 3 points (left/middle/right) which go linearly in Lab.

Ilya Zakharevich; HOME