Lab color space

In the XYZ color system using tristimulus values themselves as the absolute color space, it is known that the amount of color difference that can be recognized by humans differs considerably depending on the color region. The Lab color system, as an absolute color space, was devised as a uniform color space closer to human perception (see the figure below). Originally developed by Hunter, the CIE (International Commission on Illumination) made improvements in 1976 and called it the L*a*b* color system. In the Lab system colors are represented by three numerical values, L*, a*, and b* (* is read as "star"). Usually, the "Lab" color system means the CIE L*a*b* color system.

An ellipse represents the color difference discrimination limit (referred to as MacAdam's ellipse). The ellipses are enlarged. In the xy color space, the size of the ellipse varies considerably from place to place. On the other hand, in the Lab color space, the difference in the size of the ellipse is small, showing that the color space is much more uniform.
* Illuminant C is assumed for the Lab space above.

Generally, human sensation tends to be proportional to the logarithm of the stimulus value, not to the stimulus value itself (the Weber-Fechner law). The sense of brightness is no exception. The values of L*, a*, and b* can be given by converting the values of XYZ with a simple conversion formula that expresses the characteristics of vision (see this graph). Specifically, the converted value of Y is L* (lightness), and the difference [(conversion of X)−(conversion of Y)] multiplied by a constant is a*, and the difference [(conversion of Y)−(conversion of Z)] multiplied by a constant is b*. Values of L*, a*, and b* can also be measured with a device such as a colorimeter (the device converts the tristimulus values by software). In addition, since Lab is a uniform color space close to human perception, the distance between two points in Lab space is often defined as color difference. The Lab color system is widely used in the field of color science because absolute colors can be expressed by numerical values and they are close to human sensation. Adobe Photoshop also supports the Lab color system (assuming D50 as the illuminant).

L* is an abbreviation of Lightness. The value varies between 0 and 100. As perceived by humans, L* of yellow is large and L* of blue is small. a* is the component in the direction of red and green, and color becomes reddish with + and becomes greenish with -. b* is the component in the direction of yellow and blue, and color becomes yellowish with + and becomes bluish with -. The center at a* = 0, b* = 0 is gray. Colors with large absolute values of a* or b* and far from the center have higher saturation. The direction determined by the values of a* and b* corespond to hue. In the figure, a sphere is shown for simplicity, but the value of a* and b* varies depending on brightness and hue, and the color gamut does not actually become a sphere. For example, the color gamut of sRGB and Adobe RGB looks like a distorted parallelepiped in L*a*b* space (see below). The Lab color system is a numerical representation of Munsell's intuitive color solid.

Lab color system. The figure on the right is a cross section at L* = 75.
Point C corresponds to a color with L* = 75, a* = 30, b* = 35.

The figure below shows the color gamut of sRGB in L*a*b* space. The color gamut is a parallelepiped in the XYZ space, but distorted by the transformation in the Lab space. Each vertex of this figure corresponds to primary colors (RGB and CMY) and black and white. Adobe RGB has a wider color gamut (especially in the green direction) than sRGB. On the other hand, P3-D65 has a more extended gamut in red-green region than sRGB.


Color gamut reproducible in sRGB (projection in the Lab* space)	The color gamut of sRGB (innermost), P3-D65 and Adobe RGB as the top view in the Lab* space. The outer surface is the color gamut of the optimal color solid (MacAdam limit).

GIF animations that represent the color gamut of sRGB, P3-D65, Adobe RGB, and the optimal color solid in the L*a*b* space have been created for your reference.

(Note) If you use "Grayscale" in "Mode" when converting RGB images to monochrome with Photoshop, the images will be converted to L* in Lab color system and become natural images. On the other hand, if the saturation of an RGB mode image is reduced by "Tone Correction", S decreases based on the HSL model, and the brightness of yellow and blue becomes unnatural. If you convert the image mode from RGB to Lab before correction, you can lower the saturation based on Lab.

[Reference] Munsell color solid

As a traditional color model, the Munsell color solid expressing a color by hue (Hue), saturation (Chroma), and lightness (Value) is widely known. This model was invented by Munsell in the early 20th century. Munsell color solids are close to our senses, with yellow lightness being high and blue lightness being low (figure below).


Munsell color solid (Solid Type)	Munsell color solid (A part)

Munsell color solid (Munsell
system - tree)

Munsell color solid (Tree type)

The figure below is a plot of the published Munsell color values converted to L*, a*, b* with illuminant D50. Munsell model seems to have higher saturation in the yellow direction than L*a*b*, and to have a wider hue interval in the yellow-green direction. However, it can be seen that the lines with the same saturation are arranged almost concentrically and that the color spaces are similar to each other.

Munsell colors with value 5 plotted in the L*a*b* space.
Concentric lines represent saturation 2, 4, ... from the center.

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T. Fujiwara