Like L*u*v*, L*a*b* (often abbreviated as LAB or Lab) is a colorspace defined in 1976 by CIE with the goal of perceptual uniformity. L*a*b* is also designed to be a device-independent description of color.
L* defines lightness, which is the corrected form of luminance. a* and b* define green-red and yellow-blue balance, respectively, with the origin where the two axes cross being fully desaturated. Negative a* is green, and negative b* is blue.
L*a*b* is defined in terms of CIE XYZ as follows. The terms of XYZ are first divided by the XYZ coordinates of the chosen reference white to create Xn Yn Zn. (This is usually the D65 illuminant.)
Then, for each component, a prime is calculated by a piecewise function:
x' = Xn(1/3) for Xn > 0.008856
x' = (7.787 × Xn) + (16 / 116) for Xn ≤ 0.008856
(Repeat using Yn and Zn to obtain y' and z'.)
Finally, we can calculate L*a*b*:
L* = (116 × y') - 16
a* = 500 × (x' - y')
b* = 200 × (y' - z')
The definition of a* and b* in particular are based on the opponent-process theory of vision. However, since humans tend to think about color differently than it is actually perceived, it is difficult to use L*a*b* to create a particular color. As such, this colorspace is not much used for raw input; it is instead used by humans for running filters that are most effective in Lab mode. Lab is also a superset of most other color spaces, so it also finds use as an intermediate space while converting between others, e.g. RGB↔CMYK. The most famous application to use Lab is Photoshop.