Lab color space

Advantages

Unlike the RGB and CMYK color models, Lab color is designed to approximate human vision. It aspires to perceptual uniformity, and its L component closely matches human perception of lightness, although it does not take the Helmholtz–Kohlrausch effect into account. Thus, it can be used to make accurate color balance corrections by modifying output curves in the a and b components, or to adjust the lightness contrast using the L component. In RGB or CMYK spaces, which model the output of physical devices rather than human visual perception, these transformations can be done only with the help of appropriate blend modes in the editing application.

Because Lab space is much larger than the gamut of computer displays, printers, or even human vision, a bitmap image represented as Lab requires more data per pixel to obtain the same precision as an RGB or CMYK bitmap. In the 1990s, when computer hardware and software were limited to storing and manipulating mostly 8-bit/channel bitmaps, converting an RGB image to Lab and back was a very lossy operation. With 16-bit/channel and floating-point support now common, the loss due to quantization is negligible.

In addition, many of the "colors" within Lab space fall outside the gamut of human vision, and are therefore purely imaginary; these "colors" cannot be reproduced in the physical world. Though color management software, such as that built into image editing applications, will pick the closest in-gamut approximation, changing lightness, chroma, and sometimes hue in the process, author Dan Margulis claims that this access to imaginary colors is useful, going between several steps in the manipulation of a picture.

Differentiation

Some specific uses of the abbreviation in software, literature etc.

CIELAB

CIE L*a*b* (CIELAB) is a color space specified by the International Commission on Illumination (French Commission internationale de l'éclairage, hence its CIE initialism). It describes all the colors visible to the human eye and was created to serve as a device-independent model to be used as a reference.

The three coordinates of CIELAB represent the lightness of the color (L* = 0 yields black and L* = 100 indicates diffuse white; specular white may be higher), its position between red/magenta and green (a*, negative values indicate green while positive values indicate magenta) and its position between yellow and blue (b*, negative values indicate blue and positive values indicate yellow). The asterisk (*) after L, a and b are pronounced star and are part of the full name, since they represent L*, a* and b*, to distinguish them from Hunter's L, a, and b, described below.

Since the L*a*b* model is a three-dimensional model, it can be represented properly only in a three-dimensional space. Two-dimensional depictions include chromaticity diagrams: sections of the color solid with a fixed lightness. It is crucial to realize that the visual representations of the full gamut of colors in this model are never accurate; they are there just to help in understanding the concept.

Because the red-green and yellow-blue opponent channels are computed as differences of lightness transformations of (putative) cone responses, CIELAB is a chromatic value color space.

A related color space, the CIE 1976 (L*, u*, v*) color space (a.k.a. CIELUV), preserves the same L* as L*a*b* but has a different representation of the chromaticity components. CIELAB and CIELUV can also be expressed in cylindrical form (CIELCH and CIELCH_uv, respectively), with the chromaticity components replaced by correlates of chroma and hue.

Since CIELAB and CIELUV, the CIE has been incorporating an increasing number of color appearance phenomena into their models, to better model color vision. These color appearance models, of which CIELAB is a simple example, culminated with CIECAM02.

Perceptual differences

This topic is covered in more detail at Color difference.

The nonlinear relations for L*, a*, and b* are intended to mimic the nonlinear response of the eye. Furthermore, uniform changes of components in the L*a*b* color space aim to correspond to uniform changes in perceived color, so the relative perceptual differences between any two colors in L*a*b* can be approximated by treating each color as a point in a three-dimensional space (with three components: L*, a*, b*) and taking the Euclidean distance between them.

RGB and CMYK conversions

There are no simple formulas for conversion between RGB or CMYK values and L*a*b*, because the RGB and CMYK color models are device-dependent. The RGB or CMYK values first must be transformed to a specific absolute color space, such as sRGB or Adobe RGB. This adjustment will be device-dependent, but the resulting data from the transform will be device-independent, allowing data to be transformed to the CIE 1931 color space and then transformed into L*a*b*.

Range of coordinates

As mentioned previously, the L* coordinate ranges from 0 to 100. The possible range of a* and b* coordinates is independent of the color space that one is converting from, since the conversion below uses X and Y, which come from RGB.

Forward transformation

where

Here, X_n, Y_n and Z_n are the CIE XYZ tristimulus values of the reference white point (the subscript n suggests "normalized"). Under Illuminant D65 with normalization Y = 100, the values are

The division of the domain of the f function into two parts was done to prevent an infinite slope at t = 0. The function f was assumed to be linear below some t = t₀, and was assumed to match the t^1/3 part of the function at t₀ in both value and slope. In other words:

The intercept f(0) = c was chosen so that L* would be 0 for Y = 0: c = 16/116 = 4/29. The above two equations can be solved for m and t₀:

where δ = 6/29.

Reverse transformation

The reverse transformation is most easily expressed using the inverse of the function f above:

where

and where δ = 6/29.

Hunter Lab

L is a correlate of lightness, and is computed from the Y tristimulus value using Priest's approximation to Munsell value:

where Y_n is the Y tristimulus value of a specified white object. For surface-color applications, the specified white object is usually (though not always) a hypothetical material with unit reflectance that follows Lambert's law. The resulting L will be scaled between 0 (black) and 100 (white); roughly ten times the Munsell value. Note that a medium lightness of 50 is produced by a luminance of 25, since 100 25 / 100 = 100 ⋅ 1 / 2

a and b are termed opponent color axes. a represents, roughly, Redness (positive) versus Greenness (negative). It is computed as:

where K_a is a coefficient that depends upon the illuminant (for D65, K_a is 172.30; see approximate formula below) and X_n is the X tristimulus value of the specified white object.

The other opponent color axis, b, is positive for yellow colors and negative for blue colors. It is computed as:

where K_b is a coefficient that depends upon the illuminant (for D65, K_b is 67.20; see approximate formula below) and Z_n is the Z tristimulus value of the specified white object.

Both a and b will be zero for objects that have the same chromaticity coordinates as the specified white objects (i.e., achromatic, grey, objects).

The name for the system is an attribution to Richard S. Hunter.

Approximate formulas for Ka and Kb

In the previous version of the Hunter Lab color space, K_a was 175 and K_b was 70. Hunter Associates Lab discovered that better agreement could be obtained with other color difference metrics, such as CIELAB (see above) by allowing these coefficients to depend upon the illuminants. Approximate formulae are:

which result in the original values for Illuminant C, the original illuminant with which the Lab color space was used.

As an Adams chromatic valence space

Adams chromatic valence color spaces are based on two elements: a (relatively) uniform lightness scale, and a (relatively) uniform chromaticity scale. If we take as the uniform lightness scale Priest's approximation to the Munsell Value scale, which would be written in modern notation:

and, as the uniform chromaticity coordinates:

where k_e is a tuning coefficient, we obtain the two chromatic axes:

and

which is identical to the Hunter Lab formulas given above if we select K = K_a/100 and k_e = K_b/K_a. Therefore, the Hunter Lab color space is an Adams chromatic valence color space.

Cylindrical representation: CIELCh or CIEHLC

The CIELCh color space is a CIELab cube color space, where instead of Cartesian coordinates a*, b*, the cylindrical coordinates C* (chroma, relative saturation) and h° (hue angle, angle of the hue in the CIELab color wheel) are specified. The CIELab lightness L* remains unchanged.

The conversion of a* and b* to C* and h° is done using the following formulas:

Conversely, given the polar coordinates, conversion to Cartesian coordinates is achieved with:

The LCh color space is not the same as the HSV, HSL or HSB color spaces, although their values can also be interpreted as a base color, saturation and lightness of a color. The LCh values are a polar coordinate transformation of what is technically defined RGB cube color space. LCh is still perceptually uniform.

Further, H and h are not identical, because HSL space uses as primary colors the three additive primary colors red, green, blue (H = 0, 120, 240°). Instead, the LCh system uses the four physiological elementary colors yellow, green, blue and red (h = 90, 180, 270, 360°). h = 0 means the achromatic colors, that is, the gray axis.

The simplified spellings LCh, LCH and HLC are common, but the latter presents a different order. HCL color space (Hue-Chroma-Luminance) on the other hand is a commonly used alternative name for the L*C*h(uv) color space, also known as the cylindrical representation or polar CIELUV.