Lightness 25%

Lightness 50%

Lightness 75%

Without further qualification, "Lab" color space refers to that of Hunter (Richard S Hunter, JOSA, 38, p 661 (1948)), which is an Adams Chromatic Valance Space. It is not proper to refer to CIELAB as simply "Lab," not just because it is not an Adams Chromatic Valance Space, but also because it is ambiguous and confusing. Lab color at luminance 25% File links The following pages link to this file: Lab color space Categories: GFDL images ... Lab color at luminance 25% File links The following pages link to this file: Lab color space Categories: GFDL images ... Lab color at neutral luminance File links The following pages link to this file: Lab color space Categories: GFDL images ... Lab color at neutral luminance File links The following pages link to this file: Lab color space Categories: GFDL images ... Lab color at luminance 75% File links The following pages link to this file: Lab color space Categories: GFDL images ... Lab color at luminance 75% File links The following pages link to this file: Lab color space Categories: GFDL images ...

Hunter Lab Color Space

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

where Yn 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 and which follows Lambert's law.. The result will be Ls scaled between 0 (black) and 100 (white); roughly 10 times Munsell value. Note, however, that a mid-range Lightness of 50 is produced not by a Y of 50, but rather of 25.

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

where K_a is a coefficient which depends upon the illuminant (for D65, Ka is 172.30; see approximate formula below) and Xn 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 which depends upon the illuminant (for D65, K_b is 67.20; see approximate formula below) and Zn is the Z tristimulus value of the specified white object.

["Hunter Lab Color Scale," Insight on Color, 8:9 (August 1-15, 1996). Reston, VA, USA: Hunter Associates Laboratories.]

Both a and b will be zero for objects which have the same chromaticity coordinates as the specified white objects. Usually this is the case for neutrals.

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. Apparently, Hunter Associates Lab discovered that better agreement could be obtained with other color difference metrics, such as CIELAB (see below) 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.

The Hunter Lab Color Space as an Adams Chromatic Valance Space

Adams Chromatic Valance spaces are based on two elements: a (relatively) uniform lightness scale, and a (relatively) uniform chromaticity diagram. [E Q Adams, "X-Z planes in the 1931 I.C.I. system of colorimetry," JOSA, 32:3, p 168-173 (March, 1942).] If we take as the uniform lightness scale Priest's approximation to the Munsell Value scale, which would be written in modern notation: The International Commission on Illumination (usually known as the CIE for its French-language name Commission Internationale de lEclairage) is the international authority on light, illumination, colour, and colour spaces. ...

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 formulae 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 Valance space.

CIE 1976 L*, a*, b* Color Space (CIELAB)

CIE L*a*b* (CIELAB) is the most complete color model used conventionally to describe all the colors visible to the human eye. It was developed for this specific purpose by the International Commission on Illumination (Commission Internationale d'Eclairage, hence its CIE initialism). The * after L, a and b are part of the full name, since they represent L*, a* and b*, derived from L, a and b. CIELAB is an Adams Chromatic Value Space. A color model is an abstract mathematical model describing the way colors can be represented as tuples of numbers, typically as three or four values or color components (e. ... The International Commission on Illumination (usually known as the CIE for its French-language name Commission Internationale de lEclairage) is the international authority on light, illumination, colour, and colour spaces. ... Acronyms and initialisms are abbreviations formed from the initial letter or letters of words, such as NATO and XHTML, and are pronounced in a way that is distinct from the full pronunciation of what the letters stand for. ...

The three parameters in the model represent the lightness of the color (L*, L*=0 yields black and L*=100 indicates white), its position between 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 Lab color model has been created to serve as a device independent, absolute model to be used as a reference. Therefore 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, but they are inherently inaccurate. In computer graphics, the gamut, or color gamut, is a certain complete subset of colors. ...

Since the Lab model is a three dimensional model, it can only be represented properly in a three dimensional space. A useful feature of the model however is that the first parameter is extremely intuitive: changing its value is like changing the brightness setting in a TV set. Therefore only a few representations of some horizontal "slices" in the model are enough to conceptually visualize the whole gamut, assuming that the luminance would be represented on the vertical axis.

CIE 1976 L*a*b* is based directly on the CIE 1931 XYZ color space as an attempt to linearize the perceptibility of color differences, using the color difference metric described by the MacAdam ellipse. The non-linear relations for L*, a*, and b* are intended to mimic the logarithmic response of the eye. Coloring information is referred to the color of the white point of the system, subscript n. In the study of the perception of color, one of the first mathematically defined color spaces was the CIE XYZ color space (also known as CIE 1931 color space), created by the International Commission on Illumination (CIE) in 1931. ... In the study of the perception of color, a MacAdam ellipse is the region on a chromaticity diagram which contains all colors which are indistinguishable, to the average human eye, from the color at the center of the ellipse. ... A white point is one of a number of reference illuminants used in colorimetry which serve to define the color white. Depending on the application, different definitions of white are needed to give acceptable results. ...

XYZ to CIE L*a*b* (CIELAB) and CIELAB to XYZ conversions

The forward transformation

where

for

otherwise

Here X_n, Y_n and Z_n are the CIE XYZ tristimulus values of the reference white point. A white point is one of a number of reference illuminants used in colorimetry which serve to define the color white. Depending on the application, different definitions of white are needed to give acceptable results. ...

The division of the f(t) function into two domains was done to prevent an infinite slope at t=0. f(t) 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:

			(match in value)
			(match in slope)

The value of b was chosen to be 16/116. The above two equations can be solved for a and t₀:

where δ = 6 / 29. Note that 16 / 116 = 2δ / 3

The reverse transformation

The reverse transformation is as follows (with δ = 6 / 29 as mentioned above):

1. define
2. define
3. define
4. if then    else
5. if then    else
6. if then    else

XYZ to CIELUV & CIELUV to XYZ conversions

The forward transformation

CIE 1976 L*u*v* (CIELUV) is based directly on CIE XYZ and is another attempt to linearize the perceptibility of color differences. The non-linear relations for L*, u*, and v* are given below:

The quantities u_n' and v_n' refer to the reference white point or the light source. (For example, for the 2° observer and illuminant C, u_n' = 0.2009, v_n' = 0.4610.) Equations for u' and v' are given below: A white point is one of a number of reference illuminants used in colorimetry which serve to define the color white. Depending on the application, different definitions of white are needed to give acceptable results. ...

.

The reverse transformation

The transformation from (u',v') to (x,y) is:

.

The transformation from CIELUV to XYZ is performed as following:

RGB and CMYK conversions

Programmers and others often seek a formula for conversion between RGB or CMYK values and L*a*b*, not understanding that RGB and CMYK are not absolute color spaces and so have no precise relation to an absolute color space such as L*a*b*. To convert between RGB and L*a*b*, for example, it is necessary to determine or assume an absolute color space for the RGB data, such as sRGB or Adobe RGB. For each of these absolute spaces, there are standard techniques for converting to and from the XYZ absolute color space (see for example SRGB color space#Specification of the transformation) which can be combined with the above transformations to convert them to L*a*b*. The RGB color model is an additive model in which red, green and blue (often used in additive light models) are combined in various ways to reproduce other colors. ... This article or section does not cite its references or sources. ... An absolute color space is a color space in which colors are unambiguous, where they do not depend on any external factors. ... CIE 1931 xy chromaticity diagram showing the gamut of the sRGB color space and location of the primaries. ... The Adobe RGB color space is an RGB color space developed by Adobe Systems in 1998. ... CIE 1931 xy chromaticity diagram showing the gamut of the sRGB color space and location of the primaries. ...