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# CIE 1976 L*a*b* color model

The CIE 1976 L*a*b* color model is based on the CIE 1964 color model which was further enhanced because of two problems with the specification of colors in terms of tristimulus values and chromaticity space. Firstly, this specification is not easily interpreted in terms of the psychophysical dimensions of color perception namely, brightness, hue, and colourfulness. Secondly, the XYZ system and the associated chromaticity diagrams are not perceptually uniform. The second of these points is a problem if we wish to estimate the magnitude of the difference between two color stimuli. The need for a uniform colour space led to a number of non-linear transformations of the CIE 1931 XYZ space and finally resulted in the specification of one of these transformations as the CIE 1976 L* a* b* color space.

In fact in 1976 the CIE specified two color spaces; one of these was intended for use with self-luminous colors and the other was intended for use with surface colors. The other model was the CIE 1976 L*u*v* color model being described in more detail below. These notes are principally concerned with the latter known as CIE 1976 L* a* b* color space or CIELAB.

CIELAB allows the specification of color perceptions in terms of a three-dimensional space. The L*-axis is known as the lightness and extends from 0 (black) to 100 (white). The other two coordinates a* and b* represent redness-greeness and yellowness-blueness respectively. Samples for which a* = b* = 0 are achromatic and thus the L*-axis represents the achromatic scale of greys from black to white.

## L*a*b* color algorithm

The quantities L*, a*, and b* are obtained from the tristimulus values according to the following transformations: for Y/Yn > 0.008856 for Y/Yn <= 0.008856 for X/Xn >  0.008856) for X/Xn <=  0.008856 for  Z/Zn >  0.008856 for Z/Zn <=  0.008856

where Xn, Yn, and Zn are the tristimulus values of the illuminant (perfect reflecting diffuser) that was used for the calculation of X, Y, and Z of the sample.

## L*a*b* color differences

Color differences will be measured as total difference of the L*, a* and b* values of a sample and the standard using the following equations:

∆L* = L*sample - L*standard

positive ∆L* means, the sample is lighter than the standard
negative ∆L* means, the sample is darker than the standard

∆a* = a*sample - a*standard

positive ∆a* means, the sample is redder than the standard
negative ∆a* means, the sample is greener than the standard

∆b* = b*sample - b*standard

positive ∆b* means, the sample is yellower than the standard
negative ∆b* means, the sample is bluer than the standard

In addition, there are two other delta values that are related to this scale, ∆C* and ∆H*. The ∆C* is the difference in chroma between the sample and standard as described in a polar coordinate system. The ∆H* is the difference in hue angle between the sample and standard as described in a polar coordinate system.

∆C* = C*sample - C*standard where (this is called meric chroma) ## References

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