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Hunter Lab

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Hunter Lab (also known as Hunter L,a,b) is a color space defined in 1948[1][2] by Richard S. Hunter. It was designed to be computed via simple formulas from the CIEXYZ space, but to be more perceptually uniform. Hunter named his coordinates L, a and b. Hunter Lab was a precursor to CIELAB, created in 1976 by the International Commission on Illumination (CIE), which named the coordinates for CIELAB as L*, a*, b* to distinguish them from Hunter's coordinates.[3][4]

Formulation

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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 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, due to the square root proportionality.

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

where Ka is a coefficient that 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 Kb is a coefficient that depends upon the illuminant (for D65, Kb is 67.20; see approximate formula below) and Zn is the Z tristimulus value of the specified white object.[5]

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).

Approximate formulas for Ka and Kb

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In the previous version of the Hunter Lab color space, Ka was 175 and Kb was 70. Hunter Associates Lab discovered[citation needed] 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

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Adams chromatic valence color spaces are based on two elements: a (relatively) uniform lightness scale and a (relatively) uniform chromaticity scale.[6] If we take as the uniform lightness scale Priest's approximation to the Munsell Value scale, which would be written in modern notation as:

and, as the uniform chromaticity coordinates:

where ke 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 = Ka/100 and ke = Kb/Ka. Therefore, the Hunter Lab color space is an Adams chromatic valence color space.

References

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  1. ^ Hunter, Richard Sewall (July 1948). "Photoelectric Color-Difference Meter". JOSA. 38 (7): 661. (Proceedings of the Winter Meeting of the Optical Society of America)
  2. ^ Hunter, Richard Sewall (December 1948). "Accuracy, Precision and Stability of New Photo-electric Color-Difference Meter". JOSA. 38 (12): 1094. (Proceedings of the Thirty-Third Annual Meeting of the Optical Society of America)
  3. ^ Hunter, Richard Sewall (July 1948). "Photoelectric Color-Difference Meter". JOSA. 38 (7): 661. (Proceedings of the Winter Meeting of the Optical Society of America)
  4. ^ Hunter, Richard Sewall (December 1948). "Accuracy, Precision, and Stability of New Photo-electric Color-Difference Meter". JOSA. 38 (12): 1094. (Proceedings of the Thirty-Third Annual Meeting of the Optical Society of America)
  5. ^ Hunter Labs (1996). "Hunter Lab Color Scale". Insight on Color 8 9 (August 1–15, 1996). Reston, VA, USA: Hunter Associates Laboratories.
  6. ^ Adams, E.Q. (1942). "X-Z planes in the 1931 I.C.I. system of colorimetry". JOSA. 32 (3): 168–173. Bibcode:1942JOSA...32..168A. doi:10.1364/JOSA.32.000168.