# CIE 1964 color space

The CIE 1964 (U*, V*, W*) color space, also known as CIEUVW, is based on the CIE 1960 UCS:[1]

$U^*=13W^*(u-u_0), \quad V^*=13W^*(v-v_0), \quad W^*=25Y^{1/3}-17$

where (u0, v0) is the white point and Y is the luminous tristimulus value of the object. The asterisks in the exponent indicates that the variable represent a more perceptually uniform color space than its predecessor (compare with CIELAB).

Wyszecki invented the UVW color space in order to be able to calculate color differences without having to hold the luminance constant. He defined a lightness index W* by simplifying expressions suggested earlier by Ladd and Pinney,[2] and Glasser et al..[3] The chromaticity components U* and V* are defined such that the white point maps to the origin, as in Adams chromatic valence color spaces. This arrangement has the benefit of being able to express the loci of chromaticities with constant saturation simply as (U*)2 + (V*)2 = C for a constant C. Furthermore, the chromaticity axes are scaled by the lightness "so as to account for the apparent increase or decrease in saturation when the lightness index is increased or decreased, respectively, and the chromaticity (u, v) is kept constant".[4]

## Chromaticity and color difference

The chromaticity co-efficients were chosen "on the basis of the spacing of the Munsell system. A lightness difference ΔW = 1 is assumed to correspond to a chromatic-ness difference $\sqrt{\Delta U^2 +\Delta V^2} = 13$ (approximately)."[4]

With the co-efficients thus selected, the color difference in CIEUVW is simply the Euclidean distance:

$\Delta E_{CIEUVW}=\sqrt{ (\Delta U^*)^2 + (\Delta V^*)^2 + (\Delta W^*)^2}$

## References

1. ^ Janos Schanda (2007). Colorimetry: Understanding the CIE System. Wiley Interscience. p. 81.
2. ^ Ladd, J.H.; Pinney, J.E. (September 1955). "Empirical relationships with the Munsell Value scale". Proceedings of the Institute of Radio Engineers 43 (9): 1137. doi:10.1109/JRPROC.1955.277892.
3. ^ Glasser, L.G.; A.H. McKinney, C.D. Reilly, and P.D. Schnelle (October 1958). "Cube-root color coordinate system". JOSA 48 (10): 736–740. doi:10.1364/JOSA.48.000736.
4. ^ a b Wyszecki, Günther (November 1963). "Proposal for a New Color-Difference Formula". Journal of the Optical Society of America (JOSA) 53 (11): 1318–1319. doi:10.1364/JOSA.53.001318. Note: The asterisks are not used in the paper.