# CIE 1960 color space

The Planckian locus on the MacAdam (u, v) chromaticity diagram. The normals are lines of equal correlated color temperature.

The CIE 1960 color space ("CIE 1960 UCS", variously expanded Uniform Color Space, Uniform Color Scale, Uniform Chromaticity Scale, Uniform Chromaticity Space) is another name for the (u, v) chromaticity space devised by David MacAdam.[1]

The CIE 1960 UCS does not define a luminance or lightness component, but the Y tristimulus value of the XYZ color space or a lightness index similar to W* of the CIE 1964 color space are sometimes used.[2]

Today, the CIE 1960 UCS is mostly used to calculate correlated color temperature, where the isothermal lines are perpendicular to the Planckian locus. As a uniform chromaticity space, it has been superseded by the CIE 1976 UCS.

## Background

Judd determined that a more uniform color space could be found by a simple projective transformation of the CIEXYZ tristimulus values:[3]

${\displaystyle {\begin{pmatrix}''R''\\''G''\\''B''\end{pmatrix}}={\begin{pmatrix}3.1956&2.4478&-0.1434\\-2.5455&7.0492&0.9963\\0.0000&0.0000&1.0000\end{pmatrix}}{\begin{pmatrix}X\\Y\\Z\end{pmatrix}}}$

(Note: What we have called "G" and "B" here are not the G and B of the CIE 1931 color space and in fact are "colors" that do not exist at all.)

Judd was the first to employ this type of transformation, and many others were to follow. Converting this RGB space to chromaticities one finds[4][clarification needed The following formulae do not agree with u=R/(R+G+B) and v=G/(R+G+B)]

Judd's UCS, with the Planckian locus and the isotherms from 1,000K to 10,000K, perpendicular to the locus. Judd then translated these isotherms back into the CIEXYZ color space. (The colors used in this illustration are illustrative only and do not correspond to the true colors represented by the respective points.)
${\displaystyle u={\frac {0.4661x+0.1593y}{y-0.15735x+0.2424}}}$
${\displaystyle v={\frac {0.6581y}{y-0.15735x+0.2424}}}$

or equivalently (for comparative purposes with the equations to follow):

${\displaystyle u={\frac {5.5932x+1.9116y}{12y-1.882x+2.9088}}}$
${\displaystyle v={\frac {7.8972y}{12y-1.882x+2.9088}}}$

MacAdam simplified Judd's UCS for computational purposes:

${\displaystyle u={\frac {4x}{12y-2x+3}}}$
${\displaystyle v={\frac {6y}{12y-2x+3}}}$

The Colorimetry committee of the CIE considered MacAdam's proposal at its 14th Session in Brussels for use in situations where more perceptual uniformity was desired than the (x,y) chromaticity space,[5] and officially adopted it as the standard UCS the next year.[6]

## Relation to CIE XYZ

The CIE 1960 UCS, also known as the MacAdam (u,v) chromaticity diagram. Colors outside the colored triangle cannot be represented on most computer screens.

U, V, and W can be found from X, Y, and Z using:

${\displaystyle U=\textstyle {\frac {2}{3}}X}$
${\displaystyle V=Y\,}$
${\displaystyle W=\textstyle {\frac {1}{2}}(-X+3Y+Z)}$

Going the other way:

${\displaystyle X=\textstyle {\frac {3}{2}}U}$
${\displaystyle Y=V}$
${\displaystyle Z=\textstyle {\frac {3}{2}}U-3V+2W}$

We then find the chromaticity variables as:

${\displaystyle u={\frac {U}{U+V+W}}={\frac {4X}{X+15Y+3Z}}}$
${\displaystyle v={\frac {V}{U+V+W}}={\frac {6Y}{X+15Y+3Z}}}$

We can also convert from u and v to x and y:

${\displaystyle x={\frac {3u}{2u-8v+4}}}$
${\displaystyle y={\frac {2v}{2u-8v+4}}}$

## Relation to CIELUV

${\displaystyle u^{\prime }=u\,}$
${\displaystyle v^{\prime }=\textstyle {\frac {3}{2}}v\,}$

## References

1. ^ MacAdam, David Lewis (August 1937). "Projective transformations of I.C.I. color specifications". JOSA. 27 (8): 294–299. doi:10.1364/JOSA.27.000294.
2. ^ Arun N. Netravali, Barry G. Haskell (1986). Digital Pictures: Representation, Compression, and Standards (2E ed.). Springer. p. 288. ISBN 0-306-42195-X.
3. ^ Judd, Deane B. (January 1935). "A Maxwell Triangle Yielding Uniform Chromaticity Scales". JOSA. 25 (1): 24–35. doi:10.1364/JOSA.25.000024. An important application of this coordinate system is its use in finding from any series of colors the one most resembling a neighboring color of the same brilliance, for example, the finding of the nearest color temperature for a neighboring non-Planckian stimulus. The method is to draw the shortest line from the point representing the non-Planckian stimulus to the Planckian locus.
4. ^ OSA Committee on Colorimetry (November 1944). "Quantitative data and methods for colorimetry". JOSA. 34 (11): 633–688. (recommended reading)
5. ^ CIE (January 1960). "Brussels Session of the International Commission on Illumination". JOSA. 50 (1): 89–90. The use of the following chromaticity diagram is provisionally recommended whenever a diagram yielding color spacing perceptually more nearly uniform than the (xy) diagram is desired. The chromaticity diagram is produced by plotting 4X/(X + 15Y + 3Z) as abscissa and 6Y/(X + 15Y + 3Z) as ordinate, in which X, Y, and Z are the tristimulus values corresponding to the 1931 CIE Standard Observer and Coordinate System.
6. ^ "Official Recommendations". Publication No. 004: Proceedings of the CIE Session 1959 in Bruxelles. 14th Session. A. Brussels: International Commission on Illumination. 1960. p. 36.