CIE 1960 color space explained

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 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 As a uniform chromaticity space, it has been superseded by the CIE 1976 UCS.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]

\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]

u _{\rm} = (0 . 4661 x +0 . 1593 y)/(y -0 . 15735 x +0 . 2424) = (5 . 5932 x +1 . 9116 y)/(12 y -1 . 882 x +2 . 9088) v _{\rm} = (0 . 6581 y)/(y -0 . 15735 x +0 . 2424) = (7 . 8972 y)/(12 y -1 . 882 x +2 . 9088)

MacAdam simplified Judd's UCS for computational purposes:

u = (4 x)/(12 y -2 x +3) v = (6 y)/(12 y -2 x +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

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

U = style{ (2)/(3) }XV = Y W = style{ (1)/(2) }(-X+3Y+Z)Going the other way:X = style{ (32}U)/() Y = V Z = style{ (3)/(2) }U-3V+2WWe then find the chromaticity variables as:u = (U{U + V + W} =)/((4 X)/(X +15 Y +3 Z)) v = (V{U + V + W} =)/((6 Y)/(X +15 Y +3 Z)) We can also convert from u and v to x and y:x = (3 u)/(2 u -8 v +4) y = (2 v)/(2 u -8 v +4)

Relation to CIE 1976 UCS

See main article: CIELUV.

u ^{\prime} = u v ^{\prime} = style{ (3)/(2) }v\,

References

1. David MacAdam. David Lewis. MacAdam. Projective transformations of I.C.I. color specifications. JOSA. 27. 8. August 1937. 294–299. 10.1364/JOSA.27.000294.
2. Book: Arun Netravali

   . Digital Pictures: Representation, Compression, and Standards. Springer. 0-306-42195-X. Arun N. Netravali, Barry G. Haskell. Arun Netravali. 2E. 288. 1986.

3. A Maxwell Triangle Yielding Uniform Chromaticity Scales. JOSA. Deane B.. Judd. 25. 1. January 1935. 24–35. 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.. 10.1364/JOSA.25.000024.
4. JOSA. Quantitative data and methods for colorimetry. 34. 11. November 1944. OSA Committee on Colorimetry. 633–688. (recommended reading)
5. Brussels Session of the International Commission on Illumination. International Commission on Illumination. JOSA. 50. 1. January 1960. 89–90. CIE. 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. Brussels . 1960 . . Official Recommendations . 36 . 14th Session . Publication No. 004: Proceedings of the CIE Session 1959 in Bruxelles . A.

External links

• Free Windows utility to generate chromaticity diagrams. Delphi source included.