CIE 1960 color space

Background

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

: \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

: u_{\rm Judd}=\frac{0.4661x+0.1593y}{y-0.15735x+0.2424} = \frac{5.5932x+1.9116y}{12y-1.882x+2.9088}

: v_{\rm Judd}=\frac{0.6581y}{y-0.15735x+0.2424} = \frac{7.8972y}{12y-1.882x+2.9088}

MacAdam simplified Judd's UCS for computational purposes:

: u = \frac{4x}{12y - 2x + 3}

: 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, and officially adopted it as the standard UCS the next year.

Relation to CIE XYZ

U, V, and W can be found from X, Y, and Z using: :U= \textstyle{\frac{2}{3}}X :V=Y, :W=\textstyle{\frac{1}{2}}(-X+3Y+Z) Going the other way: :X=\textstyle{\frac 32}U :Y=V :Z=\textstyle{\frac{3}{2}}U-3V+2W We then find the chromaticity variables as: :u =\frac U{U+V+W}= \frac{4X}{X + 15Y +3Z} :v =\frac V{U+V+W}= \frac{6Y}{X + 15Y + 3Z} We can also convert from u and v to x and y: :x = \frac{3u}{2u - 8v + 4} :y = \frac{2v}{2u - 8v + 4}

Relation to CIE 1976 UCS

Main article: CIELUV

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

References

References

1. MacAdam, David Lewis. (August 1937). "Projective transformations of I.C.I. color specifications". [[JOSA]].
2. Arun N. Netravali, Barry G. Haskell. (1986). "Digital Pictures: Representation, Compression, and Standards". Springer.
3. Judd, Deane B.. (January 1935). "A Maxwell Triangle Yielding Uniform Chromaticity Scales". [[JOSA]].
4. OSA Committee on Colorimetry. (November 1944). "Quantitative data and methods for colorimetry". [[JOSA]].
5. CIE. (January 1960). "Brussels Session of the International Commission on Illumination". [[JOSA]].
6. (1960). "Official Recommendations". [[International Commission on Illumination]].