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{{About|an obsolete version of the [[International Commission on Illumination|CIE]] [[color space]]|the video color model|YUV}}
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[[File:Planckian-locus.png|thumb|400px|The Planckian locus on the MacAdam {{nobr|(''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 {{nobr|(''u'', ''v'')}} [[chromaticity]] space devised by [[David MacAdam]].<ref>{{cite journal|authorlink=David MacAdam|first=David Lewis|last=MacAdam|title=Projective transformations of I.C.I. color specifications| journal=[[JOSA]]|volume=27|issue=8|date=August 1937|pages=294–299| url=http://www.opticsinfobase.org/abstract.cfm?URI=josa-27-8-294|doi=10.1364/JOSA.27.000294}}</ref>
 
The CIE 1960 UCS does not define a [[luminance (relative)|luminance]] or [[lightness (color)|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.<ref>{{cite book|title=Digital Pictures: Representation, Compression, and Standards|publisher=Springer|isbn=0-306-42195-X|author=Arun N. Netravali, Barry G. Haskell|authorlink=Arun Netravali|edition=2E|page=288| url=http://books.google.com/?id=-TXYfZrCBuQC&pg=PA288&dq=Riemannian+munsell|year=1986}}</ref>
 
Today, the CIE 1960 UCS is mostly used to calculate [[correlated color temperature]], where the [[isotherm (contour line)|isotherm]]al lines are perpendicular to the [[Planckian locus]]. As a uniform chromaticity space, it has been superseded by the [[CIELUV|CIE 1976 UCS]].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:<ref>{{cite journal|title=A Maxwell Triangle Yielding Uniform Chromaticity Scales|journal=[[JOSA]]|first=Deane B.|last=Judd|volume=25|issue=1|date=January 1935|pages=24–35| url=http://www.opticsinfobase.org/abstract.cfm?URI=josa-25-1-24| quote=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.|doi=10.1364/JOSA.25.000024}}</ref>
 
<math>\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}</math>
 
(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<ref>{{cite journal|journal=[[JOSA]]|title=Quantitative data and methods for colorimetry|volume=34|issue=11|date=November 1944|author=OSA Committee on Colorimetry| pages=633–688|url=http://www.opticsinfobase.org/abstract.cfm?URI=josa-34-11-633}} (recommended reading)</ref>{{Clarify|date=August 2013|post-text=The following formulae do not agree with u=R/(R+G+B) and v=G/(R+G+B)}}
 
[[File:Judd's-UCS.png|thumb|400px|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.)]]
 
<math>u=\frac{0.4661x+0.1593y}{y-0.15735x+0.2424}</math>
 
<math>v=\frac{0.6581y}{y-0.15735x+0.2424}</math>
 
or equivalently (for comparative purposes with the equations to follow):
 
<math>u=\frac{5.5932x+1.9116y}{12y-1.882x+2.9088}</math>
 
<math>v=\frac{7.8972y}{12y-1.882x+2.9088}</math>
 
MacAdam simplified Judd's UCS for computational purposes:
 
<math>u = \frac{4x}{12y - 2x + 3}</math>
 
<math>v = \frac{6y}{12y - 2x + 3}</math>
 
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,<ref>{{cite journal| url=http://www.opticsinfobase.org/abstract.cfm?URI=josa-50-1-87| title=Brussels Session of the International Commission on Illumination|authorlink=International Commission on Illumination|journal=[[JOSA]]|volume=50|issue=1|date=January 1960|pages=89–90|author=CIE|quote=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 {{nobr|4''X''/(''X'' + 15''Y'' + 3''Z'')}}  as  abscissa  and {{nobr|6''Y''/(''X'' + 15''Y'' + 3''Z'')}}  as ordinate,  in which  ''X'', ''Y'', and ''Z''  are the  tristimulus  values  corresponding to the  1931  CIE  Standard  Observer  and  Coordinate  System.}}</ref> and officially adopted it as the standard UCS the next year.<ref>{{Cite web|location=Brussels|year=1960|author=CIE|authorlink=International Commission on Illumination|contribution=Official Recommendations|page=36|series=14th Session|title=Publication No. 004: Proceedings of the CIE Session 1959 in Bruxelles|volume=A|url=http://cie.kee.hu/newcie/main/withdrawn.html}}</ref>
 
==Relation to CIEXYZ==
[[File:CIE UVW Diagramme de chromaticité 002.png|thumb|right|400px|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:
:<math>U= \textstyle{\frac{2}{3}}X</math>
:<math>V=Y\,</math>
:<math>W=\textstyle{\frac{1}{2}}(-X+3Y+Z)</math>
Going the other way:
:<math>X=\textstyle{\frac 32}U</math>
:<math>Y=V</math>
:<math>Z=\textstyle{\frac{3}{2}}U-3V+2W</math>
We then find the [[chromaticity]] variables as:
:<math>u =\frac U{U+V+W}= \frac{4X}{X + 15Y +3Z}</math>
:<math>v =\frac V{U+V+W}= \frac{6Y}{X + 15Y + 3Z}</math>
We can also convert from ''u'' and ''v'' to ''x'' and ''y'':
:<math>x = \frac{3u}{2u - 8v + 4}</math>
:<math>y = \frac{2v}{2u - 8v + 4}</math>
 
==Relation to CIELUV==
:<math>u^\prime = u\,</math>
:<math>v^\prime = \textstyle{\frac{3}{2}}v\,</math>
 
==References==
<references/>
 
==External links==
* [http://www.efg2.com/Lab/Graphics/Colors/Chromaticity.htm Free Windows utility to generate chromaticity diagrams.] Delphi source included.
 
{{color space}}
 
 
 
[[Category:Color space]]

Latest revision as of 15:14, 18 November 2014

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