CIELUV

In colorimetry, the CIE 1976 (L*, u*, v*) color space, also known as the CIELUV color space, is a color space adopted by the International Commission on Illumination (CIE) in 1976, as a simple to compute transformation of the 1931 CIE XYZ color space, but which attempted perceptual uniformity. It is extensively used for applications such as computer graphics which deal with colored lights. Although additive mixtures of different colored lights will fall on a line in CIELUV's uniform chromaticity diagram, such additive mixtures will not, contrary to popular belief, fall along a line in the CIELUV color space unless the mixtures are constant in lightness.

Historical background

CIELUV is an Adams Chromatic Valance space, and is an update of the CIE 1964 U*V*W* color space. The differences include a slightly modified lightness scale, and a modified uniform chromaticity scale (in which one of the coordinates, v', is 1.5 times as large as its predecessor, v). CIELUV and CIELAB were adopted simultaneously by the CIE when no clear consensus could be formed behind only one or the other of these two color spaces.

CIELUV uses a translational (Judd type) white point adaptation. This can produce useful results when working with a single illuminant, but can predict imaginary colors (i.e., outside the spectrum locus) when attempting to use it as a chromatic adaptation transform. The translational adaptation transform used in CIELUV has also been shown to perform poorly in predicting corresponding colors.

XYZ → CIELUV, CIELUV → XYZ conversions

The forward transformation

CIE 1976 L*u*v* (CIELUV) is based directly on CIE XYZ and is another attempt to define an encoding with uniformity in the perceptibility of color differences. The non-linear relations for L*, u*, and v* are given below:

${\begin{array}{rcl}L^{*}&=&\left\{{\begin{array}{ll}116(Y/Y_{n})^{1/3}-16,&Y/Y_{n}>(6/29)^{3}\\(29/3)^{3}(Y/Y_{n}),&Y/Y_{n}\leq (6/29)^{3}\end{array}}\right.\\u^{*}&=&13L^{*}(u'-u_{n}')\\v^{*}&=&13L^{*}(v'-v_{n}')\end{array}}$

The quantities $u_{n}'$ and $v_{n}'$ are the (u', v') chromaticity coordinates of a "specified white object," which may be termed the white point. In reflection mode, this is often (but not always) taken as the (u', v') of the perfect reflecting diffuser under that illuminant. (For example, for the 2° observer and illuminant C, $u_{n}'=0.2009$, $v_{n}'=0.4610$.) Equations for u' and v' are given below:

${\begin{array}{lcccc}u'&=&4X/(X+15Y+3Z)&=&4x/(-2x+12y+3)\\v'&=&9Y/(X+15Y+3Z)&=&9y/(-2x+12y+3)\end{array}}$

The reverse transformation

The transformation from (u',v') to (x,y) is:

$x=27u'/(18u'-48v'+36)\,$

$y=12v'/(18u'-48v'+36)\,$.

The transformation from CIELUV to XYZ is performed as follows:

${\begin{array}{rcl}u'&=&u^{*}/(13L^{*})+u'_{n}\\v'&=&v^{*}/(13L^{*})+v'_{n}\\\\Y&=&\left\{{\begin{array}{ll}Y_{n}\cdot (L^{*})\cdot (3/29)^{3},&L^{*}\leq 8\\Y_{n}((L^{*}+16)/116)^{3},&L^{*}>8\end{array}}\right.\\\\X&=&-9Yu'/((u'-4)v'-u'v')\\Z&=&(9Y-15v'Y-v'X)/3v'\end{array}}$