106.51.253.42 at 10:00, 6 November 2014

2014-11-06T10:00:00Z

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	~~In [[colorimetry]], the '''CIE 1976 (''L'', ''u'', ''v''*) color space''', commonly known by its abbreviation '''CIELUV''',~~ is ~~a [[color space]] adopted by the [[International Commission on Illumination]] (CIE) in 1976, as a simple-to-compute transformation of the 1931 [[CIE 1931 color space\|CIE XYZ color space]],~~ but which attempted [[Color_difference#Tolerance\|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]] (dubbed the ''CIE 1976 UCS''), 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 (color)\|lightness]].		Andera is what you can call her but she never truly liked that title. To perform lacross is some thing he would never give up. Invoicing is my profession. North Carolina is the location he loves most but now he is considering other options.<br><br>my blog best psychic readings [[http://www.indosfriends.com/profile-253/info/ click here]]

	~~==Historical background==~~
	CIELUV is an [[Adams chromatic valence color space]], and is an update of the [[CIE 1964 color space\|CIE 1964 (''U'', ''V'', ''W''*) color space]] (CIEUVW). The differences include a slightly modified [[Lightness (color)\|lightness]] scale, and a modified uniform chromaticity scale in which one of the coordinates, ''v''′, is 1.5 times as large as ''v'' its [[CIE 1960 color space\|1960 predecessor]]. 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 Judd-type (translational) [[white point]] adaptation (in contrast with CIELAB, which uses a "wrong" [[von Kries transform]]).<ref>{{cite journal\|first=Deane B.\|last=Judd\|~~title=Hue saturation and lightness of surface colors with chromatic illumination\|journal=[[JOSA]]\|volume=30\|issue=1\|date=January 1940\|pages=2–32\| url=http://www.opticsinfobase.org/abstract.cfm?URI=josa-30-1-2\|doi=10.1364/JOSA.30.000002}}</ref> This can produce useful results when working with a single illuminant, but can predict [[imaginary color]]s (i.e., outside the [[spectral locus]]) when attempting to use it as a [[chromatic adaptation transform]].<ref name="Fairchild1998">Mark D Fairchild, ''Color Appearance Models.~~'' Reading, MA: Addison-Wesley, 1998.</ref> The translational adaptation transform used in CIELUV has also been shown to~~ perform poorly in predicting corresponding colors.<ref name="Alman1989">D. H. Alman, R. S. Berns, G. D. Snyder, and W. A. Larson, "Performance testing of color difference metrics using a color-tolerance dataset." ''Color Research and Application,'' '''21''':174-188 (1989).</ref>

	~~== XYZ → CIELUV and CIELUV → XYZ conversions ==~~
	~~For typical images, ''u''* and ''v''* range ±100. By definition, {{nobr\|0 ≤ ''L''* ≤ 100}}, except for specular highlights{{elucidate\|date=February 2013}}.{{citation needed\|date=February 2013}}~~

	~~===The forward transformation===~~
	CIELUV is based on CIEUVW and is another attempt to define an encoding with uniformity in the perceptibility of [[color difference]]s.<ref name=schanda/> The non-linear relations for ''L'', ''u'', and ''v''* are given below:<ref name=schanda>{{cite book\|title=Colorimetry: Understanding the CIE System\|first=János\|last=Schanda\|publisher=Wiley Interscience\|year=2007\|isbn=978-0-470-04904-4\|quote=As 24/116 is ~~not a simple ratio, in~~ some publications the 6/29 ratio is used, in others the approximate value of 0.008856 (used in earlier editions of CIE 15). Similarly some authors prefer to use instead of 841/108 the expression (1/3)×(29/6)<sup>2</sup> or the approximate value of 7.~~787, or instead of 16/116 the ratio 4/29.\|pages=61–64}}</ref>~~

	~~:<math>~~
	~~\begin{align}~~
	~~L^* &= \begin{cases}~~
	~~\left(\frac{29}{3}\right)^3 Y / Y_n,& Y / Y_n \le \left(\frac{6}{29}\right)^3 \\~~
	~~116 \left( Y / Y_n \right)^{1/3} - 16,& Y / Y_n > \left(\frac{6}{29}\right)^3~~
	~~\end{cases}\\~~
	~~u^* &= 13 L^*\cdot (u^\prime - u_n^\prime) \\~~
	~~v^* &= 13 L^*\cdot (v^\prime - v_n^\prime)~~
	~~\end{align}</math>~~

	The quantities ''u''′<sub>''n''</sub> and ''v''′<sub>''n''</sub> are the {{nobr\|(''u''′, ''v''′)}} chromaticity coordinates of a "specified white object" – which may be termed the [[white point]] – and ''Y''<sub>''n''</sub> is ~~its luminance~~. ~~In reflection mode, this~~ is ~~often (~~but not always) taken as the {{nobr\|(''u''′, ''v''′)}} of the [[Diffuser (optics)\|perfect reflecting diffuser]] under that illuminant. (For example, for the [[standard colorimetric observer\|2° observer]] and [[standard illuminant]] C, {{nobr\|1=''u''′<sub>''n''</sub> = 0.2009}}, {{nobr\|1=''v''′<sub>''n''</sub> = 0.4610}}.) Equations for ''u''′ and ''v''′ are given below:<ref name="CIE15point2">''Colorimetry,'' second edition: CIE publication 15.2. Vienna: Bureau Central CIE, 1986.</ref><ref name=poynton/>

	~~:<math>\begin{align}~~
	~~u^\prime &= \frac{4 X}{X + 15 Y + 3 Z} &= \frac{4 x}{-2 x + 12 y + 3} \\~~
	~~v^\prime &= \frac{9 Y}{X + 15 Y + 3 Z} &= \frac{9 y}{-2 x + 12 y + 3}~~
	~~\end{align}</math>~~

	~~===The reverse transformation===~~
	~~[[Image:CIE 1976 UCS.png\|right\|thumb\|300px\|{{nobr\|(''u''′, ''v''′)}} chromaticity diagram, also known as the CIE 1976 UCS (uniform chromaticity scale) diagram.]]~~
	~~The transformation from {{nobr\|(''u''′, ''v''′)}} to {{nobr\|(''x'', ''y'')}}~~ is~~:<ref name=poynton/>~~

	~~:<math>\begin{align}~~
	~~x &= \frac{9u^\prime}{6u^\prime - 16v^\prime + 12}\\~~
	~~y &= \frac{4v^\prime}{6u^\prime - 16v^\prime + 12}~~
	~~\end{align}</math>~~

	~~The transformation from CIELUV to XYZ is performed as follows:<ref name=poynton/>~~

	~~:<math>\begin{align}~~
	~~u^\prime&= \frac{u^}{13L^} + u^\prime_n \\~~
	~~v^\prime&= \frac{v^}{13L^} + v^\prime_n \\~~
	~~Y &= \begin{cases}~~
	~~Y_n \cdot L^* \cdot \left(\frac{3}{29}\right)^3,& L^* \le 8 \\~~
	~~Y_n \cdot \left(\frac{L^* + 16}{116}\right)^3,& L^* > 8~~
	~~\end{cases}\\~~
	~~X &= Y \cdot \frac{9u^\prime}{4v^\prime} \\~~
	~~Z &= Y \cdot \frac{12 - 3u^\prime - 20v^\prime}{4v^\prime} \\~~
	~~\end{align}</math>~~

	~~==Cylindrical representation==~~
	The [[cylindrical coordinate system\|cylindrical]] version of CIELUV is known as CIE LCh<sub>uv</sub>, where ''C''*<sub>''uv''</sub> is the [[colorfulness\|chroma]] and ''h''<sub>''uv''</sub> is the [[hue]]:<ref name=poynton/>

	~~:<math>C_{uv}^* = \sqrt{(u^)^2 + (v^)^2}</math>~~

	~~:<math>h_{uv} = \operatorname{atan2}(v^,u^),</math>~~
	~~where [[atan2]] function, a "two-argument arctangent", computes the [[polar coordinates\|polar]] angle from a Cartesian coordinate pair~~.

	~~Furthermore, the saturation correlate can be defined as:~~

	:<~~math~~>~~s_{uv} = \frac{C^}{L^} = 13 \sqrt{(u^\prime - u^\prime_n)^2 + (v^\prime - v^\prime_n)^2}~~<~~/math~~>

	~~Similar correlates of chroma and hue, but not saturation, exist for CIELAB. See [[Colorfulness#Saturation\|Colorfulness]] for more discussion on saturation.~~

	~~==Color and hue difference==~~
	~~The~~ [[color difference]] can be calculated using the [[Euclidean distance]] of the {{nobr\|(''L'', ''u'', ''v'')}} co-ordinates.<ref name=poynton>{{cite book\|first=Charles\|last=Poynton\|title=Digital Video and HDTV\| publisher=Morgan-Kaufmann\|isbn=1-55860-792-7\|year=2003\|pages=226}}</ref> It follows that a chromaticity distance of <math>\sqrt{(\Delta u')^2 + (\Delta v')^2}=1/13</math> corresponds to the same Δ''E''<sub>''uv''</sub> as a lightness difference of {{nobr\|1=Δ''L''* = 1}}, in direct analogy to CIEUVW.

	The Euclidean metric can also be used in CIELCH, with that component of Δ''E''<sub>''uv''</sub> attributable to difference in hue as<ref name=schanda/> {{nobr\|1=Δ''H'' = {{radic\|''C''<sub>1</sub>''C''<sub>2</sub>}} 2 sin (Δ''h''/2)}}, where {{nobr\|1=Δ''h'' = ''h''<sub>2</sub> – ''h''<sub>1</sub>}}.

	~~==References==~~
	~~<references/>~~

	~~==External links==~~
	* [http://www.~~efg2~~.com/~~Lab/Graphics~~/~~Colors~~/~~Chromaticity.htm Chromaticity diagrams, including the CIE 1931, CIE 1960, CIE 1976]~~

	~~{{Color space}}~~



	~~[[Category:Color space~~]]

en>Ildeguz at 22:51, 26 January 2014

2014-01-26T22:51:48Z

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Lie algebra bundle - Revision history

106.51.253.42 at 10:00, 6 November 2014

en>Ildeguz at 22:51, 26 January 2014

en>BattyBot: changed {{Unreferenced}} to {{Refimprove}} & general fixes using AWB (7916)