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[[File:Lab color space.png|thumb|right| The CIE 1976 (''L''*, ''a''*, ''b''*) color space (CIELAB), showing only colors that fit within the [[sRGB color space|sRGB]] gamut (and can therefore be displayed on a typical computer display). Each axis of each square ranges from -128 to 128.]]
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A '''''Lab'' color space''' is a [[opponent process|color-opponent]] space with dimension '''''L''''' for [[lightness (color)|lightness]] and '''''a''''' and '''''b''''' for the color-opponent dimensions, based on nonlinearly compressed [[CIE XYZ color space]] coordinates.
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The dimensions of the '''[[Richard S. Hunter|Hunter]] 1948 ''L'', ''a'', ''b'' color space''' are ''L'', ''a'', and ''b''.<ref name="Hunter1948a">{{cite journal|title=Photoelectric Color-Difference    Meter|first=Richard Sewall|last=Hunter|journal=[[JOSA]]|volume=38|issue=7|pages=661|date=July 1948| url=http://www.opticsinfobase.org/abstract.cfm?URI=josa-38-7-651}} (Proceedings of the Winter Meeting of the Optical Society of America)</ref><ref name="Hunter1948b">{{cite journal|title= Accuracy, Precision, and Stability of New Photo-electric Color-Difference Meter|first=Richard Sewall|last=Hunter|journal=[[JOSA]]|volume=38|issue=12|pages=1094|date=December 1948| url=http://www.opticsinfobase.org/abstract.cfm?URI=josa-38-12-1092}} (Proceedings of the Thirty-Third Annual Meeting of the Optical Society of America)</ref> However, ''Lab'' is now more often used as an informal abbreviation for the '''CIE 1976 (''L*'', ''a*'', ''b*'') color space''' (or CIELAB). The difference between Hunter and CIE color coordinates is that the CIE coordinates are based on a cube root transformation of the color data, while the Hunter coordinates are based on a square root transformation.
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Both spaces are derived from the "master" space [[CIE 1931 color space|CIE 1931 XYZ color space]], which can predict which [[spectral power distribution]]s will be perceived as the same color (see [[Metamerism (color)|metamerism]]), but which is not particularly [[color difference#Tolerance|perceptually uniform]].<ref>[http://www.brucelindbloom.com/UPLab.html A discussion and proposed improvement], Bruce Lindbloom</ref> Strongly influenced by the [[Munsell color system]], the intention of both "Lab" color spaces is to create a space that can be computed via simple formulas from the ''XYZ'' space but is more perceptually uniform than ''XYZ''.<ref>[http://www.handprint.com/HP/WCL/color7.html#CIELUV Explanation of this history], Bruce MacEvoy</ref> ''Perceptually uniform'' means that a change of the same amount in a color value should produce a change of about the same visual importance. When storing colors in limited precision values, this can improve the reproduction of tones.  Both Lab spaces are relative to the [[white point]] of the ''XYZ'' data they were converted from.  Lab values do not define absolute colors unless the white point is also specified.  Often, in practice, the white point is assumed to follow a standard and is not explicitly stated (e.g., for "absolute colorimetric" [[rendering intent]] ICC ''L*a*b*'' values are relative to [[standard illuminant|CIE standard illuminant]] D50, while they are relative to the unprinted substrate for other rendering intents).<ref name="ICC4"/>
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The lightness correlate in CIELAB is calculated using the cube root of the [[relative luminance]].
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The L*a*b* color space includes all perceivable colors, which means that its gamut exceeds those of the RGB and CMYK color models (for example, ProPhoto RGB includes about 90% all perceivable colors). One of the most important attributes of the L*a*b*-model is device independence. This means that the colors are defined independent of their nature of creation or the device they are displayed on.  The L*a*b* color space is used, e.g. in Adobe Photoshop when graphics for print have to be converted from RGB to CMYK, as the L*a*b* gamut includes both the RGB and CMYK gamut. Also it is used as an interchange format between different devices as for its device independency.
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[[File:Example of LAB color enhancement.jpg|right|thumb|200px|An example of color enhancement using LAB colorspace in Photoshop. The left side of the photo is enhanced, the right side is normal.]]
 
Unlike the [[RGB color model|RGB]] and [[CMYK color model|CMYK]] color models, ''Lab'' color is designed to approximate human vision.  It aspires to perceptual uniformity, and its ''L'' component closely matches human perception of lightness, although it does not take the [[Helmholtz–Kohlrausch effect]] into account. Thus, it can be used to make accurate color balance corrections by modifying output [[Curve (tonality)|curves]] in the ''a'' and ''b'' components, or to adjust the lightness contrast using the ''L'' component. In RGB or CMYK spaces, which model the output of physical devices rather than human visual perception, these transformations can be done only with the help of appropriate [[blend modes]] in the editing application.
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Because ''Lab'' space is much larger than the [[gamut]] of computer displays, printers, or even human vision, a bitmap image represented as Lab requires more data per pixel to obtain the same precision as an RGB or CMYK bitmap. In the 1990s, when computer hardware and software were limited to storing and manipulating mostly 8-bit/channel bitmaps, converting an RGB image to Lab and back was a very lossy operation.  With 16-bit/channel support now common, the loss due to quantization is negligible.
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In addition, many of the "colors" within Lab space fall outside the gamut of human vision, and are therefore purely imaginary; these "colors" cannot be reproduced in the physical worldThough color management software, such as that built into image editing applications, will pick the closest in-gamut approximation, changing [[lightness]], [[colorfulness|chroma]], and sometimes [[hue]] in the process, author [[Dan Margulis]] claims that this access to [[imaginary color]]s is useful, going between several steps in the manipulation of a picture.<ref name="margulis">{{cite book|title=Photoshop Lab Color: The Canyon Conundrum and Other Adventures in the Most Powerful Colorspace|isbn=0-321-35678-0|first=Dan|last=Margulis|year=2006|publisher=Peachpit ; Pearson Education|location=Berkeley, Calif. : London}}</ref>
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Some specific uses of the abbreviation in software, literature etc.
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* In [[Adobe Photoshop]], image editing using "Lab mode" is CIELAB D50.<ref name="margulis"/><ref>[http://web.archive.org/web/20081207061220/http://kb.adobe.com/selfservice/viewContent.do?externalId=310838 The Lab Color Mode in Photoshop], Adobe TechNote 310838</ref>
 
* In [[ICC profile]]s, the "Lab color space" used as a [[color management#Profile connection space|profile connection space]] is CIELAB D50.<ref name="ICC4">International Color Consortium, ''Specification ICC.1:2004-10 (Profile version 4.2.0.0) Image technology colour management — Architecture, profile format, and data structure,'' (2006).</ref><!-- The TIFF Specification is very careful to specify the CIELAB color space; no possible confusion with Hunter Lab here. -->
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* In [[TIFF]] files, the CIELAB color space may be used.<ref name="TIFF6">''[http://partners.adobe.com/asn/developer/PDFS/TN/TIFF6.pdf TIFF: Revision 6.0]'' Adobe Developers Association, 1992</ref>
 
* In [[PDF]] documents, the "Lab color space" is CIELAB.<ref>[http://www.adobe.com/products/creativesuite/pdfs/cscolormgmt.pdf Color Consistency and Adobe Creative Suite]</ref><ref>[http://www.state.nj.us/njded/legal/reader.pdf Adobe Acrobat Reader 4.0 User Guide] "The color model Acrobat Reader uses is called CIELAB…"</ref>
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==CIELAB==
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'''CIE ''L*a*b*'' (CIELAB)''' is the most complete{{Citation needed|reason=Are there really any colors that cannot be represented in CIE XYZ?|date=May 2009}}  [[color space]] specified by the [[International Commission on Illumination]] (French ''Commission internationale de l'éclairage'', hence its ''CIE'' [[initialism]]). It describes all the [[color vision|colors visible]] to the human eye and was created to serve as a device-independent model to be used as a reference.


The three coordinates of CIELAB represent the lightness of the color ('''''L*''''' = 0 yields black and '''''L*''''' = 100 indicates diffuse white; specular white may be higher), its position between red/magenta and green ('''''a*''''', negative values indicate green while positive values indicate magenta) and its position between yellow and blue ('''''b*''''', negative values indicate blue and positive values indicate yellow). The asterisk (*) after ''L'', ''a'' and ''b'' are pronounced ''star'' and are part of the full name, since they represent ''L''*, ''a''* and ''b''*, to distinguish them from Hunter's ''L'', ''a'', and ''b'', described below.
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Since the ''L*a*b*'' model is a three-dimensional model, it can be represented properly only in a three-dimensional space.<ref>[http://www.brucelindbloom.com/index.html?WorkingSpaceInfo.html 3D representations of the ''L*a*b*'' gamut], Bruce Lindbloom.</ref> Two-dimensional depictions include chromaticity diagrams: sections of the [[color solid]] with a fixed lightness. It is crucial to realize that the visual representations of the full [[gamut]] of colors in this model are never accurate; they are there just to help in understanding the concept.
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Because the red-green and yellow-blue opponent channels are computed as differences of lightness transformations of (putative) cone responses, CIELAB is a [[Adams chromatic valence color space#Chromatic value|chromatic value]] color space.
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A related color space, the CIE 1976 (''L''*, ''u''*, ''v''*) color space (a.k.a. [[CIELUV]]), preserves the same ''L*'' as ''L*a*b*'' but has a different representation of the chromaticity components. CIELAB and CIELUV can also be expressed in cylindrical form (CIELCH<ref>[http://www.hunterlab.com/appnotes/an09_96a.pdf CIE-L*C*h Color Scale]</ref> and [[CIELUV_color_space#Cylindrical_representation|CIELCH<sub>uv</sub>]], respectively), with the chromaticity components replaced by correlates of [[Chrominance|chroma]] and [[hue]].
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Since CIELAB and CIELUV, the CIE has been incorporating an increasing number of [[color appearance phenomena]] into their models, to better model color vision. These [[color appearance model]]s, of which CIELAB is a simple example,<ref>{{cite book|title=Color Appearance Models|first=Mark D.|last=Fairchild|year=2005|publisher=John Wiley and Sons|isbn=0-470-01216-1|page=340|chapter=Color and Image Appearance Models| url=http://books.google.com/?id=8_TxzK2B-5MC&pg=PA340&dq=cielab+color+appearance+model}}</ref> culminated with [[CIECAM02]].
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===Perceptual differences===
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The nonlinear relations for ''L*'', ''a*'', and ''b*'' are intended to mimic the nonlinear response of the eye. Furthermore, uniform changes of components in the ''L*a*b*'' color space aim to correspond to uniform changes in perceived color, so the relative perceptual differences between any two colors in ''L*a*b*'' can be approximated by treating each color as a point in a three-dimensional space (with three components: ''L*'', ''a*'', ''b*'') and taking the [[Euclidean distance]] between them.<ref name="Jain89">{{cite book|title=Fundamentals of Digital Image Processing|first=Anil K.|last=Jain|pages=68, 71, 73|year=1989|publisher=[[Prentice Hall]]|location=New Jersey, United States of America|isbn=0-13-336165-9}}</ref>
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===RGB and CMYK conversions===
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There are no simple formulas for conversion between [[RGB color model|RGB]] or [[CMYK color model|CMYK]] values and ''L*a*b*'', because the RGB and CMYK color models are device-dependent. The RGB or CMYK values first must be transformed to a specific [[absolute color space]], such as [[sRGB color space|sRGB]] or [[Adobe RGB color space|Adobe RGB]]. This adjustment will be device-dependent, but the resulting data from the transform will be device-independent, allowing data to be transformed to the [[CIE 1931 color space]] and then transformed into ''L*a*b*''.
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=== Range of coordinates ===
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As mentioned previously, the ''L''* coordinate ranges from 0 to 100. The possible range of ''a''* and ''b''* coordinates is independent of the color space that one is converting from, since the conversion below uses X and Y, which come from RGB.
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==CIELAB-CIEXYZ conversions==
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:<math>\begin{align}
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  L^\star &= 116 f(Y/Y_n) - 16\\
  a^\star &= 500 \left[f(X/X_n) - f(Y/Y_n)\right]\\
  b^\star &= 200 \left[f(Y/Y_n) - f(Z/Z_n)\right]
\end{align}</math>


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\end{cases}</math>
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Here, ''X''<sub>''n''</sub>, ''Y''<sub>''n''</sub> and ''Z''<sub>''n''</sub> are the [[CIE XYZ]] tristimulus values of the reference [[white point]] (the subscript n suggests "normalized").
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The division of the domain of the ''f''(''t'') function into two parts was done to prevent an infinite slope at {{nobr|1=''t'' = 0}}. ''f''(''t'') was assumed to be linear below some {{nobr|1=''t'' = ''t''<sub>0</sub>}}, and was assumed to match the ''t''<sup>1/3</sup> part of the function at ''t''<sub>0</sub> in both value and slope. In other words:
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:<math>\begin{align}
 
   t_0^{1/3} &= a t_0 + b & \text{ (match in value)}\\
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\end{align}</math>
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The intercept {{nobr|1=''f''(0) = ''b''}} was chosen so that ''L''* would be 0 for {{nobr|1=''Y'' = 0}}: {{nobr|1=''b'' = 16/116 = 4/29}}. The above two equations can be solved for ''a'' and ''t''<sub>0</sub>:
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:<math>\begin{align}
  a &= \tfrac13\delta^{-2} &= 7.787037\ldots\\
  t_0 &= \delta^3 &= 0.008856\ldots
\end{align}</math>


where {{nobr|1=''δ'' = 6/29}}.<ref>
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{{cite book
 
| title = Colorimetry
  <li>[http://metransparent.nfrance.com/~k1001/spip.php?article8359&lang=ar&id_forum=8701/ http://metransparent.nfrance.com/~k1001/spip.php?article8359&lang=ar&id_forum=8701/]</li>
| author = János Schanda
 
| publisher = Wiley-Interscience
  <li>[http://co-at-work.zib.de/phorum/read.php?3,456984 http://co-at-work.zib.de/phorum/read.php?3,456984]</li>
| year = 2007
 
| isbn = 978-0-470-04904-4
  <li>[http://www.sebalo.info/spip/spip.php?article14 http://www.sebalo.info/spip/spip.php?article14]</li>
| page = 61
 
| url = http://books.google.com/?id=uZadszSGe9MC&pg=PA61&dq=lab+color+6-29+16-116
  <li>[http://jz.791.com/news/html/?225736.html http://jz.791.com/news/html/?225736.html]</li>
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===Reverse transformation===
 
 
</ul>
The reverse transformation is most easily expressed using the inverse of the function ''f'' above:
 
:<math>\begin{align}
  Y &= Y_n f^{-1}\left(\tfrac{1}{116}\left(L^*+16\right)\right)\\
  X &=  X_n f^{-1}\left(\tfrac{1}{116}\left(L^*+16\right) + \tfrac{1}{500}a^*\right)\\
  Z &=  Z_n f^{-1}\left(\tfrac{1}{116}\left(L^*+16\right) - \tfrac{1}{200}b^*\right)\\
\end{align}</math>
 
where
 
:<math>f^{-1}(t) = \begin{cases}
  t^3 & \text{if } t > \tfrac{6}{29} \\
3\left(\tfrac{6}{29}\right)^2\left(t - \tfrac{4}{29}\right) & \text{otherwise}
\end{cases}</math>
 
==Hunter Lab==
 
'''''L''''' is a correlate of [[Lightness (color)|lightness]], and is computed from the ''Y'' [[tristimulus]] value using Priest's approximation to [[Munsell]] value:
 
: <math>L=100\sqrt{Y / Y_n}</math>
 
where ''Y''<sub>''n''</sub> is the ''Y'' tristimulus value of a specified white object. For surface-color applications, the specified white object is usually (though not always) a hypothetical material with unit reflectance that follows [[Lambert's law]]. The resulting ''L'' will be scaled between 0 (black) and 100 (white); roughly ten times the Munsell value. Note that a medium lightness of 50 is produced by a luminance of 25, since <math>100 \sqrt{25/100} = 100 \cdot 1/2</math>
 
'''''a''''' and '''''b''''' are termed [[opponent color]] axes. ''a'' represents, roughly, Redness (positive) versus Greenness (negative). It is computed as:
 
: <math>a=K_a\left(\frac{X/X_n-Y/Y_n}{\sqrt{Y/Y_n}}\right)</math>
 
where <math>K_a</math> is a coefficient that depends upon the illuminant (for D65, K<sub>a</sub> is 172.30; see approximate formula below) and <math>X_n</math> is the ''X'' tristimulus value of the specified white object.
 
The other opponent color axis, ''b'', is positive for yellow colors and negative for blue colors. It is computed as:
 
: <math>b=K_b\left(\frac{Y/Y_n-Z/Z_n}{\sqrt{Y/Y_n}}\right)</math>
 
where ''K''<sub>''b''</sub> is a coefficient that depends upon the illuminant (for [[CIE Standard Illuminant D65|D65]], ''K''<sub>''b''</sub> is 67.20; see approximate formula below) and ''Z''<sub>''n''</sub> is the ''Z'' tristimulus value of the specified white object.<ref>Hunter Labs (1996). "Hunter Lab Color Scale". ''Insight on Color'' '''8''' 9 (August 1–15, 1996). Reston, VA, USA: Hunter Associates Laboratories.</ref>
 
Both ''a'' and ''b'' will be zero for objects that have the same [[chromaticity]] coordinates as the specified white objects (i.e., achromatic, grey, objects).
 
===Approximate formulas for ''K''<sub>''a''</sub> and ''K''<sub>''b''</sub>===
 
In the previous version of the Hunter ''Lab'' color space, ''K''<sub>''a''</sub> was 175 and ''K''<sub>''b''</sub> was 70. Hunter Associates Lab discovered{{cn|date=December 2013}} that better agreement could be obtained with other color difference metrics, such as CIELAB (see above) by allowing these coefficients to depend upon the illuminants. Approximate formulae are:
 
: <math>K_a\approx\frac{175}{198.04}(X_n+Y_n)</math>
 
: <math>K_b\approx\frac{70}{218.11}(Y_n+Z_n)</math>
 
which result in the original values for Illuminant ''C'', the original illuminant with which the ''Lab'' color space was used.
 
===As an Adams chromatic valence space===
 
[[Adams chromatic valence color space]]s are based on two elements: a (relatively) uniform lightness scale, and a (relatively) uniform [[chromaticity]] scale.<ref name=Adams1942>{{cite journal
| title = X-Z planes in the 1931 I.C.I. system of colorimetry
| url = http://www.opticsinfobase.org/abstract.cfm?id=49502
| author = Adams, E.Q.
| journal = [[JOSA]]
| volume = 32
| issue = 3
| pages = 168–173
| year = 1942
| doi = 10.1364/JOSA.32.000168
}}</ref> If we take as the uniform lightness scale Priest's approximation to the Munsell Value scale, which would be written in modern notation: <!-- FIXME: needs more citations, more explanation (historical discussion, etc), and if possible some pictures. -->
 
: <math>L=100\sqrt{Y / Y_n}</math>
 
and, as the uniform chromaticity coordinates:
 
: <math>c_a=\frac{X/X_n}{Y/Y_n}-1=\frac{X/X_n-Y/Y_n}{Y/Y_n}</math>
 
: <math>c_b=k_e\left(1-\frac{Z/Z_n}{Y/Y_n}\right)=k_e\frac{Y/Y_n-Z/Z_n}{Y/Y_n}</math>
 
where ''k''<sub>''e''</sub> is a tuning coefficient, we obtain the two chromatic axes:
 
: <math>a=K\cdot L\cdot c_a=K\cdot 100\frac{X/X_n-Y/Y_n}{\sqrt{Y/Y_n}}</math>
 
and
 
: <math>b=K\cdot L\cdot c_b=K\cdot 100 k_e \frac{Y/Y_n-Z/Z_n}{\sqrt{Y/Y_n}}</math>
 
which is identical to the Hunter ''Lab'' formulas given above if we select {{nobr|1=''K'' = ''K''<sub>''a''</sub>/100}} and {{nobr|1=''k''<sub>''e''</sub> = ''K''<sub>''b''</sub>/''K''<sub>''a''</sub>}}. Therefore, the Hunter Lab color space is an [[Adams chromatic valence color space]].
 
== See also ==
* [[Color theory]]
* [[HSL and HSV]]
* [[RGB color model]]
* [[CMYK color model]]
 
== References ==
{{reflist|2}}
 
== External links ==
* [http://www.cs.rit.edu/~ncs/color/a_spaces.html Demonstrative color conversion applet]
* [http://docs-hoffmann.de/cielab03022003.pdf CIELAB Color Space] by Gernot Hoffmann, includes explanations of L*a*b* conversion formulae, graphical depictions of various gamuts plotted in L*a*b* space, and PostScript code for performing the color transformations.
* [https://www.byk.com/fileadmin/BYK/downloads/support-downloads/instruments/theory/color/en/Intro_Solid_Color.pdf Color Differences]  
{{Color space}}
 
 
 
[[Category:Color space]]

Latest revision as of 16:03, 10 December 2014

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