Econophysics: Difference between revisions

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{{Expert-subject|Color|talk=Terrible lede|date=December 2011}}
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{{multiple image
| direction = vertical
| width = 220
| image1 = Surfing in Hawaii unmodified.jpg|caption1 = Original image, with relatively muted colors
| image2 = Surfing in Hawaii+50 LCh chroma.jpg|caption2 = L*C*h ([[CIELAB]]) chroma increased 50%
| image3 = Surfing in Hawaii+50 saturation.jpg|caption3 = [[HSL and HSV|HSL]] saturation increased 50%; notice that changing HSL saturation also affects the perceived lightness of a color
| image4 = Surfing in Hawaii L* channel.jpg|caption4 = CIELAB lightness preserved, with ''a''* and ''b''* stripped, to make a [[grayscale]] image
}}
 
In [[colorimetry]] and [[color theory]], '''colorfulness''', '''chroma''', and '''saturation''' are related but distinct concepts referring to the perceived intensity of a specific [[color]]. ''Colorfulness'' is the degree of difference between a color and [[grey|gray]]. ''Chroma'' is the colorfulness relative to the [[brightness]] of another color that appears white under similar viewing conditions. Saturation is the colorfulness of a color relative to its own brightness.<ref>Mark D. Fairchild. “[http://www.cis.rit.edu/fairchild/PDFs/AppearanceLec.pdf Color Appearance Models: CIECAM02 and Beyond]”.  Slides from a tutorial at the IS&T/SID 12th Color Imaging Conference.  9 November 2004.  Retrieved 19 September 2007.</ref> Though this general concept is intuitive, terms such as ''chroma'', ''saturation'', ''purity'', and ''intensity'' are often used without great precision, and even when well-defined depend greatly on the specific [[color model]] in use.
 
A highly colorful stimulus is vivid and intense, while a less colorful stimulus appears more muted, closer to gray. With no colorfulness at all, a color is a “neutral” gray (an image with no colorfulness in any of its colors is called ''[[grayscale]]'').  With three attributes—colorfulness (or chroma or saturation), [[lightness (color)|lightness]] (or brightness), and [[hue]]—any color can be described. {{citation needed|date=December 2012}}
 
== Saturation ==
[[Image:saturationdemo.png|thumb|left|60px|Scale of saturation (0% at bottom and it is black and white).]]
Saturation is one of three coordinates in the [[HSL and HSV]] [[color space]]s. Note that virtually all computer software implementing these spaces use a very rough approximation to calculate the value they call "saturation" (such as the formula described for [[HSL and HSV#Formal specifications|HSV]]), and this value has little, if anything, to do with the description shown here.
 
The saturation of a color is determined by a combination of light intensity and how much it is distributed across the spectrum of different wavelengths. The purest (most saturated) color is achieved by using just one wavelength at a high intensity, such as in laser light. If the intensity drops, then as a result the saturation drops.  To desaturate a color of given intensity in a [[subtractive color|subtractive]] system (such as [[watercolor]]), one can add [[white]], [[black]], [[gray (color)|gray]], or the hue's [[complementary color|complement]].
 
Various correlates of saturation follow.
 
; [[CIELUV]] : The ''chroma'' normalized by the lightness:
 
:<math>s_{uv}=\frac{C^*_{uv}}{L^*}=13 \sqrt{(u'-u'_n)^2+(v'-v'_n)^2}</math>
 
where {{nobr|(''u''′<sub>''n''</sub>, ''v''′<sub>''n''</sub>)}} is the chromaticity of the white point, and chroma is defined below.<ref>{{Cite book|last=Schanda|first=János|title=Colorimetry: Understanding the CIE System|publisher=[[Wiley Interscience]]|year=2007|isbn=978-0-470-04904-4 | url = http://books.google.com/?id=g8VDAgAACAAJ&dq=intitle:Colorimetry+intitle:Understanding+intitle:the+intitle:CIE+intitle:System|postscript=<!--None--> }}, page 88.</ref>
 
By analogy, in [[CIELAB]] this would yield:
 
:<math>s_{ab}=\frac{C^*_{ab}}{L^*}=\frac{\sqrt{{a^*}^2+{b^*}^2}}{L^*}</math>
 
The CIE has not formally recommended this equation since CIELAB has no chromaticity diagram, and this definition therefore lacks direct correlation with older concepts of saturation.<ref>{{cite book|url=http://books.google.com/?id=CU7-2ZLGFpYC&pg=PA124&dq=%22correlate+of+saturation%22+cielab+chroma+lightness+chromaticity|title=The Focal Encyclopedia of Photography|publisher=Focal Press|editor=Leslie D. Stroebel, Richard D. Zakia|isbn=0-240-51417-3|year=1993|page=124|first=Robert William Gainer|last=Hunt}}</ref> Nevertheless, this equation provides a reasonable predictor of saturation, and demonstrates that adjusting the lightness in CIELAB while holding {{nobr|(''a''*, ''b''*)}} fixed does affect the saturation.
 
But the following formula is in agreement with the human perception of saturation:
The formula proposed by Eva Lübbe is in agreement with the verbal definition of Manfred Richter: Saturation is the proportion of pure chromatic color in the total color sensation.<ref>{{Cite book|last=Lübbe|first=Eva|title=Colours in the Mind - Colour Systems in Reality- A formula for colour saturation|publisher=[Book on Demand]|year=2010|isbn=978-3-7881-4057-1 }}</ref>
 
:<math>S_{ab}=\frac{C^*_{ab}}{\sqrt{{C^*_{ab} }^2+{L^*}^2}} 100 % </math>
 
where ''S''<sub>''ab''</sub> is the saturation, ''L''* the  lightness and ''C''*<sub>''ab''</sub> is the chroma of the color.
 
; [[CIECAM02]] : The square root of the ''colorfulness'' divided by the ''brightness'':
 
:<math>s=\sqrt{M/Q}</math>
 
This definition is inspired by experimental work done with the intention of remedying [[CIECAM97s]]'s poor performance.<ref name=ciecam02>{{cite conference|title=The CIECAM02 Color Appearance Model|booktitle=IS&T/SID Tenth Color Imaging Conference|last=Moroney|first=Nathan|coauthors=Fairchild, Mark D.; Hunt, Robert W.G.; Li, Changjun; Luo, M. Ronnier; Newman, Todd|url=http://www.polybytes.com/misc/Meet_CIECAM02.pdf|location=[[Scottsdale, Arizona]]|isbn=0-89208-241-0|date=November 12, 2002|publisher=The [[Society for Imaging Science and Technology]]|format=PDF}}
</ref><ref>{{cite conference|title=Magnitude estimation for scaling saturation|first=Lu-Yin G.|last=Juan|coauthor=Luo, Ming R.|url=http://spiedl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PSISDG004421000001000575000001&idtype=cvips&gifs=yes|  booktitle=[[Proceedings of SPIE]]|volume=4421|conference=9th Congress of the International Colour Association|editors=Robert Chung, Allan Rodrigues|date=June 2002|pages=575–578|doi=10.1117/12.464511}}</ref> ''M'' is proportional to the chroma ''C'' ({{nobr|1=''M'' = ''CF''<sub>''L''</sub><sup>0.25</sup>}}), thus the CIECAM02 definition bears some similarity to the CIELUV definition. An important difference is that the CIECAM02 model accounts for the viewing conditions through the parameter ''F''<sub>''L''</sub>.<ref name=ciecam02/>
 
== Excitation purity ==
 
[[Image:Excitation Purity.svg|300px|thumb|right|'''Excitation purity''' is the relative distance from the white point. Contours of constant purity can be found by shrinking the spectral locus about the white point. The points along the line segment have the same hue, with p<sub>e</sub> increasing from 0 to 1 between the white point and position on the [[Spectral colors|spectral locus]] (position of the color on the horseshoe shape in the diagram) or (as at the saturated end of the line shown in the diagram) position on the [[line of purples]].]]
 
The '''excitation purity''' (purity for short) of a stimulus is the difference from the illuminant's [[white point]] to the furthest point on the chromaticity diagram with the same hue ([[dominant wavelength]] for [[monochromatic]] sources); using the [[CIE 1931 color space]]:<ref>{{cite book|isbn=0-240-51417-3|url=http://books.google.com/?id=CU7-2ZLGFpYC&pg=PA121&dq=%22excitation+purity%22
|title=The Focal Encyclopedia of Photography|publisher=[[Focal Press]]|first=Leslie D.|last=Stroebel|coauthor=Zakia, Richard D.|page=121|year=1993|edition=3E}}</ref>
 
:<math>p_e = \sqrt{\frac{(x - x_n)^2 + (y - y_n)^2}{(x_I - x_n)^2 + (y_I - y_n)^2}}</math>
 
where {{nobr|(''x''<sub>''n''</sub>, ''y''<sub>''n''</sub>)}} is the chromaticity of the white point and {{nobr|(''x''<sub>''I''</sub>, ''y''<sub>''I''</sub>)}} is the point on the perimeter whose line segment to the white point contains the chromaticity of the stimulus. Different color spaces, such as CIELAB or CIELUV may be used, and will yield different results.
 
== Chroma in CIE 1976 L*a*b* and L*u*v* color spaces ==
 
{{See also|Psychophysics}}
 
The naïve definition of saturation does not specify its response function. In the CIE XYZ and RGB color spaces, the saturation is defined in terms of additive color mixing, and has the property of being proportional to any scaling centered at white or the white point illuminant. However, both color spaces are nonlinear in terms of psychovisually perceived [[color difference]]s. It is also possible—and sometimes desirable—to define a saturation-like quantity that is linearized in term of the psychovisual perception.
 
In the [[Lab color space|CIE 1976 L*a*b* and L*u*v* color spaces]], the unnormalized '''chroma''' is the radial component of the cylindrical coordinate CIE L*C*h (lightness, chroma, hue) representation of the L*a*b* and L*u*v* color spaces, also denoted as CIE L*C*h(a*b*){{Citation needed|date=January 2011}} or CIE L*C*h for short, and CIE L*C*h(u*v*). The transformation of {{nobr|(''a''*, ''b''*)}} to {{nobr|(''C''*<sub>''ab''</sub>, ''h''<sub>''ab''</sub>)}} is given by:
 
:<math>C_{ab}^* = \sqrt{a^{*2} + b^{*2}}</math>
:<math>h_{ab} = \arctan \frac{b^{*}}{a^{*}}</math>
 
and analogously for CIE L*C*h(u*v*).
 
The chroma in the CIE L*C*h(a*b*) and CIE L*C*h(u*v*) coordinates has the advantage of being more psychovisually linear, yet they are non-linear in terms of linear component color mixing. And therefore, chroma in CIE 1976 L*a*b* and L*u*v* color spaces is very much different from the traditional sense of "saturation".
 
===Chroma in color appearance models===
 
Another, psychovisually even more accurate, but also more complex method to obtain or specify the saturation is to use the color appearance model, like [[CIECAM]]. The '''chroma''' component of the LCh (lightness, chroma, hue) coordinate, and becomes a function of parameters like the chrominance and physical brightness of the illumination, or the characteristics of the emitting/reflecting surface, which is also psychovisually more sensible.
 
== References ==
 
{{reflist}}
 
{{Color topics}}
 
[[Category:Color]]

Latest revision as of 22:11, 16 November 2014

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