Post's inversion formula: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
en>A. Pichler
mNo edit summary
en>Billlion
→‎top: "powerful home computers' sounds like Laplace transform inversion is a hobby! Still not happy with the sentence
 
Line 1: Line 1:
'''Adams chromatic valence''' color spaces are a class of [[color space]]s suggested by [[Elliot Quincy Adams]].<ref name=adams43>{{cite conference|title=Chromatic Valence as a Correlate of Munsell Chroma|authorlink=Elliot Quincy Adams|first=Elliot Quincy|last=Adams|booktitle=Proceedings of the Twenty-Eighth Annual Meeting of the [[Optical Society of America]]|pages=683|date=October 1943|location=Pittsburg, PA|volume=33|issue=12|url=http://www.opticsinfobase.org/abstract.cfm?URI=josa-33-12-679 }}</ref> Two important Adams chromatic valence spaces are [[CIELUV]] and [[Lab color space|Hunter Lab]].
Hi there. Allow me start by introducing the writer, her name is Sophia. Ohio is exactly where my home is but my husband desires us to transfer. I am really fond of to go to karaoke but I've been taking on new things lately. Distributing manufacturing has been his profession for some time.<br><br>Feel free to surf to my blog :: [http://www.skullrocker.com/blogs/post/10991 love psychic readings]
 
Chromatic value/valence spaces are notable for incorporating the opponent process model, and the empirically-determined 2½ factor in the red/green vs. blue/yellow chromaticity components (such as in [[CIELAB]]).
 
==Chromatic value==
In 1942, Adams suggested chromatic ''value'' color spaces.<ref name=adams42>{{cite journal|first=Elliott Quincy|last=Adams|authorlink=Elliot Quincy Adams|title=X-Z planes in the 1931 I.C.I. system of colorimetry|journal=[[JOSA]]|volume=32|issue=3|pages=168–173|date=March 1942| url=http://www.opticsinfobase.org/abstract.cfm?id=49502|doi=10.1364/JOSA.32.000168}}</ref><ref>{{cite book|
url=http://books.google.com/?id=vK5DK9vqyCgC&pg=RA2-PA136&dq=%22Chromatic+Valence%22
|title=The Measurement of Appearance|first=Richard Sewall|last=Hunter|coauthors=Harold, Richard Wesley|publisher=[[John Wiley & Sons]]-[[IEEE]]|isbn=0-471-83006-2|year=1987}}</ref> Chromatic value, or ''chromance''<!-- sic. see 1942 paper -->, refers to the intensity of the [[opponent process]] responses, and is derived from Adams' theory of color vision.<ref>{{cite book|url=http://books.google.com/?id=T1NS5wI3H4UC&pg=PA6&lpg=PA6&dq=%22chromatic+valence%22+%22chromatic+response%22|title=Color in Electronic Displays|first=Heino|last=Widdel|coauthors=Post, David Lucien|pages=5–6|isbn=0-306-44191-8|publisher = [[Springer Science+Business Media|Springer]]|year=1992}}</ref><ref>{{cite book|url=http://books.google.com/?id=-fNJZ0xmTFIC&pg=RA1-PA161&dq=%22chromatic+response%22+%22color+matching%22|title=The Science of Color|page=161|isbn=0-444-51251-9|year=2003|publisher=[[Elsevier]]|first=Steven K.|last=Shevell}}</ref><ref>{{cite journal|title=A Theory of Color Vision|first=Elliot Quincy|last=Adams|date=January 1923|volume=30|issue=1|journal=Psychological Review| url=http://content.apa.org/journals/rev/30/1/56.pdf|doi=10.1037/h0075074|pages=56}}</ref>
 
A chromatic value space consists of three components:
 
* <math>V_Y,</math> the [[lightness (color)|Munsell-Sloan-Godlove value function]]: <math>V_Y^2=1.4742Y-0.004743Y^2</math>
* <math>V_X-V_Y</math>, the red-green chromaticity dimension, where <math>V_X</math> is the value function applied to <math>(y_n/x_n)X</math> instead of Y
* <math>V_Z-V_Y</math>, the blue-yellow chromaticity dimension, where <math>V_Z</math> is the value function applied to <math>(y_n/z_n)Z</math> instead of Y
 
A chromatic value diagram is a plot of <math>V_X-V_Y</math> (horizontal axis) against <math>0.4(V_Z-V_Y)</math> (vertical axis). The 2½ scale factor is intended to make radial distance from the [[white point]] correlate with the [[Munsell color system#Chroma|Munsell chroma]] along any one hue radius (i.e., to make the diagram perceptually uniform). For [[achromatic]] surfaces, <math>(y_n/x_n)X=Y=(y_n/z_n)Z</math> and hence <math>V_X-V_Y=0</math>, <math>V_Z-V_Y=0</math>. In other words, the white point is at the origin.
 
Constant differences along the chroma dimension did not ''appear'' different by a corresponding amount, so Adams proposed a new class of spaces, which he termed chromatic ''valence''. These spaces have "nearly equal radial distances for equal changes in Munsell chroma".<ref name=adams43/>
 
==Chromance==
 
In chromaticity scales, lightness is factored out, leaving two dimensions. Two lights with the same [[spectral power distribution]], but different luminance, will have identical [[chromaticity]] coordinates. The familiar CIE (''x'', ''y'') [[chromaticity diagram]] is very perceptually non-uniform; small perceptual changes in chromaticity in greens, for example, translate into large [[color difference|distances]], while larger perceptual differences in chromaticity in other colors are usually much smaller.
 
Adams suggested a relatively simple uniform chromaticity scale in his 1942 paper:<ref name=adams42/>
<math>\frac{y_n}{x_n}X-Y</math> and <math>\frac{y_n}{z_n}Z-Y</math>
 
where <math>x_n, y_n, z_n</math> are the chromaticities of the reference white object (the ''n'' suggests [[normalize]]d). (Adams had used smoked [[magnesium oxide]] under [[standard illuminant|CIE Illuminant C]] but these would be considered obsolete today. This exposition is generalized from his papers.)
 
Objects which have the same chromaticity coordinates as the white object usually appear neutral, or fairly so, and normalizing in this fashion ensures that their coordinates lie at the origin. Adams plotted the first one the horizontal axis and the latter, multiplied by 0.4, on the vertical axis. The scaling factor is to ensure that the contours of constant chroma (saturation) lie on a circle. Distances along any radius from the origin are proportional to [[colorfulness|colorimetric purity]].
 
The chromance diagram is not invariant to brightness, so Adams normalized each term by the Y tristimulus value:
<math>\frac{y_n}{x_n}\frac{X}{Y}=\frac{x/x_n}{y/y_n}</math> and <math>\frac{y_n}{z_n}\frac{Z}{Y}=\frac{z/z_n}{y/y_n}</math>
 
These expressions, he noted, depended only on the chromaticity of the sample. Accordingly, he called their plot a "constant-brightness chromaticity diagram". This diagram does not have the white point at the origin, but at (1,1) instead.
 
== Chromatic valence ==
 
Chromatic valence spaces incorporate two relatively [[perceptual uniformity|perceptually uniform]] elements: a [[chromaticity]] scale, and a [[lightness (color)|lightness]] scale. The lightness scale, determined using the [[lightness (color)|Newhall-Nickerson-Judd value function]], forms one axis of the color space:
 
<math>Y=1.2219V_J-0.23111V_J^2+0.23951V_J^3-0.021009V_J^4+0.0008404V_J^5</math>
 
The remaining two axes are formed by multiplying the two uniform chromaticity coordinates by the lightness, V<sub>J</sub>:
 
<math>\frac{X/x_n}{Y/y_n}-1=\frac{X/x_n-Y/y_n}{Y/y_n}</math>
 
<math>\frac{Z/z_n}{Y/y_n}-1=\frac{Z/z_n-Y/y_n}{Y/y_n}</math>
 
This is essentially what Hunter used in his [[Lab color space]]. As with chromatic value, these functions are plotted with a scale factor of 2⅛ to give nearly equal radial distance for equal changes in Munsell chroma.<ref name=adams43/>
 
==Color difference==
 
Adams' color spaces rely on the [[Munsell]] [[value (colorimetry)|value]] for lightness. Defining chromatic valence components <math>W_X=\left(\frac{x/x_n}{y/y_n}-1\right) V_J</math> and <math>W_Z= \left(\frac{z/z_n}{y/y_n}-1\right)V_J</math>, we can determine the [[color difference|difference between two colors]] as:<ref name=little>{{cite journal|title=Evaluation of Single-Number Expressions of Color Difference|first=Angela C.|last=Little|date=February 1963|volume=53|issue=2|pages=293–296|journal=[[JOSA]]|url=http://www.opticsinfobase.org/abstract.cfm?URI=josa-53-2-293|doi=10.1364/JOSA.53.000293 }}</ref>
 
<math>\Delta E=\sqrt{(0.5 \Delta V_J)^2+(\Delta W_X)^2 + (0.4 \Delta W_Z)^2}</math>
 
where V<sub>J</sub> is the [[lightness (color)|Newhall-Nickerson-Judd value function]] and the 0.4 factor is incorporated to better make differences in W<sub>X</sub> and W<sub>Z</sub> perceptually correspond to one another.<ref name=adams43/>
 
In chromatic value color spaces, the chromaticity components are <math>W_X=V_X-V_Y</math> and <math>W_Z=V_Z-V_Y</math>. The difference is:<ref name=little/>
 
<math>\Delta E=\sqrt{(0.23 \Delta V_Y)^2+(\Delta W_X)^2 + (0.4 \Delta W_Z)^2}</math>
 
where the [[lightness (color)|Munsell-Sloan-Godlove value function]] is applied to the tristimulus value indicated in the subscript. (Note that the two spaces use different lightness approximations.)
 
==References==
 
<references/>
 
[[Category:Color space]]

Latest revision as of 17:24, 14 July 2014

Hi there. Allow me start by introducing the writer, her name is Sophia. Ohio is exactly where my home is but my husband desires us to transfer. I am really fond of to go to karaoke but I've been taking on new things lately. Distributing manufacturing has been his profession for some time.

Feel free to surf to my blog :: love psychic readings