1323:(presumably due to the argument for the exponential; the specification used 25 instead of 25° in the denominator; I made the degrees explicit). One may certainly rewrite the equations to use radians, but any software implementation should be tested against published values to make sure the implementation is correct. Many test cases are designed to trip up naive implementations. I don't see the radian-degree conversions as a big deal - a few extra multiplications that can be hidden using macros/functions such as
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2766:{\displaystyle \Delta C={\sqrt {\left({2+{{\bar {r}} \over {256}}}\right)\times \Delta R^{2}+4\times \Delta G^{2}+\left({2+{{255-{\bar {r}}} \over {256}}}\right)\times \Delta B^{2}}}={\sqrt {\left({2+{{189} \over {256}}}\right)\times 122^{2}+4\times 120^{2}+\left({2+{{255-189} \over {256}}}\right)\times 118^{2}}}={\sqrt {129794.359375}}}
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average eccentricity, Ēch, for this is 2.2 and 2.1 for perceptibility/acceptability for the same color system. The article clearly says: "The average radius over all the ellipses Řch on the other hand gives the average relation between a distance unit in the chromatic plane and a JND." This would imply that 1JND = Rch x DE*--: -->
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Is there any source on this sqrt(2*ΔR^2 + 4*ΔG^2 + 3*ΔB^2) weighted equation? I've been experimenting with my own weighted equations using MacAdam ellipses of just noticeable difference and it seems that these weights are almost backwards. Green has the largest ellipses of just noticeable difference,
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RGB weights are for use with linear values. Since linear light isn't perceived linear then simple weights - as explained - is naive. If weighting that factors gamma was intended then the explanation for why it doesn't work is misleading or at least incomplete. If not, then the whole discussion of RGB
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In the initial square root of the sum of the squares formula, it references ∆H', but the following equations only reference ∆H'bar and ∆h'. I think it is referring to ∆h', but am not certain. These equations should be case sensitive, so could someone with more precise knowledge verify and correct the
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Worse, I feel is that it omits any discussion of computability and the various approximations. If somebody came to the site and wanted to know about color differences they would be asked to implement a bunch of very cryptic formulae rather than noting the actual fairly good approximations or device
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In the proposed formulation, S_C and S_H depends only frome the first color, with the result that the distance of the first color from the second is not equal to the distance of the second color from the first, violating one of the most basic properties of any metric. Is there someone with acces to
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My own results are more like sqrt(9*ΔR^2 + 5*ΔG^2 + 11*ΔB^2) based on the reciprocal of the major radii of the ellipses in the sRGB primaries areas or sqrt(15*ΔR^2 + 11*ΔG^2 + 17*ΔB^2) based on the reciprocal of the width of ellipses in the sRGB primaries measured perpendicular to lines radiating
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I have problems with DE* ~ 2.3 for JND. I feel that this is a bad interpretation of the original article by Mahy et al. (Color Res. Appl. 1994, 19(2), 105). Table II of said article denotes the average ellipse radius, Řch, as 2.3 for CIELAB perceptibility/acceptability data of surface colors. The
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Sadly, colorists use degrees rather than radians; its easy to add or subtract 360; 2π not so much. The color difference definition and secondary sources use degrees, so this article should use degrees. WP is not a how-to guide. An earlier version of this article used radians (see above), but then
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The paragraph does not have a proper reference; a name (last name only, but the author is known to me) and a year do not constitute an acceptable citation. I cannot check whether the text is supported by a reliable reference. Please provide a proper citation, and explain what color difference is
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The thing is, distinguishing values of, say, Green is NOT the same as "differentiating between hues in that area". When green transitions into yellow, it is the RED channel that differs, not the GREEN channel. When green transitions into cyan, it is the BLUE channel that differs, not the GREEN
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directly, stick it in a function that not only does the degree conversion, but also checks for the degenerate case and returns 0 to 360°; turns out that function is needed for some colorspace conversions anyway. The problem with not doing the conversions is the risk of messing up somewhere; if
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How important is it that it is degrees? Would converting everything to radians (taking care to make them in the range where appropriate, as is suggested for degrees currently) give an equivalent result? Most intrinsic functions seem to use radians rather than degrees, and it seems weird to go
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I agree, the formula initially posted was wrong. We must use a delta H* that represents the difference in hue as an euclidian distance. Furthermore the original author posted a formula different from the one in the two references cited. I corrected this and added a reference to the best source
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Using notation not sanctioned by the CIE for a CIE Total Color
Difference is not encyclopedic. With respect to the Mahy study, a proper reference is needed, and exactly what color difference he used must be specified. Otherwise, that section of text may be deleted as not properly referenced.
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In color difference 94, isn't the "h1 - h2" term adjusted so it is not greater than pi? h is an angle, if this is really using LCh coordinates. But I've seen other formulas that seem to calculate a dH term from a, b and C. I'm unsure about the accuracy of this section of the article now.
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3049:{\displaystyle \Delta C={\sqrt {2\times \Delta R^{2}+4\times \Delta G^{2}+3\times \Delta B^{2}+{{{\bar {r}}\times (\Delta R^{2}-\Delta B^{2})} \over {256}}}}={\sqrt {2\times 122^{2}+4\times 120^{2}+3\times 118^{2}+{{189\times (122^{2}-118^{2})} \over {256}}}}={\sqrt {129848.75}}}
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red the second largest, and blue the smallest, thus green should have the smallest number, red the second smallest, and blue the largest since the ellipse size is inversely proportional to how good human vision is at differentiating between hues in that area.
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It also overlooks the many CIELUV/CIELAB predecessors and subsequent alternatives (e.g., Wandell's S-CIELAB). It should at least be mentioned that there are other color-difference measures and the entry restricts attention to the CIE-sanctioned ones.
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Personal observation told me that in small areas (dozens) of pixels, white and yellow can under some circumstances be difficult to distinguish. I suspect this has to do with gamma values of monitors, and possibly age. Anyone information on that?
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In the CIEDE2000 section, it looks like a1, a2, b1, and b2 are missing stars, but I'm not familiar enough with this stuff to say for sure. If they're not missing stars then it should be clarified what a1, a2, b1, and b2 are supposed to be.
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These sections omit mention of CIELUV and the associated formulae, creating the false impression that CIELAB was the first and only CIE-sanctioned color space for calculating color differences in terms of
Euclidean distance, circa 1976.
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Can you provide any academic or research source material that suggests this is the best color difference function? ∆E2000 is mostly considered the best, with some people advocating for newer difference formulas based on CAM16 UCS.
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I do not understand this note: The formulae below should use degrees rather than radians; the issue is significant for RT. Can someone in the know just edit the section to make that note redundant, then remove it?
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These results actually don't seem to work all that well, however using the distance from D65 to a ring of
Munsell hues as weights seems to work better. 0.80769 Red, 1.00000 Green, 0.63636 Blue.
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DE* = 0.43 for 1JND. For DE94(1,1,1) Rch = 1.0 which would put DE94 = 1.0 for 1JND. This correlates well with visual color discrimination done by various individuals in our laboratories.
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2141:{\displaystyle {\text{ difference}}={\text{ lineardifference}}\times (({\text{ sRGBbrightness2}}-{\text{ sRGBbrightness1}})\div ({\text{ linearbrightness2}}-{\text{ linearbrightness1}}))}
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What is the variable a* in the CIEDE2000 formula? The a* in LAB? Thus, the formula needs both LAB and LCH (not that that is a problem since you get one from the other)?
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1274:{\displaystyle T=1-0.17\cos({\bar {H}}^{\prime }-\pi /6)+0.24\cos(2{\bar {H}}^{\prime })+0.32\cos(3{\bar {H}}^{\prime }+\pi /30)-0.20\cos(4{\bar {H}}^{\prime }-21\pi /60)}
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Your edit did not remove the Mahy reference, so that is clearly not the issue. You edit did modify Mahy's JND finding, something that you still fail to recognize.
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You are right, the asterisks were missing (see ref #12), now added. Note that Bruce
Lindbloom (ref #13) does not use the asterisks but naked 'a' and 'b'.--
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equations do not match the referenced source formulation, and I am unable to show that the posted equations are mathematically equivalent formulations.
1925:{\displaystyle {\text{ lineardifference}}={\text{ rederror}}\times 0.212671+{\text{ greenerror}}\times 0.715160+{\text{ blueerror}}\times 0.072169}
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Please note the MathJax/LaTeX implementation used in
Knowledge understand the Western notation with a decimal DOT for separating a fraction part:
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then convert linearbrightness1 and linearbrightness2 to produce 2 new variables sRGBbrightness1 and sRGBbrightness2 then the final difference is:
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white and yellow differ only by the blue channel, and also color differences are easier to distinguish on darker colors than on brighter colors.
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2057:{\displaystyle {\text{ linearbrightness2}}={\text{ red2}}\times 0.212671+{\text{ green2}}\times 0.715160+{\text{ blue2}}\times 0.072169}
1993:{\displaystyle {\text{ linearbrightness1}}={\text{ red1}}\times 0.212671+{\text{ green1}}\times 0.715160+{\text{ blue1}}\times 0.072169}
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When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
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When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
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2200:{\displaystyle {\text{ difference}}={\text{ lineardifference}}\times ({\text{ derivativeof}}({\text{ sRGBbrightness1}}))}
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https://web.archive.org/web/20151010064956/http://www.xrite.com/documents/literature/en/L10-024_Color_Tolerance_en.pdf
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In the CIE 1994 formula for delta_H_star_ab, shouldn't the last term read delta_C_star_ab rather than delta_C_star?
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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
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1842:{\displaystyle {\text{ rederror}}\times 0.299+{\text{ greenerror}}\times 0.587+{\text{ blueerror}}\times 0.114}
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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with
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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with
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being referred to by Mahy. Until such time, the paragraph is deleted for lack of a reliable reference.
1588:. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit
1485:. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit
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or, if linearbrightness1 and linearbrightness2 are the same, use the derivative of sRGB instead:
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The source does not have the second formula, so some editor did the manipulation that dropped a
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before doing mass systematic removals. This message is updated dynamically through the template
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before doing mass systematic removals. This message is updated dynamically through the template
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There is a source. But it's a source written by a programmer that tweaked the numbers based on
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3167:. But be aware many readers may get confused with such notation in English-language text. --
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If you want to force a comma, surround it with curly braces to avoid a space after it:
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We should write about it. CALMAN (I think) is already using it and said it is better.
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If you found an error with any archives or the URLs themselves, you can fix them with
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If you found an error with any archives or the URLs themselves, you can fix them with
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I found in the references that the ∆H' must have been left out, it should be added:
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But at the same time this part seems to (as far as I can tell) imply it is radians.
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Actually no, what you gotta do is convert sRGB to linear RGB, then use this formula
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Would it be possible for someone with more knowledge about this to clarify ?
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http://www.xrite.com/documents/literature/en/L10-024_Color_Tolerance_en.pdf
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45:) and some terms that are used in it may be different or absent from other
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is referenced but not defined. I'll change it soon if no one corrects me
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I just looked over this comment again and the simpler way to say it is:
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434:{\displaystyle \Delta H'=2{\sqrt {C'_{1}C'_{2}}}sin(\Delta h'/2)}
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of R, G and B, weighted by 0.299, 0.587 and 0.114 respectively.
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http://www.brucelindbloom.com/index.html?Eqn_DeltaE_CIE2000.html
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I am having problems understanding from the article whether
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Let's compare the results of calculations of two formulas.
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for additional information. I made the following changes:
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for additional information. I made the following changes:
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the actual CIE1994 standard document that could confirm?
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https://www.youtube.com/watch?v=t9ntP01MceQ&t=502
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As you can see, the formulas give different results.
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2334:{\displaystyle {\bar {r}}={{250+128} \over 2}=189}
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3216:from D65 white as an approximation of hue.
1757:component weighting needs to be rethought.
675:{\displaystyle \Delta {\bar {H}}^{\prime }}
1580:I have just modified one external link on
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3314:https://www.itu.int/rec/R-REC-BT.2124/en
847:This part seems to imply it is degrees,
138:-related subjects on Knowledge. Help us
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2460:{\displaystyle \Delta B=248-130=118}
2418:{\displaystyle \Delta G=249-129=120}
2376:{\displaystyle \Delta R=250-128=122}
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2278:Formulas are not equivalent
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837:{\displaystyle {\bar {H}}'}
712:. Looks like just a typo. –
593:{\displaystyle {\bar {H}}'}
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160:Knowledge:WikiProject Color
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1577:Hello fellow Wikipedians,
1531:(last update: 5 June 2024)
1474:Hello fellow Wikipedians,
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3159:{\displaystyle 123{,}456}
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3131:{\displaystyle 123,456}
3099:{\displaystyle 123.456}
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1373:) 16 October 2017 (UTC)
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3243:— Preceding
3240:
3218:— Preceding
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3210:
3077:KyberPrizrak
3061:KyberPrizrak
3058:
2775:
2469:
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2180:derivativeof
2152:
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1936:
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1765:David Billen
1759:— Preceding
1755:
1686:
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1661:
1636:source check
1615:
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1576:
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1526:source check
1505:
1499:
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1456:173.228.4.22
1450:— Preceding
1447:
1424:— Preceding
1419:
1389:
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256:DonPMitchell
252:
229:— Preceding
225:
212:
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181:
142:articles to
133:
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87:WikiProjects
42:
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2776:Formula 2:
2470:Formula 1:
1430:150.251.3.1
1327:instead of
1325:sind(angle)
214:Gggustafson
28:written in
3333:Categories
2161:difference
2077:difference
1899:greenerror
1816:greenerror
1673:Report bug
1563:Report bug
1493:(Redacted)
3268:channel.
3144:123{,}456
3042:129848.75
1913:blueerror
1830:blueerror
1656:this tool
1649:this tool
1546:this tool
1539:this tool
1391:Therealdp
714:jacobolus
326:formula?
3317:ZBalling
3257:contribs
3245:unsigned
3232:contribs
3220:unsigned
2052:0.072169
2038:0.715160
2024:0.212671
1988:0.072169
1974:0.715160
1960:0.212671
1920:0.072169
1906:0.715160
1892:0.212671
1885:rederror
1802:rederror
1773:contribs
1761:unsigned
1720:Lovibond
1690:Lovibond
1662:Cheers.—
1552:Cheers.—
1452:unsigned
1426:unsigned
1363:unsigned
1299:NeruYume
231:unsigned
43:traveled
3288:Artoria
3187:−ΔB/256
3154:123,456
3110:123,456
3094:123.456
3084:123.456
2226:TDcolor
1586:my edit
1483:my edit
1333:atan2()
793:KlappCK
566:, only
307:SiriusB
272:SMandon
249:delta h
184:on the
140:improve
77:B-class
39:defense
3169:CiaPan
2031:green2
1967:green1
600:, and
83:scale.
3284:vibes
2045:blue2
1981:blue1
1934:then
1837:0.114
1823:0.587
1809:0.299
292:Hixie
157:Color
135:color
106:Color
35:color
3321:talk
3274:talk
3253:talk
3228:talk
3195:talk
3191:Glrx
3173:talk
3065:talk
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2249:alex
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2017:red2
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1738:talk
1734:Glrx
1724:talk
1709:talk
1705:Glrx
1694:talk
1460:talk
1434:talk
1411:talk
1395:talk
1371:talk
1346:talk
1342:Glrx
1303:talk
1287:talk
1218:0.20
1164:0.32
1124:0.24
1073:0.17
797:talk
761:and
634:talk
456:talk
332:talk
311:talk
296:talk
276:talk
260:talk
239:talk
218:talk
176:High
146:and
144:good
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