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## Metric Spaces

I reverted to the previous version, but I think the new rewrite pointed out some weaknesses in the previous version.

• I don't think introducing the XYZ Euclidean metric is helpful. Such a metric is never used in color analysis any more than some weird metric is used in measuring distances in 3-space. Yes, we can define some weird metric in 3-space, but there is a "natural" metric - the Euclidean metric. In the same way, the natural metric for color space is the perceptual one estimated by MacAdam, and others. I realize that a Euclidean metric is implicitly used when talking about the fact that the MacAdam ellipses are in fact ellipses and not circles, but I don't think the idea should be given such formal recognition.
• Speaking of formality, I think the highly mathematical explanation is good, but should be preceeded by a plain English version, in the flavor of the restored version (but more precise).

If you don't want to attempt a rewrite, I will soon give it a try. PAR 03:10, 17 August 2005 (UTC)

I chaged a few words to be mathematical precise, but generally agree with the rest. --Ylai 23:21, 17 August 2005 (UTC)

For those with no background in metric topology, the section about metric spaces is still not going to make any sense. I think instead it would be useful to show a picture of what these ellipses look like in a less-distorted (w.r.t. MacAdam metric) color space, and give some descriptive indication of the type of transformation between the two, with or without some math to go along with that. In general, it seems a lot of the technical math-y parts of the color articles in Wikipedia don't have a good written explanation of what the math means. I realize this is not an easy job, but it would be very valuable, as most of those looking up color spaces are unlikely to have an undergraduate level math background. --jacobolus (t) 07:25, 28 October 2006 (UTC)

## CIE ab space

There is a sentence in the article which reads:

The CIE ab space with the natural metric d, defined by MacAdam's measurements gives a metric space that is homeomorphic to the CIE xy space with d' and in this space the MacAdam ellipses become circles.

I have never heard of the "CIE ab space" (nor the CIE xy space for that matter) and I would like to delete this sentence unless someone can explain it to me. PAR 11:06, 21 February 2007 (UTC)

Maybe it means CIELAB space. Not sure, myself. 22:13, 21 February 2007 (UTC)
If thats the case, it does not transform MacAdam ellipses to perfect circles. It comes close, but is not exact. I will delete the sentence, or modify it. PAR 05:04, 22 February 2007 (UTC)

## Ellipse or bean

Was the research by MacAdam doen for all colors or only the colors in a section of CIExy color space (with Y=50)? If it was for all colors would it then not be more likely that the ellipses / circles (2D) would be beans/spheres (3D)? BartYgor 13:13, 15 July 2007 (UTC)

MacAdam's original research was for a fixed luminance of about 48 cd/m^2. Brown and MacAdam subsequently investigated the effects of varying luminance, and developed what are known as "Brown-MacAdam ellipsoids" which specify discrimination along the luminance axis as well. They found that the projection of these ellipsoids onto chromaticity space were fairly constant in size from 3 to 30 cd/m^2. Wyszecki and Fielder also measured discrimination ellipsoids under somewhat different conditions. For an excellent discussion of all of these points, see chapter 5.4 of "Color Science, 2nd Edition" by Wyszecki and Stiles. PAR 14:21, 15 July 2007 (UTC)

## General formular for MacAdam ellipses

I have been looking for a way to generate a MacAdam Ellipse around an arbitrary point in a given color space but I have not been successful. If such a method exists it might be worth including it, since the experimental data hardly covers, for instance, the complete CIE diagram.--Thorseth (talk) 10:51, 20 August 2008 (UTC)

Ok, I might have solved this. Using the system L*u*v* every point in a colordiagram has a "MacAdam circle" of approximately the same size. --Thorseth (talk) 09:16, 21 January 2009 (UTC)
I found an attempt at an analytical solution, I have added the info in the history section and will be looking at it if I get time.--Thorseth (talk) 09:30, 8 August 2012 (UTC)
I am working with color perception and I am looking for the matrix form of the MacAdam ellipses. I'll be grateful if you could give me some imformation to search. — Preceding unsigned comment added by Marie.dafonsec (talkcontribs) 18:30, 11 September 2012 (UTC)

Even simpler than this: an important metric used be the lighting industry is the "n-step" macadam ellipse with n being the number of std. deviations from the target (if I understand correctly ... would be useful if an expert can verify) —Preceding unsigned comment added by 74.229.239.186 (talk) 00:38, 23 October 2008 (UTC)

Well, n-step ellipse is just a widening of the "uncertainty" in color matching. I think it would be ok to mention this in the article.--Thorseth (talk) 09:16, 21 January 2009 (UTC)

## Analytical solution claim

I removed the following paragraph

In 2008 an analytical solution was suggested by Alluvada [1] that predict the shape of the ellipses.

because that clearly non-peer-reviewed paper does not predict or model anything, even though the abstract may suggest otherwise. --Ma Baker (talk) 15:47, 12 January 2013 (UTC)

1. ^ Alluvada, Prashanth (June 1, 2008). "Analytical Equations to the Chromaticity Cone: Algebraic Methods for Describing Color" (PDF). http://arxiv.org. Retrieved August 6, 2012. External link in `|publisher=` (help)