MacAdam ellipse
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In the study of the perception of color, a MacAdam ellipse is the region on a chromaticity diagram which contains all colors which are indistinguishable, to the average human eye, from the color at the center of the ellipse. As such it defines the concept of distance in a color space.
In the study of color perception, the first question that usually comes to mind is "what color is it?". In other words, we wish to develop a method of specifying a particular color which allows us to differentiate it from all other colors. It has been found that three quantities are needed to specify a particular color. For example, the relative amounts of red, green and blue in a color will serve to specify that color completely. This question was first approached by a number of researchers in the 1930's and their results were formalized in the specification of the CIE XYZ color space.
The second question we might ask, given two colors, is "how much different are these two colors?". Just as the first question was answered by developing a color space in which three numbers specified a particular color, we are now asking effectively, how far apart are two colors in this color space? This particular question was first approached by D.L. MacAdam and his results were published in 1942. MacAdam set up an experiment in which a trained observer viewed two different colors. One of the colors (the "test" color) was fixed, but the other was adjustable by the observer, and the observer was asked to adjust that color until it matched the test color. This match was, of course, not perfect, since the human eye, like any other instrument, has limited accuracy. It was found by MacAdam, however, that all of the matches made by the observer fell into an ellipse on the CIE chromaticity diagram, which is a standard method of displaying chromaticity. The measurements were made at 25 points on the chromaticity diagram, and it was found that the size of the ellipses on the diagram varied widely depending on the test color. These 25 ellipses measured by MacAdam, for a particular observer (denoted "PGN") are shown on the chromaticity diagram on the right.
These ellipses embody a method of measuring distance in color space. In other words, they define a metric in color space. Each of the ellipses are, by definition, circles of equal radius, and the only reason that they appear to be ellipses of different sizes in the chromaticity diagram is because the CIE xy space is warped (with respect to this metric).
In more mathematical terms, the MacAdam ellipses are elliptical if we assume a Euclidean metric d' in the CIE xy vector space, which is not the natural metric for the color space. 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.
A number of attempts have been made to define a color space which is not as distorted as the CIE XYZ space. The most notable of these are the CIELUV and CIELAB color spaces. Although both of these spaces are less distorted than the CIE XYZ space, they are not completely free of distortion.
[edit] References
- MacAdam, D.L., Visual sensitivities to color differences in daylight, J. Opt. Soc. Am., 32, 247 (1942).
- Wyszecki, Günter and W.S. Stiles, Color Science -- Concepts and Methods, Quantitative Data and Formula (2nd edition), Wiley-Interscience. (July 28, 2000). ISBN 0-471-39918-3
