MacAdam ellipse
A MacAdam ellipse , according to David L. (ewis) MacAdam , is the circumference in the CIExy diagram around a reference color tone in which the comparison colors are perceived as being equally spaced .
The problem
MacAdam worked long and hard with the discrepancy between the introduced 1931 CIE xy diagram to characterize the color space and the perception ( perception ) of color contrasts between colors.
He found that the distances in the CIExy diagram do not correspond to the perceived distances: color tones that are the same distance in the diagram from any reference color tone are perceived as differently strong in color contrast by normal-sighted , non- color-blind test subjects .
The same strong color contrasts on the CIE base are therefore not on the outline of a circle around the reference color, as previously assumed , but on the outline of such a MacAdam ellipse . For the three-dimensional CIE color space, the relationships are even more complex, approximately ellipsoids are determined.
The solution
This problem can be eliminated by correspondingly distorting the CIE xy color space. At the beginning of the development of the CIE system, various attempts were made to solve this problem of colorimetry . Over the years, the CIE has developed several color spaces and color tables that better correspond to color perception, for example
- CIE 1960 UCS (1960)
- CIE L * u * v * (CIELUV) (1976) and
- CIE L * a * b * (CIELAB) (1976).
As a “by-product”, CIELUV also has a representation corresponding to the standard color table with better equidistance than the color table of the CIE 1960 UCS.
Contrary to the CIE recommendations, the CIExy color table is still the most frequently presented in the literature. The color- type- dependent sensitivity of the perception of the color stimulus recognized by MacAdam has not yet been finally eliminated in the color spaces and is constantly being changed and improved, e.g. B. by the DIN99 color space . Aided by improved computing power, formulas with a higher computational effort than in 1931 are now possible, since at that time calculations were only possible with slide rules or by hand.
The XYZ values result from the spectral distribution and only through further conversion do the values of the color spaces recommended by the CIE result. In accordance with the logarithmic relationship between the valence Y and the stimulus triggered, the XYZ color space is transformed into the Luv and Lab color space as an approximation to the logarithm using a cube root .
The problem with the solution
MacAdam determined the ellipses by a single test person comparing color samples over months. The complete measurement data is based on the color perception of a single person. On the other hand, the color perceptions of different people differ from one another. Thus, the MacAdam ellipses are to be rated as correspondingly weak with regard to their general validity, as well as with regard to accuracy and applicability.