MacAdam-Ellipse

A MacAdam ellipse, according to David L. ( EWIS ) MacAdam, is that the extent CIExy diagram to a reference hue around, in which the comparison colors are perceived as equidistant.

The problem

MacAdam engaged in long and hard with the discrepancy between the 1931 introduced CIExy diagram for the characterization of the color space and the perception ( perception ) of color contrasts between colors.

He found that the distances in CIExy - graph does not correspond to the perceived distances. From any reference color in the diagram lying equidistant hues are strongly felt by normal vision, not color-blind subjects in the color contrast as different.

Equally strong color contrasts are therefore on the CIE sole not as anticipated on the outline of a circle around the reference hue, but on the outline of such a MacAdam ellipse. For the three-dimensional CIE color space, the situation is even more complex, approximately ellipsoids are determined.

The solution

A solution to this problem can be solved by corresponding distortion of the CIE - xy color space. At the beginning of the development of the CIE system, different attempts have been made to solve this problem of colorimetry. The CIE has developed over the years, several color spaces and color plates, better suited to the perception of color, such as the CIE 1960 UCS (1960), CIE L * u * v * ( CIELUV ) (1976) and CIE L * a * b * ( CIELAB) (1976). CIELUV has a " by-product " is also one of the standard color chart corresponding representation with better equidistance as the color chart of the CIE 1960 UCS. Contrary to CIE recommendations, the CIE xy chromaticity diagram is still presented in the literature most frequently. The recognized by MacAdam farbartabhängige sensitivity of the perception of the color stimulus has not yet been eliminated in the color spaces and experiences constantly changes and improvements. Benefiting from improved computing power formulas have now become possible with higher computational effort than in 1931, since then calculations were only possible with slide rule or by hand.

From the spectral distribution of the XYZ values ​​and therefrom by further conversion only the values ​​recommended by the CIE color spaces arise. According to the logarithmic relationship between the valence of Y and triggered stimulus is transformed by the XYZ color space to Luv and Lab color space using the cube root as an approximation to the logarithm.

The problem with the solution

MacAdam ellipses determined by a single subject for months has compared the color pattern. The complete measurement data based on color vision of one man. On the other hand, the color perception of different people are different. Thus, the MacAdam ellipses are to be valued in accordance with terms of their universality in terms of accuracy and applicability.

• Color system