How many MacAdam ellipses are there?

Abstract

In a classic series of experiments MacAdam and others measured chromatic discrimination around many points in chromaticity space. They characterized these contours using ellipses. Theorists have attempted to predict these shapes from physiologically based theories (e.g., Silberstein, 1945; Stiles, 1946). Parameters of the ellipsoids may be expressed as a unique linear transformation mapping the ellipsoid into a unit sphere. Whereas this transformation has six degrees of freedom, most measurements of chromatic discrimination only vary three independent degrees of freedom in the stimulus conditions: the color coordinates of the point in color space. It is not surprising, therefore, that our analysis of the MacAdam ellipsoid parameters shows that they are confined to a small region of the 6-D space of possible parameter values. We have collected new data using disk-annuli spatial targets and different temporal waveforms to increase the dimensionality of the stimulus parameters. We ask whether the new ellipses have parameters outside the region spanned by the basic MacAdam ellipse conditions. That is, we analyze whether the parameters of the MacAdam ellipsoids are limited by the number of degrees of freedom in the stimulus conditions or by the number of degrees of freedom in the processes of visual sensitivity.