Advanced Color Geometry

Abstract

It is assumed that surfaces of equal brightness are ellipsoids in the (X,Y,Z)-color space, that the centers of all of those ellipsoids are at the origin, and that one ellipse, which lies in the plane Y=0, is common to all ellipsoids. This special set of surfaces of the second degree is used for defining a non-Euclidean distance, a measure of the distance between two colors. Theoretical sensitivity ellipses are found in the chromaticity diagram if this measure is applied to infinitesimal distances. The result is compared with MacAdam’s wellknown sensitivity ellipses. Distances between white and spectral colors are discussed and compared with observed numbers of just perceptible steps. Finally, a theoretical hue discrimination curve is computed for equal brightness and compared with average observations. An excellent agreement above 495 mµ is marred by a complete failure below this wavelength. Here the assumption of equal brightness breaks down.