The derivation of XYZ tristimulus spaces: A comparison of two alternative methods

Abstract

We illustrate how an XYZ representation of tristimulus space can be developed from a given set of color-matching functions. The results of two alternative principles are presented. The first is predominantly based on geometrical considerations and criteria referring to the chromaticity diagram. This method unambiguously defines the XYZ representation by requiring that the spectrum locus in the two-dimensional chromaticity diagram deviate as little as possible from that of a chosen reference diagram - the Judd-Vos (x′, y′) diagram. The second principle is based on a constrained root mean square minimization of the difference between the color-matching functions of the new XYZ representation and those of the Judd-Vos reference system. In effect, the latter principle corresponds to minimizing the difference between two three-dimensional tristimulus spaces. Both methods are general in that they can be applied to any set of color-matching data. In particular, they may be useful in the development of a chromaticity diagram based on physiological fundamentals. © 2000 John Wiley & Sons, Inc.