Projective Transformations of I C I Color Specifications

The use of the I. C. I. 1931 Standard Observer and Coordinate System for Colorimetry for all general color specifications and calculations is urged for the elimination of confusion in the field of colorimetry. Methods for constructing other coordinate systems are exhibited, and interpretations are given for the eight independent constants in the equations for transformation from the I. C. I. to other coordinate systems. Expressions are derived for the luminosity coefficients in terms of the constants of the equations for the transformation of coordinates. The possibility of assigning luminosity coefficients without restricting the shape of the spectrum locus is discussed, and an example is given. The assignment of luminosity coefficients interferes with the assignment of the shape of the spectrum locus only in the case of three equal luminosity coefficients. In general, two of the eight degrees of freedom which are available in the defining equations of a trichromatic coordinate system are eliminated by the assignment of the luminosity coefficients. Except in the case of three equal luminosity coefficients, four of the six remaining degrees of freedom are eliminated when the shape of the spectrum locus is established. One additional degree of freedom is eliminated when the size of the spectrum locus is assigned. The final degree of freedom is most profitably used for the purpose of simplifying the transformation equations. The entire discussion is based on well-known principles of transformation of color mixture data and projective geometry; no assumptions other than those underlying standard trichromatic color specification are made, and no conclusions of physiological or psychological import are justified.