The Structure of Colorimetry

Abstract

We consider the structure of colorimetry, essentially of Graßmann’s threedimensional linear space that summarized metamery (confusion of spectral distributions) for the human observer. We show that the definition of an orthonormal basis for this space requires a scalar product in both the space of physical beams, and the representation space on which Graßmann’s manifold is mapped. The former of these scalar products has to be constructed on the basis of considerations of physics and physiology. The present standards (CIE) are very awkward. The latter of these scalar products can be choosen for reasons of convenience. After these choices “color space” becomes a “true image” of the space of physical beams, apart from the fact that all but three of the infinitely many dimensions are lost (the metamery). We show that the key operator of modern colorimetry, Cohen’s “Matrix-R” (the projector on fundamental space that rejects the “metameric black” part of arbitrary physical beams) also requires these scalar products for its definition. In the literature such inner products are (implicitly) assumed with the unfortunate result that the awkward CIE definition is willy nilly accepted as the only possibility.