Color measurement and color theory: II. Opponent-colors theory

Quantitative opponent-colors theory is based on cancellation of redness by admixture of a standard green, of greenness by admixture of a standard red, of yellowness by blue, and of blueness by yellow. The fundamental data are therefore the equilibrium colors: the set A₁ of lights that are in red/green equilibrium and the set A₂ of lights that are in yellow/blue equilibrium. The result that a cancellation function is linearly related to the color-matching functions can be proved from more basic axioms, particularly, the closure of the set of equilibrium colors under linear operations. Measurement analysis treats this as a representation theorem, in which the closure properties are axioms and in which the colorimetric homomorphism has the cancellation functions as two of its coordinates.Consideration of equivalence relations based on opponent cancellation leads to a further step: analysis of equivalence relations based on direct matching of hue attributes. For additive whiteness matching, this yields a simple extension of the representation theorem, in which the third coordinate is luminance. For other attributes, precise representation theorems must await a better qualitative characterization of various nonlinear phenomena, especially the veiling of one hue attribute by another and the various hue shifts.