Color and color mixture: Scalar and vector fundamentals

Abstract

This article explores the consequences of the Wyszecki hypothesis, that every color stimulus (radiometric function) comprises two parts, a fundamental and a residual. (Wyszecki's terms were fundamental color stimulus and metameric black.) The fundamental alone is processed by the visual system and evokes the color sensation. The residual is not processed and is without effect on color sensations. Metamers, color stimuli evoking the identical color sensation but with different radiometric functions, have the same fundamental but different residuals. Matrix R, an orthogonal projector, resolves any radiometric function into its fundamental and residual. Unlimited numbers of metamers may be generated by adding other residuals to the same fundamental. The color‐matching equation has historically been written with tristimulus values as coefficients, but so written, the equation balances only psychologically. When the stinuli of the color‐matching equation are replaced by the fundamentals processed by the visual system (after the residuals are ejected by matrix‐R operations), the equation balances psychologically, physically, and mathematically. Wyszecki's fundamental has two representations, the scalar fundamental as conceived by Wyszecki and the vector fundamental as developed in this article. Vector fundamentals define a fixed, invariant, fundamental color space governed by Euclidean geometry. The properties of this space are explored. The article develops relationships between color‐matching functions, fundamentals, and orthonormal color functions. Two new specifications for color stimuli or sensations are introduced, tricolor values and tricolor coordinates. The article assumes knowledge of ordinary algebra and geometry, and procedures for computation of tristimulus values.