Vector magnitude operation in color vision models: derivation from signal detection theory

Using the theory of signal detection, we have derived an expression for the detectability of a visual stimulus in terms of the general zone theory of color and brightness vision. This derived relationship elicidates the theoretical foundation of the Guth vector model for color vision by showing that the nonlinear vector magnitude operation used by Guth may arise from the observer decision-making process. Testable predictions of stimulus detectability are generated by the derived expression.