Illumination-invariance of Plateau's midgray

Abstract

In a classical experiment Plateau [(1872). Sur la mesure des sensations physiques, et sur la loi qui lie l’intensité de la cause excitante. Bulletins de L’Academie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique, 2me Série, 33, 376–388] found that the midgray operation is illumination-invariant. Falmagne [(1985). Elements of psychophysical theory. New York: Oxford University Press] provided a formalization of this finding that gives rise to two functional equations, the solutions of which determine the possible forms of the psychophysical function. This approach is generalized so that it explicitly refers to the illuminance, and can be applied to the experimentally well-studied class of center-surround stimuli. It is shown that the illumination-invariance of both cross-context matches and Plateau's midgray specify the psychophysical function up to an increasing function of the relative luminance of stimulus/illumination and center/surround, respectively. Relating this result to that implied by Wallach's ratio principle clarifies the role of Plateau's midgray in experimental research on achromatic color perception. Further generalizing the framework extends its scope to more complex experimental settings and the therein observed invariances.