[Bisection with achromatic colors: Plateau's classical experiment]

Experimental data on the perception of achromatic colors nearly exclusively rely on ordinal information from color matching. As already as in 1872, however, J. Plateau introduced the method of bisection for investigating the psychophysical invariances under illumination changes. Moreover, J.-C. Falmagne provided a formal characterization of the findings of this classical experiment that leads to a restriction of the possible form of the respective psychophysical function. This approach, however, has to be generalized in order to develop a theoretical description of the perception of achromatic colors under illumination changes. The illumination invariance of the bisection operation observed by Plateau, and the bisymmetry condition that characterizes its consistency, were investigated in two experiments using decremental center-surround configurations of achromatic colors. Both conditions constitute key assumptions of the suggested formal framework. Instead of directly producing the perceived midgreys, they were determined indirectly by applying the method of constant stimuli. As a result of statistically testing individual data, the illumination invariance turned out to hold for five out of twelve subjects, while the data of nine out of twelve subjects satisfied bisymmetry. Possible explanations of these findings and their impact on the formulation of a psychophysical theory of the perception of achromatic colors are discussed.