Lightness Constancy: Shades are compensated in perception, scattering light not

Luminance of three-dimensional achromatic objects under given illumination depends on remittance of the material, shading and scattering light (mutual illumination of opposed surfaces). We studied perception of lightness of six flat surfaces, three exposed to direct illumination, three in the shade in opposite position, thus allowing mutual illumination of neighboring pairs. Six achromatic cardboards forming a logarithmic scale of remittance (step factor = 1.2) were used. Direct illumination increased the luminance of the cardboards by a factor of two with respect to those in the shade. The luminance sequence of the cardboards varied with their positions in light and shade. Altogether there are 720 permutations of the sequence of the six cardboards. For any of the 720 permutations selected for the experiments, the subjects tried to report the lightness sequence correctly in spite of the different luminance sequences. The difference between the empirical lightness sequence reported by the subjects and the physically measured sequence according to remittance was taken as the measure of lightness constancy. We used Kendall´s rank correlation coefficient τ, which is τR=1 if the two above sequences are identical. We also calculated τL from the empirical and the luminance sequences. If the subjects were unable to perceive the lightness, they would report the luminance sequence with τL=1 and τRτL (with exception of control experiments in which the sequence according to lightness and luminance happened to be the same physically, yielding τR=τL=1 correctly). Thus, lightness constancy of three-dimensional objects under asymmetric illumination as reported since more than 100 years (summary e.g. in A. L. Gilchrist: Lightness, Brightness, and Transparency, 1994) has been confirmed quantitatively with our novel method. In addition, a quantitative result concerning mutual illumination can be derived from our data. Mutual illumination of cardboards can change the luminance sequence as a consequence of neighborhood. From a light cardboard under direct illumination more light is scattered to and reflected by its dark neighbor in the shaded position, than from the same cardboards in exchanged position. We calculated the degree of lightness constancy separately for those cases, in which the luminance sequence was not changed by mutual illumination, and those were the difference with the lightness sequence was increased and decreased. Separate calculations of these groups revealed that the effect of local scattering light makes it more difficult to detect the correct lightness. Mutual illuminations increasing the difficulty resulted in less constancy (τR smaller), whereas mutual illumination resulting in greater similarity of the lightness and luminance sequences (thus reducing the difficulty) yielded better constancy (τR greater). The effect of light scattered locally at three-dimensional objects is not taken into account in the process leading to lightness constancy of perception