Information integration study of Metelli's and Morinaga's theories of achromatic transparency

Information integration methodology was used to test Metelli's and Morinaga's theories of achromatic transparency. Stimuli were transparent achromatic disks on a background formed by two adjacent horizontal rectangles. The common border of these rectangles divided each disk in two halves. Let P and Q be the luminances of the left and right halves of a disk and let A and B be those of the left and right rectangles, respectively. Transparency is given by the ratio (P - Q)/(A - B) in Metelli's theory and is given by a weighted average of the ratios (P - Q)/(A - Q) and (P - Q)/(P - B) in Morinaga's theory. Participants rated the transparency of disks with A and B fixed and P and Q combined factorially. Morinaga's theory closely predicted the resulting pattern of curves and Metelli's theory predicted it incorrectly. Morinaga's theory could also account well for individual differences in the ratings of transparency. The results support the general idea that transparency depends on the integration of photometric luminance information rather than on the integration of perceived lightness information.