Linear and nonlinear transparencies in stereopsis

When the product of a vertical square-wave grating (contrast envelope) and a horizontal sinusoidal grating (carrier) are viewed binocularly with different disparity cues they can be perceived transparently at different depths. We found, however, that the transparency was asymmetric; it only occurred when the envelope was perceived to be the overlaying surface. When the same two signals were added, the percept of transparency was symmetrical; either signal could be seen in front of or behind the other at different depths. Differences between these multiplicative and additive signal combinations were examined in two experiments. In one, we measured disparity thresholds for transparency as a function of the spatial frequency of the envelope. In the other, we measured disparity discrimination thresholds. In both experiments the thresholds for the multiplicative condition, unlike the additive condition, showed distinct minima at low envelope frequencies. The different sensitivity curves found for multiplicative and additive signal combinations suggest that different processes mediated the disparity signal. The data are consistent with a two-channel model of binocular matching, with multiple depth cues represented at single retinal locations.