Langley, K., Fleet, D.J., and Hibbard, P.
Linear and nonlinear transparency in binocular vision.
Proceedings of the Royal Society (London) B, 265: 1837-1845, August 1998

When the product of a vertical squares-wave grating (contrast envelope) and a horizontal sinusoidal grating (carrier) are view binocularly with different disparity cues, they can be perceived transparently. We found, however, that the the percept of transparency was asymmetric. It only occurred when the envelope was perceived to lie in front of the carrier. When the same two signals were added the percept of transparency was symmetric; either signal could be seen in front of or behind the other. 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 maxima at low envelope frequencies. The different sensitivity curves found for multiplicative and additive signal combinations suggests 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.
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