Several studies (Vision Research 15 (1975) 583; Perception 9 (1980) 671) have shown that binocular fusion is limited by the disparity gradient (disparity/distance) separating image points, rather than by their absolute disparity values. Points separated by a gradient >1 appear diplopic. These results are sometimes interpreted as a constraint on human stereo matching, rather than a constraint on fusion. Here we have used psychophysical measurements on stereo transparency to show that human stereo matching is not constrained by a gradient of 1. We created transparent surfaces composed of many pairs of dots, in which each member of a pair was assigned a disparity equal and opposite to the disparity of the other member. For example, each pair could be composed of one dot with a crossed disparity of 6' and the other with uncrossed disparity of 6', vertically separated by a parametrically varied distance. When the vertical separation between the paired dots was small, the disparity gradient for each pair was very steep. Nevertheless, these opponent-disparity dot pairs produced a striking appearance of two transparent surfaces for disparity gradients ranging between 0.5 and 3. The apparent depth separating the two transparent planes was correctly matched to an equivalent disparity defined by two opaque surfaces. A test target presented between the two transparent planes was easily detected, indicating robust segregation of the disparities associated with the paired dots into two transparent surfaces with few mismatches in the target plane. Our simulations using the Tsai-Victor model show that the response profiles produced by scaled disparity-energy mechanisms can account for many of our results on the transparency generated by steep gradients.
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