What is the depth of a sinusoidal grating?

Stereo matching of a textured surface is, in principle, ambiguous because of the quasi-repetitive nature of texture. Here, we used a perfectly repetitive texture, namely a sinusoidal grating, to examine human stereo matching for repetitive patterns. Observers matched the depth of a vertical grating segment, 6-deg wide and presented in a rectangular envelope at or near the disparity of the segment edges. The interocular phase of the carrier also influenced stereo matching, producing shifts in depth arrayed around the plane specified by the edges. The limiting disparity for the edge matches was 40-60 arcmin, independent of the spatial frequency of the carrier. One explanation for these results is that first-order disparity energy mechanisms, tuned to lower spatial frequencies, respond to the edge disparities, while showing little response to the interocular phase of the carrier. In principle, these first-order low frequency mechanisms could account for edge-based stereo matching at high contrasts. But, edge matching is also observed at carrier contrasts as low as 5%, where these low frequency mechanisms are unlikely to detect the grating stimulus. This result suggests that edge matching for gratings depends on coarse-scale second-order stereo mechanisms, similar to the second-order mechanisms that have been proposed for encoding two-dimensional texture. We conclude that stereo matching of gratings (or any other texture) depends on a combination of responses in both coarse-scale second-order and fine-scale first-order disparity mechanisms.

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