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Suzanne P McKee, Bart Farell, Preeti Verghese; The cost of resolving stereo ambiguity. Journal of Vision 2003;3(9):63. doi: https://doi.org/10.1167/3.9.63.
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The disparity range of an infinitely long sinusoidal grating would be limited to phase shifts of less than half a period, because shifts > 180 degrees are physically ambiguous. However, grating segments, 3 – 6 deg wide and presented in a rectangular envelope, are seen at or near the disparity specified by their ‘edges’. The disparity range for these segments is not constrained to phase shifts < 180 degrees; instead the range is limited to roughly 60 arcmin. Thus, the ‘edges’ disambiguate the depth of a grating (carrier) and extend its disparity range.
To study the interaction between edges and carrier, we measured how the edge disparity affects stereoacuity for small phase disparities. The disparity of the edges was varied parametrically over the 0 – 60 arcmin range, but, for any block of trials, the edge disparity was fixed. The interocular phase difference(phase disparity) was varied from trial-to-trial in small increments. Subjects judged whether the grating appeared in front or behind a small fixed probe, presented below the grating segment. To control convergence shifts, the subject aligned nonius lines before initiating a trial; grating duration was 200 msec.
The benefits of edge disambiguation come at a substantial cost in sensitivity. For a 3cpd carrier, a 20 arcmin edge disparity shifts the carrier 1 full period (360 deg). From the perspective of the carrier, sensitivity should be same for a disparity of 0 or 360 deg. To the contrary, we found that phase disparity thresholds were 2–3 times higher at an edge disparity of 20 arcmin than at 0 edge disparity (fixation plane). Shifting the grating off the fixation plane produces the same loss in sensitivity as reducing the contrast of a grating presented in the fixation plane. Generally, phase sensitivity declines with increasing pedestal (edge) disparity much like stereoacuity for bars, lines or random dots. Apparently, the stereo system treats a sinusoidal grating as a texture on a surface.
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