The role of a local reference in stereoscopic detection of depth relief

Stereoacuity thresholds have been shown to depend on the disparity of a point with respect to a slanted reference plane through neighbouring points [Curr. Biol. 12 (2002) 825]. Here we explored a wider range of conditions, including slanting the reference points about a horizontal axis and varying the spacing of the reference dots, allowing alternative hypotheses for the effect to be distinguished. The stimulus consisted of three dots; the outer two defined a line that was slanted in depth. Observers judged in which of two intervals the third, central dot was displaced from the location midway between the outer reference dots. The displacement consisted of both a disparity and a shift in the fronto-parallel plane. We compared performance for pairs of conditions in which the disparity was the same but the fronto-parallel shifts were in opposite directions. Models based purely on relative disparity predict that performance should be the same for these conditions. We found consistent differences: performance was always better when the target had a greater disparity with respect to the line joining the reference dots. The other stimulus parameters varied were: target disparity (concave/convex), stimulus size (large/small), slant sign (sky/ground) and axis (vertical/horizontal). The results suggest that either (a) disparity with respect to the line drawn through the outer reference dots or (b) difference in disparity gradients on either side of the target determines the depth discrimination threshold for these stimuli.