Discrimination of the spatial derivatives of horizontal binocular disparity

Observers discriminated the relative disparity, disparity gradient, and disparity curvature of surfaces defined by horizontal binocular disparity in random-dot stereograms. In experiment 1, thresholds for discriminating the depth of sinusoidal corrugations were very similar for different corrugation frequencies, despite large differences in disparity gradient and disparity curvature. Thus observers used a relative disparity cue in preference to a slant or curvature cue. Experiment 2 isolated the spatial derivatives of disparity by jittering the other available cues, using surfaces with square-wave, triangle-wave, and parabolic-wave profiles. Weber fractions were 4%-10% for relative disparity, 6%-12% for disparity gradient, and 15%-30% for disparity curvature. Experiment 3 confirmed this result for larger surfaces. The study supports the view that human stereoscopic vision aims to represent the local scene relative to the observer, at the expense of computing intrinsic properties of objects, such as curvature.