Disparity scaling and correction for inclined surfaces

Abstract

The horizontal disparity pattern associated with slant about a horizontal axis can be represented locally as a horizontal shear disparity. If the eyes are torsionally aligned, slant about a horizontal axis is given to close approximation by: S = tan-1 [ (1/m) tan(H) ] where H is the horizontal shear disparity and m is the eyes' vergence. Thus, to estimate slant veridically, the visual system must “scale” disparity by taking distance into account (m). The size disparity created by rotation about the vertical axis must be “corrected” for changes in azimuth (the eyes' version), but an analysis of binocular viewing geometry reveals that such correction is not required if shear disparity is measured in a particular way. We examined the estimation of slant about the horizontal axis from stereoscopic information alone when the distance and azimuth of the stimulus is varied. The stimuli were random-dot planes viewed in a custom haploscope. Perspective cues to slant were minimized by use of a sparse texture, back-projection, and randomly oriented clipping windows. Observers were asked to adjust the slant of a test plane until it matched the perceived slant of a standard plane. In the first experiment, we presented the test and standard planes at different distances (but the same azimuth). We found that observers took distance into account nearly veridically in this task. Thus, disparity scaling occurs with reasonably high accuracy. In the second experiment, we examined whether the vertical disparity gradient or eye-position signals is the predominant signal in disparity scaling. The former predominated. In the third experiment, we presented the test and standard planes at different azimuths (but the same vergence). We found that observers were able to estimate slant nearly veridically across azimuths as expected from use of horizontal shear disparity.