Do we perceive stereoscopic surfaces by combining patches of constant disparity?

Martin S. Banks, Sergei Gepshtein, Heather F. Rose

Vision Science Program, School of Optometry, University of California at Berkeley, Minor Hall 360, Berkeley, CA 94720-2020, USA

Recently we found that spatial stereoresolution (finest detectable disparity modulation) appears to be limited by a binocular-matching process that estimates the disparity of image patches and assumes that disparity is constant across the patch. In other words, this process yields piecewise estimates of depth from patches of constant disparity. This hypothesis is consistent with the behavior of disparity-selective neurons in primate V1. If disparity estimation is based on piecewise estimates, the form of the disparity-modulation waveform should have a significant effect on estimation. A square-wave provides constant-disparity patches while a sawtooth-wave does not.

To test the piecewise hypothesis, we compared detection of square-wave and sawtooth-wave corrugations using random-dot stereograms. Observers indicated on each trial the orientation of the corrugation waveform (+/- 10 deg from horizontal). In Experiment 1, the highest discriminable spatial frequency was determined for a range of dot densities. The highest frequency was somewhat higher for square- than for sawtooth-waves at high dot densities, where steroresolution is high. In Experiment 2, we varied the mixture of signal and noise dots. The noise dots were assigned random disparities and the signal dots specified a square- or sawtooth-wave. Coherence threshold (proportion of signal dots divided by total dots) was lower in most cases for the square-waves than for the sawtooth-waves. The results from both experiments suggest that the ability to detect patterns composed of constant disparity patches (square-waves) is generally greater than the ability to detect patterns that contain no constant-disparity patches (sawtooth-waves).

Our results support the idea that the binocular-matching process is based on estimating the disparity of constant-disparity patches. Thus, perceived depth maps may be constructed from piecewise estimates.