Limits of stereopsis explained by local cross-correlation

Human stereopsis has two well-known constraints: the disparity-gradient limit, which is the inability to perceive depth when the change in disparity within a region is too large, and the limit of stereoresolution, which is the inability to perceive spatial variations in disparity that occur at too fine a spatial scale. We propose that both limitations can be understood as byproducts of estimating disparity by cross-correlating the two eyes' images, the fundamental computation underlying the disparity-energy model. To test this proposal, we constructed a local cross-correlation model with biologically motivated properties. We then compared model and human behaviors in the same psychophysical tasks. The model and humans behaved quite similarly: they both exhibited a disparity-gradient limit and had similar stereoresolution thresholds. Performance was affected similarly by changes in a variety of stimulus parameters. By modeling the effects of stimulus blur and of using different sizes of image patches, we found evidence that the smallest neural mechanism humans use to estimate disparity is 3-6 arcmin in diameter. We conclude that the disparity-gradient limit and stereoresolution are indeed byproducts of using local cross-correlation to estimate disparity.