Absolute and relative disparity mechanisms revealed by an equivalent noise analysis

The precision of stereopsis and vergence are ultimately limited by internal binocular disparity noise. Here we propose an equivalent noise model with both global and local internal disparity noises to provide a unified explanation of both absolute and relative disparity thresholds. To test this model, we developed a psychophysical procedure to measure the equivalent internal disparity noise by adding external disparity noise to random-Gabor-patch stereograms. We used the method of constant stimuli to measure the minimum and maximum disparity thresholds (Dmin and Dmax) for both absolute and relative disparity. Consistent with previous studies, we found that Dmin thresholds are substantially worse for absolute disparity than for relative disparity. We tested three relative disparity mechanisms: (1) the difference between the monocular separations of targets projecting to the two eyes; (2) the direct measurement of relative disparity; and (3) the difference of absolute disparities of targets. Computing the difference of absolute disparities when detecting relative disparity, Mechanism 3 cancels global noise, resulting in a much lower relative Dmin threshold, and provides a reasonable fit to the experimental data. We also found that the presence of as much as 2400 arcsec of external disparity noise does not appear to affect the Dmax threshold. This observation suggests that Dmax is implicated in a mechanism that disregards the disparity variance of individual items, relying instead on the average disparity across all items, supporting the depth model proposed in our previous study (Ding & Levi, 2021), which posits distinct mechanisms governing Dmin and Dmax thresholds.