Persons with amblyopia have poor or absent stereopsis. One hypothesis is that they have increased internal disparity noise due to either abnormal topographic representation of receptive fields and/or abnormal vergence noise, which results in depth deficits in amblyopia. To test this hypothesis, we developed a psychophysical procedure to measure the equivalent internal disparity noise by adding external disparity noise (Gaussian position noise) to random-Gabor-patch (RGP) stereograms, i.e., adding position jitter to paired Gabor patches. The two RGP stereograms (3 cpd) with external disparity noise were presented in two temporal intervals, one with mean crossed and the other with mean uncrossed disparity. The task was to detect which interval was closer. We tested 7 (contrast) x 6 (external noise) conditions. For each condition, two staircases, one 3-up-1-down and the other 3-down-1-up, were interleaved to measure the minimum and maximum disparity thresholds (Dmin and Dmax). We found that at small external disparity noise, Dmin remains constant independent of the external noise, while at large external disparity noise, Dmin is proportional to the external noise. However, Dmax remains constant at all external disparity noise levels. Based on the assumption that Dmin is proportional to the combination of internal and external noise, the equivalent internal disparity noise can be estimated by fitting the model to the Dmin data. Compared to normal controls, amblyopic observers had much larger equivalent internal disparity noise, which partially explains the poor depth perception in amblyopic vision. On the other hand, Dmax is independent of the external disparity noise in both normal and amblyopic vision, providing a reasonable explanation why Dmax seems ‘normal’ even though there is much larger internal disparity noise in amblyopia. In conclusion, internal disparity noise appears to play an important role in depth perception and should be considered when treating depth deficits in amblyopia.
Stereo thresholds are substantially worse for detecting absolute disparity than for relative disparity. One hypothesis is that absolute disparity thresholds are more affected by internal disparity noise than relative disparity thresholds. To test this hypothesis, we measured the equivalent internal disparity noise by adding external disparity noise to random-Gabor-patch (RGP) stereograms, i.e., adding position jitter to paired Gabor patches. For measuring absolute disparity thresholds, the two RGP stereograms with external disparity noise were presented in two temporal intervals, one with mean crossed and the other with mean uncrossed disparity. The task was to detect which interval was closer. For measuring relative disparity thresholds, an RGP stereogram with different disparity polarities (crossed/uncrossed) in the top and bottom halves, was presented with external disparity noise. The task was to detect whether the top or bottom half of the stereogram was closer. We tested 5 spatial frequencies and 6 external noise conditions for both absolute and relative disparity detection. We used the constant stimulus method to measure the minimum and maximum disparity thresholds (Dmin and Dmax). We found that both Dmin and Dmax are substantially lower for relative than for absolute disparity. Dmax remained constant when external noise varied. An equivalent noise model with both global and local internal disparity noise provides a unified explanation of both relative and absolute Dmin thresholds. By assuming that the relative disparity is the difference between absolute disparities, the global internal noise is canceled in relative disparity detection, resulting in a much lower Dmin threshold for relative disparity. Modeling shows that the global internal noise was independent of spatial frequency, while the local internal noise decreased when the spatial frequency increased. Global internal disparity noise may result from vergence noise and/or the absence of conscious readout of absolute disparity, i.e., the absolute disparity anomaly.
Abstract 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.
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