Multiple channels for horizontal, but only one for vertical corrugations? A new look at the stereo anisotropy

Stereo vision displays a well-known anisotropy: disparity-defined slant is easier to detect for rotations about a horizontal axis than about a vertical axis, and low-frequency sinusoidal depth corrugations are easier to detect when the corrugations are horizontal than when they are vertical. Here, we determined disparity thresholds for vertically and horizontally oriented depth corrugations with both sinusoidal and square-wave profiles. We found that the orientation anisotropy for square waves is much weaker than for sine waves and is almost independent of frequency. This weaker anisotropy for square waves can be explained by considering the Fourier harmonics present in the stimulus. Using linear models imported from the luminance and texture perception domain, the disparity thresholds for square waves can be very well predicted from those for sine waves, for both horizontally and vertically oriented corrugations. For horizontally oriented corrugations, models based on the root mean square of the output of a single linear channel or the output of multiple linear channels worked equally well. This is consistent with previous evidence suggesting that stereo vision has multiple channels tuned to different spatial frequencies of horizontally oriented disparity modulations. However, for vertically oriented corrugations, only the root mean squared output of a single linear channel explained the data. We suggest that the stereo anisotropy may arise because the stereo system possesses multiple spatial frequency channels for detecting horizontally oriented modulations in horizontal disparity, but only one for vertically oriented modulations.