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.

^{2}and reduced to 2.8 cd/m

^{2}when viewed through the polarizing glasses; the black background had a luminance of 0.07 cd/m

^{2}and reduced to 0.05 cd/m

^{2}.

*σ*

_{dot}= 1.44 arcmin (the dots had a dimension of 5 × 5 pixels). Dots were scattered randomly but without overlap. The luminance of each pixel was calculated according to the value of the Gaussian function at the center of the pixel, thus allowing subpixel disparities. Dot density was

*ρ*= 14.08 dots/deg

^{2}, giving a Nyquist limit of

*f*

_{N}= 1.87 cycles/deg (

*f*

_{N}= 0.5

*δ*on the screen, according to the desired waveform, e.g.,

*δ*= ±

*A*/2cos(2

*πfy*) for a horizontally oriented sine wave;

*δ*= ±

*A*/2sgn(cos(2

*πfx*)) for a vertically oriented square wave, where

*A*/2 is the disparity amplitude of the grating and

*f*is its spatial frequency. Dots were given uniform disparity and remained circular even when depicted as lying on the sloping regions of sine-wave corrugations. The dot size was much less than the shortest spatial period used (50 arcmin), and disparity amplitudes were small; as we shall see in the Results (Figure 2), the maximum value of

*fA*was 0.02 while the maximum

*f*was 1.2 cpd. Thus, the disparity change that should have occurred across a dot, 2

*πσ*

_{dot}

*fA,*never exceeded 0.15 arcmin or 11% of the grating amplitude.

*worse*on vertically oriented gratings.

*fA,*which in our stimuli does not exceed 0.02. This means that the disparity amplitude is much less than the upper limit, and the distinction between opaque and transparent surfaces is negligible (because areas that would have been occluded by an opaque surface form a tiny fraction of the stimulus).

*ν*), the inverse of the peak-to-trough disparity threshold function obtained with sinusoidal corrugations (see Figures 2 and 6). Thus, to predict the threshold with this model, we first multiply the Fourier transform of the signal by the disparity sensitivity function, then take the inverse Fourier transform and finally calculate the peak value of the output signal (Campbell & Robson, 1968, their Figure 3).

*A*

_{sq}is

*f*

_{1}is the spatial frequency of the fundamental or first harmonic.

*A*

_{sin}, the peak of the filtered waveform is

*P*is the threshold for detection. Then,

*A*

_{sin}is, by definition, the peak-to-trough disparity threshold for detecting a sine wave of frequency

*f*

_{1}, and therefore

*A*

_{sin}DSF(

*f*

_{1}) = 1. The peak-to-trough disparity threshold for square waves of fundamental frequency

*f*

_{1}is therefore predicted to be

*A*

_{sq}/2 is

*A*

_{sin}, it is

*A*

_{sq}is detected if and only if

*n*. If the most detectable harmonic is the fundamental spatial frequency (if

*n*= 1), then the ratio will be 4/

*π*.

*χ*

^{2}; the lower the values, the better the fit. Note that the predictions from the three models are identical for spatial frequencies higher that 0.4 cycle/deg, so both here and in the next figure, the thresholds measured at low spatial frequencies are critical for distinguishing between the models.

*π*= 1.273, the amplitude ratio of their fundamental components. This model predicts experimental thresholds well in all subjects.

*χ*

_{rms}

^{2}values over the five subjects is 6.92, slightly worse than the mean of 4.02 for

*χ*

_{mdh}

^{2}. In almost all cases, the peak model (Δ) is far worse at predicting the experimental data.

*π*at low frequencies. The mdh model (∇) does go some way toward capturing this. For vertically oriented corrugations, the threshold ratio predicted by the mdh model can exceed the classic value of 4/

*π*. This interesting effect is due to the very steep increase in threshold at low frequencies, which does not occur for horizontally oriented disparity corrugations, nor in the luminance domain. As frequency increases from 0.05 cycle/deg, disparity thresholds for sine corrugations fall faster than the 1/

*n*decay in harmonics of the square wave. This means that it is possible for the square-wave's fifth harmonic at 5

*f*

_{1}, for example, to be above threshold, while its fundamental at

*f*

_{1}is still undetectable. Thus, the mdh model produces threshold ratios approaching 5 in some subjects. However, its threshold ratios are still substantially smaller than those observed experimentally: subjects do much better on the square-wave corrugations than predicted by this model.