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Athena Buckthought, Lew B. Stelmach; Binocular matching of oriented components in stereopsis: Psychophysics and modeling. Journal of Vision 2004;4(8):192. https://doi.org/10.1167/4.8.192.
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Stereoscopic depth perception can be modeled with the binocular energy model (Ohzawa et al.,1997), which uses linear filtering to binocularly match luminance features at different orientations. A prediction of this model is that the disparity limit for depth perception is equal to a half-cycle of the spatial frequency. Dmax (the maximum disparity for 75% correct front/back discrimination) was measured for plaids which were the sum of two sine waves, as a function of sine wave component orientations. Dmax varied reciprocally with the sine of the angle each sine wave pattern makes with the horizontal. Expressing these Dmax values as a phase angle of the horizontal spatial frequency shows them to match the half cycle limit. Adding together low and high spatial frequency plaids increased Dmax slightly above the value for the low spatial frequency component alone. Dmax was also measured for bandpass filtered noise patterns, using filters which varied in lower cut-off spatial frequency (fL), bandwidth (bw), mean orientation (theta), and range of component orientations (rT) that were passed. For narrowband patterns, Dmax varied inversely with fL. If bw and rT were held constant, generally Dmax was determined by the average horizontal spatial frequency in the image and decreased as theta approached vertical. In many cases, Dmax exceeded the half-cycle limit given by fL for the most horizontal components. However, we were able to model this data using the binocular energy function (Qian & Zhu, 1997) with oriented kernels and assuming that the outputs from complex cells at all orientations are combined using linear summation. The simulations demonstrate the variation of Dmax with spatial frequency, fL, theta and rT. This modelling resembles that for motion detection (Bischof & di Lollo, 1991; Prince et al., 2001), providing evidence that stereopsis and motion use similar mechanisms for detection of oriented components.
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