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

While Fredrik was measuring the high-frequency limit of our ability to perceive sine- and square-wave depth corrugations, Ignacio got interested in another aspect of sine- versus square-wave corrugations. For sine-wave corrugations, Brian Rogers and Mark Bradshaw had shown that at low frequencies, horizontal corrugations were easier to detect than vertical corrugations: that is, the corrugations didn't have to be so deep in order to be visible. At high frequencies, this difference becomes weaker. This result has been replicated in many different tasks, and represents a fundamental anisotropy of stereo vision. Ignacio showed that, at low frequencies, this anisotropy is not as strong with square-wave gratings as with sine-waves: low-frequency square-waves are about equally visible whether they are horizontal or vertical. To understand why this is, Ignacio considered two different models. In one model, the waveform is analysed as a whole, and it is detected if its RMS amplitude exceeds some threshold. In the other model, the waveform is analysed in separate frequency channels, assumed to have a bandwidth narrow enough that harmonics differing by 1.5 octaves activate separate channels. The grating is detected if the Fourier amplitude of any harmonic exceeds the threshold for that frequency, which we measure using sine-wave gratings. For vertical gratings, both models worked equally well, but for horizontal gratings, only the separate-channel model can capture the improved performance at low frequencies. One plausible interpretation of these results is that there is only a single channel available to detect vertical gratings, but there are a few (three, say) for horizontal gratings. This recasts the well-known stereo anisotropy in Fourier language: horizontal gratings are more visible at low frequencies because they activate a channel dedicated to these low frequencies, whereas vertical gratings are only perceived when their amplitude is large enough to activate the all-purpose channel, which is centered on intermediate frequencies. Obviously, more work is needed to test this hypothesis, and we intend to pursue this in the future, for example with a masking technique.
SerranoPedrazaRead10.pdf
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DateJanuary 17, 2012
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AuthorSerrano-Pedraza I, Read JCA