Detectability of sine- versus square-wave disparity gratings: a challenge for current models of depth perception

In 2010, my PhD student Fredrik Allenmark, my post-doctoral associate Ignacio Serrano-Pedraza and I were all thinking a lot about disparity gratings. By "gratings" here, what we mean are surfaces which are corrugated in depth, as in the two icons here. "Sine-wave gratings" are surfaces in which the corrugations are smooth waves, rather like corrugated iron, whereas "square-wave gratings" have square edges. As the corrugations get higher in frequency (i.e. up-and-down bits get closer together), it gets harder to see that the surface has this structure. "Luminance gratings", i.e. patterns of black and white stripes, have made a huge contribution to our understanding of vision. Disparity gratings have also been studied, but less extensively. We were interested in what our perception of such structures can tell us about human vision.

For his PhD project, Fredrik started with a couple of recent observations from Bruce Cumming's lab at NIH and Marty Banks' lab at Berkeley. In a linked pair of papers in The Journal of Neuroscience, these workers had shown that V1 neurons seem to respond best to frontoparallel surfaces, and had proposed that the limit of human stereoresolution -- that is, the highest-frequency gratings we can detect - is set by the size of these neurons' receptive fields. We reasoned that if this model is correct, it should be easier for us to detect square-wave gratings than sine-wave gratings. Square-wave gratings are made up of piecewise frontoparallel surfaces, to which V1 neurons respond optimally, whereas sine-wave gratings are always slanting towards or away from the observer. Fredrik first ran simulations to confirm that the model behaved as we expected, and then carried out careful experiments to see what humans perceived. To our surprise, Fredrik found that there was no difference in stereoresolution for square-wave versus sine-wave gratings. As the amplitude of high-frequency gratings increased, human performance fell to chance at the same rate for both sine-wave and square-wave gratings, whereas the model predicted that this should happen only for sine-waves.
File Size2.7 MiB
DateJanuary 17, 2012
AuthorAllenmark PF, Read JCA