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Jonathan Tong, Robert Allison, Laurie Wilcox; The perception of average slant is biased in concave surfaces. Journal of Vision 2021;21(9):2011. doi: https://doi.org/10.1167/jov.21.9.2011.
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While much is known about our perception of surface slant for planar surfaces, less attention has been paid to our ability to estimate the average slant of curved surfaces. The average slant across a surface with symmetric curvature (a parabolic surface) and globally slanted about its axis of symmetry is equivalent to that of a planar surface slanted by the same degree. Therefore, if symmetrically curved surfaces are perceived accurately, observers’ estimates of their average surface slant should be the same as for an equivalently slanted planar surface. Here we evaluated this prediction using a 2-alternative forced choice slant discrimination task. Observers (n=10) viewed a standard 15° (top-away) slanted planar surface and a comparison surface that varied in slant between 7.5° and 22.5°; both were presented stereoscopically and textured with a Voronoi pattern. In separate conditions, the comparison surface was either planar, or parabolically curved (peak displacement = 0.15m) about its axis of rotation in a concave or convex direction. Observers consistently underestimated the average slant of the concave comparison surface relative to the planar surface. This bias is predicted by the effect of curvature modulating the degree of foreshortening in the perspective projection of a slanted surface. Perspective projection also predicts overestimation of average slant in convex surfaces, however we found no such bias. We propose that imprecision in the estimation of average slant in curved surfaces, relative to planar surfaces, makes them more susceptible to the commonly reported frontoparallel bias (slant underestimation). This bias may counteract the predicted overestimation of average slant in convex surfaces. Taken together, our modelling and psychophysical results indicate that curvature modulates the pattern of foreshortening of globally slanted surfaces, which biases the estimation of average slant. This, in turn, may lead to systematic errors in our interaction with curved surfaces.
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