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Dejan Todorovic; The dependence of perceived 3D relief of 2D shaded figures on the shape of their 1D bounding contours. Journal of Vision 2009;9(8):57. doi: https://doi.org/10.1167/9.8.57.
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The spatial pattern of luminance across the image of an object (shading) is an important cue for the recovery of its 3D shape (relief). However, perceived relief does not depend only on the luminance distribution in the interior of a shaded figure, but also on the shape of its bounding contour (Witkin & Tenenbaum, 1983; Ramachandran, 1988). I have investigated this little studied effect using images consisting of vertically oriented three-cycle smooth luminance gratings with rectilinear lateral boundaries, by varying the shapes of their top and bottom boundaries. A variety of boundary geometries were used, mainly involving portions of sinusoid-like shapes with different frequencies and phases, generating figures with several types of spatial congruencies between photometric features of the shading patterns (luminance maxima and minima) and geometric features of the boundaries (peaks, troughs, inflections, cusps). These manipulations had strong and occasionally multi-stable perceptual effects: figures with essentially identical luminance profiles exhibited saliently different perceived relief and apparent illumination direction, not only in the vicinity of the top and bottom boundaries but fully throughout their interior. Some figures looked as uniformly colored, unitary illuminated highlighted shapes, whereas others appeared non-uniformly colored, and under multi-directional or unnatural illumination, similar to photographic negatives. A new class of ambiguous / reversible figures was constructed by using top and bottom boundaries with mismatched shapes. The relief-related observations were confirmed and quantified in an experiment in which 69 subjects were asked to match 24 presented figures with one of 10 provided relief profiles. Some figures induced high consensus among observers, whereas others generated a variety of perceived profiles. The results are generally consistent with a simple physics of illumination, highlight the role of boundary-induced constraints on recovering 3D shapes from ambiguous shading patterns, and are relevant for shape-from-shading algorithms and neural foundations of 3D shape perception.
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