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Andrew Schofield, Peng Sun; Shape-from-shading for grating stimuli: Slant is proportional to luminance, with some exceptions. Journal of Vision 2008;8(6):445. doi: 10.1167/8.6.445.
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© ARVO (1962-2015); The Authors (2016-present)
Humans are able to interpret luminance variations as changes in shading which are in turn interpreted as due to undulations of an illuminated surface. In general, we seem to adopt the implicit assumptions that surfaces are Lambertian and illuminated by a point source such that luminance in proportional to the angle between the surface normal and the direction of the illuminant. Thus, perceived surface slant depends on luminance. Most studies of shape-from-shading use stimuli based on simulations of solid objects viewed under a specified light source. We took an alternative approach; measuring the perceived shape of a range of grating stimuli (horizontal sine-wave, square-wave, and saw-tooth gratings). Observers set the slant of a probe disk to match the slant of the perceived surface at various points on each grating. In most cases perceived slant was proportional to luminance with mean luminance equal to zero slant (surface locally fonto-parallel). Sinusoidal luminance modulations produced sinusoidal perceived surfaces even though sinusoidal corrugations seldom produce sinusoidal shading patterns in real scenes. Square-wave luminance profiles produced triangular perceived surface profiles. Saw-tooth luminance profiles with several repetitions produced perceived surfaces that were dished or bowed (depending of the direction of the luminance ramps) with surface sections meeting at localised ridges/troughs. We found one notable exception to the general result that slant is proportional to luminance. Stimuli consisting of just two linear ramps in a saw-tooth configuration were mapped as a largely flat surface with a single central crease. The regions at the top and bottom of such stimuli were perceived to have zero slant even though luminance varied linearly in these regions and was not close to mean luminance. This result suggests that luminance edges and boundaries affect the perception of shape-from-shading even for relatively simple grating stimuli.
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