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Jan J. Koenderink, Sylvia C. Pont, Andrea J. van Doorn; A new twist to the “shading cue”. Journal of Vision 2006;6(6):260. https://doi.org/10.1167/6.6.260.
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© ARVO (1962-2015); The Authors (2016-present)
The “shading cue” is conventionally placed in the context of smooth Lambertian surfaces of uniform (unit) albedo, illuminated by a collimated, uniform beam. Under these assumptions the illuminance varies because of Lambert's cosine Law, that is with the component of the “light vector” that is normal to the surface. The illuminance pattern, or “shading”, thus contains shape information: hence “shading cue”. Formal analysis reveals that the SFS (“Shape From Shading”) problem is very ill posed. Only global solutions exist, and these are subject to an extensive group of ambiguities. Some of these ambiguities have become well known in human psychophysics.
In realistic situations the surface will be rough, rather than smooth. This induces an illumination dependent texture. We show that this texture reveals the component of the light vector along the surface, which may be called “illuminance flow”. This changes the SFS problem significantly. Local estimates of surface shape become possible, and the group of ambiguities becomes smaller. We have shown psychophysically that observers are able to detect this illuminance flow.
Since local mechanisms are much more biologically viable than global ones (solutions of partial differential equations with boundary conditions) we reconsider a number of classical illusions involving the shading cue, but this time in the presence of surface roughness. There exist simple variations on the convex/concave illusion that are disambiguated by the illuminance flow. Informal observation reveals that human observers fail to disambiguate such cases, thus giving rise to a novel set of illusions.
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