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Workshop: Symmetry and Geometry in Neural Representations

Curvature Fields from Shading Fields

Xinran Han · Todd Zickler


We re-examine the estimation of 3D shape from images that are caused by shading of diffuse Lambertian surfaces. We propose a neural model that is motivated by the well-documented perceptual effect in which shape is perceived from shading without a precise perception of lighting. Our model operates independently in each receptive field and produces a scalar statistic of surface curvature for that field. The model’s architecture builds on previous mathematical analyses of lighting-invariant shape constraints, and it leverages geometric structure to provide equivariance under image rotations and translations. Applying our model in parallel across a dense set of receptive fields produces a curvature field that we show is quite stable under changes to a surface’s albedo pattern (texture) and also to changes in lighting, even when lighting varies spatially across the surface.

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