Variable-source shading analysis

The shading on curved surfaces is a cue to shape. Current computer vision methods for analyzing shading use physically unrealistic models, have serious mathematical problems, cannot exploit geometric information if it is available, and are not reliable in practice. We introduce a novel method of accounting for variations in irradiance resulting from interreflections, complex sources and the like. Our approach uses a spatially varying source model with a local shading model. Fast spatial variation in the source is penalised, consistent with the rendering community's insight that interreflections are spatially slow. This yields a physically plausible shading model. Because modern cameras can make accurate reports of observed radiance, our method compels the reconstructed surface to have shading exactly consistent with that of the image. For inference, we use a variational formulation, with a selection of regularization terms which guarantee that a solution exists. Our method is evaluated on physically accurate renderings of virtual objects, and on images of real scenes, for a variety of different kinds of boundary condition. Reconstructions for single sources compare well with photometric stereo reconstructions and with ground truth.