Realistic photometric stereo using partial differential irradiance equation ratios

•We tackle the problem of 3D shape recovery from multiple light sources.•A physically motivated model based on PDEs is introduced.•The proposed model overcomes the state of the art in terms of modeling physical factors.•The model is independent of photometric invariants, and parametrizes specular and diffusion shading models including point light sources with arbitrary attenuation.•The adopted method allows to obtain faithful reconstructions efficiently.

Shape from shading with multiple light sources is an active research area and a diverse range of approaches have been proposed in the last decades. However, devising a robust reconstruction technique still remains a challenging goal due to several highly non-linear physical factors being involved in the image acquisition process. Recent attempts at tackling the problem via photometric stereo rely on simplified hypotheses in order to make the problem solvable. Light propagation is still commonly assumed to be uniformly oriented, and the BRDF assumed to be diffuse, with limited interest for materials giving specular reflection. Taking into account realistic point light sources, in this paper we introduce a well-posed formulation based on partial differential equations for both diffuse and specular shading models. We base our derivation on the popular approach of image ratios, which makes the model independent from photometric invariants. The practical effectiveness of our method is confirmed with a wide range of experiments on both synthetic and real data, where we compare favorably to the state of the art.

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