Shape and light directions from shading and polarization

We introduce a method to recover the shape of a smooth dielectric object from polarization images taken with a light source from different directions. We present two constraints on shading and polarization and use both in a single optimization scheme. This integration is motivated by the fact that photometric stereo and polarization-based methods have complementary abilities. The polarization-based method can give strong cues for the surface orientation and refractive index, which are independent of the light direction. However, it has ambiguities in selecting between two ambiguous choices of the surface orientation, in the relationship between refractive index and zenith angle (observing angle), and limited performance for surface points with small zenith angles, where the polarization effect is weak. In contrast, photometric stereo method with multiple light sources can disambiguate the surface orientation and give a strong relationship between the surface normals and light directions. However, it has limited performance for large zenith angles, refractive index estimation, and faces the ambiguity in case the light direction is unknown. Taking their advantages, our proposed method can recover the surface normals for both small and large zenith angles, the light directions, and the refractive indexes of the object. The proposed method is successfully evaluated by simulation and real-world experiments.