Polarimetric Helmholtz Stereopsis.

Helmholtz stereopsis (HS) exploits the reciprocity principle of light propagation (i.e., the Helmholtz reciprocity) for 3D reconstruction of surfaces with arbitrary reflectance. In this paper, we present the polarimetric Helmholtz stereopsis (polar-HS), which extends the classical HS by considering the polarization state of light in the reciprocal paths. With the additional phase information from polarization, polar-HS requires only one reciprocal image pair. We derive the reciprocity relationship of Mueller matrix and formulate new reciprocity constraint that takes polarization state into account. We also utilize polarimetric constraints and extend them to the case of perspective projection. For the recovery of surface depths and normals, we incorporate reciprocity constraint with diffuse/specular polarimetric constraints in a unified optimization framework. For depth estimation, we further propose to utilize the consistency of diffuse angle of polarization. For normal estimation, we develop a normal refinement strategy based on degree of linear polarization. Using a hardware prototype, we show that our approach produces high-quality 3D reconstruction for different types of surfaces, ranging from diffuse to highly specular.