Polarimetric Three-View Geometry

This paper theorizes the connection between polarization and three-view geometry. It presents a ubiquitous polarization-induced constraint that regulates the relative pose of a system of three cameras. We demonstrate that, in a multi-view system, the polarization phase obtained for a surface point is induced from one of the two pencils of planes: one by specular reflections with its axis aligned with the incident light; one by diffusive reflections with its axis aligned with the surface normal. Differing from the traditional three-view geometry, we show that this constraint directly encodes camera rotation and projection, and is independent of camera translation. In theory, six polarized diffusive point-point-point correspondences suffice to determine the camera rotations. In practise, a cross-validation mechanism using correspondences of specularites can effectively resolve the ambiguities caused by mixed polarization. The experiments on real world scenes validate our proposed theory.