Polarimetric Spatio-Temporal Light Transport Probing

Light can undergo complex interactions with multiple scene surfaces of different material types before being reflected towards a detector. During this transport, every surface reflection and propagation is encoded in the properties of the photons that ultimately reach the detector, including travel time, direction, intensity, wavelength and polarization. Conventional imaging systems capture intensity by integrating over all other dimensions of the light into a single quantity, hiding this rich scene information in the accumulated measurements. Existing methods can untangle these into their spatial and temporal dimensions, fueling geometric scene understanding. However, examining polarimetric material properties jointly with geometric properties is an open challenge that could enable unprecedented capabilities beyond geometric understanding, allowing to incorporate material-dependent semantics. In this work, we propose a computational light-transport imaging method that captures the spatially- and temporally-resolved complete polarimetric response of a scene. Our method hinges on a novel 7D tensor theory of light transport. We discover low-rank structures in the polarimetric tensor dimension and propose a data-driven rotating ellipsometry method that learns to exploit redundancy of the polarimetric structures. We instantiate our theory in two imaging prototypes: spatio-polarimetric imaging and coaxial temporal-polarimetric imaging. This allows us to decompose scene light transport into temporal, spatial, and complete polarimetric dimensions that unveil scene properties hidden to conventional methods. We validate the applicability of our method on diverse tasks, including shape reconstruction with subsurface scattering, seeing through scattering medium, untangling multi-bounce light transport, breaking metamerism with polarization, and spatio-polarimetric decomposition of crystals.