Light emitted from a source into a scene can undergo complex interactions with scene surfaces of different material types before being reflected. During this transport, every surface reflection is encoded in the properties of the photons that reach the detector, including time, direction, intensity, wavelength and polarization. Conventional imaging systems capture intensity by integrating over all other dimensions of the light, hiding this rich scene information. Existing methods are capable of untangling these measurements into their spatial and temporal dimensions, fueling geometric scene understanding tasks. However, examining material properties jointly with geometric properties is an open challenge that could enable unprecedented capabilities beyond geometric scene understanding, allowing for material-dependent scene understanding and imaging through complex transport. In this work, we close this gap, and 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 7D tensor theory of light transport. We discover low-rank structure in the polarimetric tensor dimension and propose a data-driven rotating ellipsometry method that learns to exploit redundancy of polarimetric structure. We instantiate our theory with two prototypes: spatio-polarimetric imaging and coaxial temporal-polarimetric imaging. This allows us, for the first time, 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 media, untangling multi-bounce light transport, breaking metamerism, and decomposition of crystals.
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