Towards 3D Computational Persicopy with an Ordinary Camera: a Separable Non-Linear Least Squares Formulation.

The ability to image a scene without a direct line of sight has been demonstrated by exploiting measurements of light transients, speckle correlations, or even soft shadows (i.e., penumbra). Here, we present a new formulation of computational periscopy with an ordinary camera: a recent method that reconstructs two-dimensional images of a hidden scene from a single photograph of penumbra by exploiting the presence of a partially known occluder in the hidden scene. Our reformulation facilitates the recovery of three-dimensional information of the non-line-of-sight (NLOS) scene from an ordinary photograph of the penumbra produced on a visible matte surface. Specifically, we decompose the hidden scene into light-reflecting components constrained to be on a transverse 2D plane, and light-occluding components represented as a coarse 3D binary-valued occupancy grid. This decomposition, thus, yields a separable non-linear least squares inverse problem for reconstructing the hidden scene, using alternating minimization methods.