We analyze multi-bounce propagation of light in an unknown hidden volume and
demonstrate that the reflected light contains sufficient information to recover
the 3D structure of the hidden scene. We formulate the forward and inverse
theory of secondary and tertiary scattering reflection using ideas from energy
front propagation and tomography. We show that using careful choice of
approximations, such as Fresnel approximation, greatly simplifies this problem
and the inversion can be achieved via a backpropagation process. We provide a
theoretical analysis of the invertibility, uniqueness and choices of
space-time-angle dimensions using synthetic examples. We show that a 2D streak
camera can be used to discover and reconstruct hidden geometry. Using a 1D high
speed time of flight camera, we show that our method can be used recover 3D
shapes of objects "around the corner"
