Algorithms for Reconstruction of hidden 3D shapes using diffused reflections

Abstract

This thesis aims at discovering algorithms to recover the geometry of hidden objects from tertiary diffuse scattering, given time of flight information. We focus on using ultra high speed capture of photons to accurately determine information about distance light travelled and using it to infer hidden geometry. We aim at investigating issues such as the feasibility, uniqueness(in solution domain) and invertibility of this problem. We also aim at formulating the forward and inverse theory of secondary and tertiary diffuse scattering using ideas from tomography. We aim at developing tomography based approaches and sparsity based methods to recover 3D shapes of objects "around the corner". 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".