61,675 research outputs found
Reconstruction of hidden 3D shapes using diffuse reflections
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"
A Primal-Dual Algorithm for Link Dependent Origin Destination Matrix Estimation
Origin-Destination Matrix (ODM) estimation is a classical problem in
transport engineering aiming to recover flows from every Origin to every
Destination from measured traffic counts and a priori model information. In
addition to traffic counts, the present contribution takes advantage of probe
trajectories, whose capture is made possible by new measurement technologies.
It extends the concept of ODM to that of Link dependent ODM (LODM), keeping the
information about the flow distribution on links and containing inherently the
ODM assignment. Further, an original formulation of LODM estimation, from
traffic counts and probe trajectories is presented as an optimisation problem,
where the functional to be minimized consists of five convex functions, each
modelling a constraint or property of the transport problem: consistency with
traffic counts, consistency with sampled probe trajectories, consistency with
traffic conservation (Kirchhoff's law), similarity of flows having close
origins and destinations, positivity of traffic flows. A primal-dual algorithm
is devised to minimize the designed functional, as the corresponding objective
functions are not necessarily differentiable. A case study, on a simulated
network and traffic, validates the feasibility of the procedure and details its
benefits for the estimation of an LODM matching real-network constraints and
observations
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