86,166 research outputs found
Radio interferometric imaging of spatial structure that varies with time and frequency
The spatial-frequency coverage of a radio interferometer is increased by
combining samples acquired at different times and observing frequencies.
However, astrophysical sources often contain complicated spatial structure that
varies within the time-range of an observation, or the bandwidth of the
receiver being used, or both. Image reconstruction algorithms can been designed
to model time and frequency variability in addition to the average intensity
distribution, and provide an improvement over traditional methods that ignore
all variability. This paper describes an algorithm designed for such
structures, and evaluates it in the context of reconstructing three-dimensional
time-varying structures in the solar corona from radio interferometric
measurements between 5 GHz and 15 GHz using existing telescopes such as the
EVLA and at angular resolutions better than that allowed by traditional
multi-frequency analysis algorithms.Comment: 12 pages, 4 figures. SPIE Proceedings, Optical
Engineering+Applications; Image Reconstruction from Incomplete Dat
TVL<sub>1</sub> Planarity Regularization for 3D Shape Approximation
The modern emergence of automation in many industries has given impetus to extensive research into mobile robotics. Novel perception technologies now enable cars to drive autonomously, tractors to till a field automatically and underwater robots to construct pipelines. An essential requirement to facilitate both perception and autonomous navigation is the analysis of the 3D environment using sensors like laser scanners or stereo cameras. 3D sensors generate a very large number of 3D data points when sampling object shapes within an environment, but crucially do not provide any intrinsic information about the environment which the robots operate within.
This work focuses on the fundamental task of 3D shape reconstruction and modelling from 3D point clouds. The novelty lies in the representation of surfaces by algebraic functions having limited support, which enables the extraction of smooth consistent implicit shapes from noisy samples with a heterogeneous density. The minimization of total variation of second differential degree makes it possible to enforce planar surfaces which often occur in man-made environments. Applying the new technique means that less accurate, low-cost 3D sensors can be employed without sacrificing the 3D shape reconstruction accuracy
A Bayesian Approach to Manifold Topology Reconstruction
In this paper, we investigate the problem of statistical reconstruction of piecewise linear manifold topology. Given a noisy, probably undersampled point cloud from a one- or two-manifold, the algorithm reconstructs an approximated most likely mesh in a Bayesian sense from which the sample might have been taken. We incorporate statistical priors on the object geometry to improve the reconstruction quality if additional knowledge about the class of original shapes is available. The priors can be formulated analytically or learned from example geometry with known manifold tessellation. The statistical objective function is approximated by a linear programming / integer programming problem, for which a globally optimal solution is found. We apply the algorithm to a set of 2D and 3D reconstruction examples, demon-strating that a statistics-based manifold reconstruction is feasible, and still yields plausible results in situations where sampling conditions are violated
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TVL<sub>1</sub>shape approximation from scattered 3D data
With the emergence in 3D sensors such as laser scanners and 3D reconstruction from cameras, large 3D point clouds can now be sampled from physical objects within a scene. The raw 3D samples delivered by these sensors however, contain only a limited degree of information about the environment the objects exist in, which means that further geometrical high-level modelling is essential. In addition, issues like sparse data measurements, noise, missing samples due to occlusion, and the inherently huge datasets involved in such representations makes this task extremely challenging. This paper addresses these issues by presenting a new 3D shape modelling framework for samples acquired from 3D sensor. Motivated by the success of nonlinear kernel-based approximation techniques in the statistics domain, existing methods using radial basis functions are applied to 3D object shape approximation. The task is framed as an optimization problem and is extended using non-smooth L1 total variation regularization. Appropriate convex energy functionals are constructed and solved by applying the Alternating Direction Method of Multipliers approach, which is then extended using Gauss-Seidel iterations. This significantly lowers the computational complexity involved in generating 3D shape from 3D samples, while both numerical and qualitative analysis confirms the superior shape modelling performance of this new framework compared with existing 3D shape reconstruction techniques
A robust inversion method for quantitative 3D shape reconstruction from coaxial eddy-current measurements
This work is motivated by the monitoring of conductive clogging deposits in
steam generator at the level of support plates. One would like to use monoaxial
coils measurements to obtain estimates on the clogging volume. We propose a 3D
shape optimization technique based on simplified parametrization of the
geometry adapted to the measurement nature and resolution. The direct problem
is modeled by the eddy current approximation of time-harmonic Maxwell's
equations in the low frequency regime. A potential formulation is adopted in
order to easily handle the complex topology of the industrial problem setting.
We first characterize the shape derivatives of the deposit impedance signal
using an adjoint field technique. For the inversion procedure, the direct and
adjoint problems have to be solved for each coil vertical position which is
excessively time and memory consuming. To overcome this difficulty, we propose
and discuss a steepest descent method based on a fixed and invariant
triangulation. Numerical experiments are presented to illustrate the
convergence and the efficiency of the method
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