Shape Reconstruction Algorithm Research Articles

Shape Reconstruction of Three-Dimensional Conducting Curved Plates Using Physical Optics, NURBS Modeling, and Genetic Algorithm

A microwave inverse scattering problem including a method for shape reconstruction of three-dimensional electrically large conducting patches with simple geometries using genetic algorithm is presented. Unknown shape reconstruction algorithm starts from the knowledge of the simulated radar cross-section (RCS) data through back-scattering far-field computation using physical optics approximation. The forward problem involves the computation of the multiple-frequency and multiple-direction RCS of three-dimensional large conducting patches modeled by nonuniform rational B-spline (NURBS) surfaces. The control points of NURBS are the geometrical parameters, which are optimized for the shape reconstruction procedure. The extended stationary phase method and critical cases, which occur in physical optics computations in the forward problem, are also discussed. Noise effect and the influence of increment in the number of control points of a NURBS over the inversion algorithm are investigated as well. Numerical results are presented to verify the operation of the proposed algorithm

On-line plasma shape reconstruction algorithm in tokamaks and its verification in the Globus-M

An on-line plasma shape reconstruction algorithm is necessary to design the plasma position and shape control system in modern tokamaks. An algorithm aimed at solving this problem is proposed. A description of the mathematical procedure is provided and experimental data incorporation is discussed. An example of an application of this algorithm is demonstrated using experimental data from Globus-M discharge #10292.

Modular Structure of Solubilized Human Apolipoprotein B-100: LOW RESOLUTION MODEL REVEALED BY SMALL ANGLE NEUTRON SCATTERING

Being intimately involved in cholesterol transport and lipid metabolism human low density lipoprotein (LDL) plays a prominent role in atherogenesis and cardiovascular diseases. The receptor-mediated cellular uptake of LDL is triggered by apolipoprotein B-100 (apoB-100), which represents the single protein moiety of LDL. Due to the size and hydrophobic nature of apoB-100, its structure is not well characterized. Here we present a low resolution structure of solubilized apoB-100. We have used small angle neutron scattering in combination with advanced shape reconstruction algorithms to generate a three-dimensional model of lipid-free apoB-100. Our model clearly reveals that apoB-100 is composed of distinct domains connected by flexible regions. The apoB-100 molecule adopts a curved shape with a central cavity. In comparison to LDL-associated apoB-100, the lipid-free protein is expanded, whereas according to spectroscopic data the secondary structure is widely preserved. Finally, the low resolution model was used as a template to reconstruct a hypothetical domain organization of apoB-100 on LDL, including information derived from a secondary structure prediction.

Reconstructing absorption and diffusion shape profiles in optical tomography by a level set technique

A shape reconstruction algorithm for optical tomography is introduced that uses a level-set formulation for the shapes. Evolution laws based on gradient directions for a cost functional are derived for two different level-set functions, one describing the absorption and one the diffusion parameter, as well as for the parameter values inside these shapes. Numerical experiments are presented in 2D that show that the new method is able to simultaneously recover shapes and contrast values of absorbing and scattering objects embedded in a moderately heterogeneous background medium from simulated noisy data.

Imaging of voids by means of a physical-optics-based shape-reconstruction algorithm.

We analyze the performance of a shape-reconstruction algorithm for the retrieval of voids starting from the electromagnetic scattered field. Such an algorithm exploits the physical optics (PO) approximation to obtain a linear unknown-data relationship and performs inversions by means of the singular-value-decomposition approach. In the case of voids, in addition to a geometrical optics reflection, the presence of the lateral wave phenomenon must be considered. We analyze the effect of the presence of lateral waves on the reconstructions. For the sake of shape reconstruction, we can regard the PO algorithm as one of assuming the electric and magnetic field on the illuminated side as constant in amplitude and linear in phase, as far as the dependence on the frequency is concerned. Therefore we analyze how much the lateral wave phenomenon impairs such an assumption, and we show inversions for both one single and two circular voids, for different values of the background permittivity.

Improving a Shape Reconstruction Algorithm with Thresholds and Multi-View Data

Abstract This paper deals with the reconstruction of the shape of unknown perfectly conducting objects from the knowledge of the scattered electric far field in a two-dimensional geometry. By adopting the Kirchhoff approximation, the problem is cast as a linear inverse one and is solved by resorting to the Singular Value Decomposition (SVD) approach. The finiteness of the available data along with the presence of the noise make undesired features on the reconstructed image arise. We here give some criteria for the choice of a threshold to cut them out from the reconstructions. Furthermore, we illustrate the processing of multi-view data.

Learning compact 3D models of indoor and outdoor environments with a mobile robot

This paper presents an algorithm for full 3D shape reconstruction of indoor and outdoor environments with mobile robots. Data is acquired with laser range finders installed on a mobile robot. Our approach combines efficient scan matching routines for robot pose estimation with an algorithm for approximating environments using flat surfaces. On top of that, our approach includes a mesh simplification technique to reduce the complexity of the resulting models. In extensive experiments, our method is shown to produce accurate models of indoor and outdoor environments that compare favorably to other methods.

Experimental validation of a PO-based shape reconstruction algorithm

The effectiveness of a linear inverse scattering algorithm for the shape reconstruction of perfectly conducting objects is experimentally validated by processing measured data. The data are collected via an automatic system for free-space measurements under reflection mode geometry. The amplitude and phase of the scattered field is measured in a multistatic and multifrequency configuration for different locations (views) of the transmitting antenna. The reliability of the measurement setup is shown by a comparison with simulated data. No a priori knowledge of the shape of the scatterers is assumed. The results of inversions of experimental data collected under single-view illumination agree well with those of inversions of synthetic data, so showing the robustness of the algorithm.

Systematic errors in small deformations measured by use of shadow-moiré topography

Phase-shift shadow-moiré topography is a noncontact optical technique for measuring the shapes of surfaces. Artifactual bands resembling isoheight surface contours are observed during measurement of small changes in shape by use of this technique. The shape-reconstruction algorithm used in shadow-moiré topography is based on a mathematical model of the fringe patterns generated on the surface to be measured. We hypothesize that the observed bands reflect systematic errors caused by ignoring height-dependent terms in the mathematical model of the fringe patterns. We test the assumption by simulating the fringe patterns for a virtual test surface by using a model that contains height-dependent terms and one term that is idealized by ignoring these terms. Small systematic errors in shape are observed only when the surface is reconstructed from fringe patterns simulated with a model containing the height-dependent terms. Shape-error curves are computed as a function of the surface height by the subtraction of the reconstructed shape from the known shape. Simulated shape-error curves agree with experimental measurements in that they show an increase in error with surface height, and both the experimental and the simulated shape-error curves contain ripples. Although the errors are small in comparison with the dimensions of the surface and are negligible in shape measurements and in most deformation measurements, they may show up as noticeable bands in images of small deformations.

Reconstructing objects from the Ipswich data set

Inverse scattering, or imaging, has many important technological applications. In this paper, we present experimental results of refractive-index reconstruction using a previously developed algorithm that is based on an enhanced diffraction tomography. In addition, we also present experimental results of a shape-reconstruction algorithm that utilizes the null-field method for solving the direct problem, and the Newton-Kantorovich technique for inversion. For testing of both algorithms, we make use of experimental scattering data contained in the Ipswich data set.

Two‐dimensional location and shape reconstruction

A method for reconstructing the location and the shape of a bounded impenetrable object from measured scattered field data is presented. The algorithm is, in principle, the same as that used for reconstructing the conductivity of a penetrable object and uses the fact that for high conductivity the skin depth of the scatterer is small, in which case the only meaningful information produced by the algorithm is the boundary of the scatterer. A striking increase in efficiency is achieved by incorporating into the algorithm the fact that for large conductivity the contrast is dominated by a large positive imaginary part. This fact, together with the knowledge that the scatterer is constrained in some test domain, constitute the only a priori information about the scatterer that is used. There are no other implicit assumptions about the location, connectivity, convexity, or boundary conditions. Some refinements of the algorithm which reduce the number of points at which the unknown function is updated are incorporated to further increase efficiency. Results of a number of numerical examples are presented which demonstrate the effectiveness of the location and shape reconstruction algorithm.