Point Matching Procedure Research Articles

Comparison of Wavelet Packet and Wavelet in Solving Arbitrary Array of Parallel Wires Integral Equations in Electromagnetics

In this paper, wavelets transformation (WT) and wavelet packet transformation (WPT) are used in solving, by the method of moments, a semicircular array of parallel wires electric field integral equation. First, the integral equation is solved by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix. Therefore, wavelet transformation and wavelet packet transformation are used to sparsify the impedance matrix, using two categories of wavelets functions, Biorthogonal (bior2.2) and Orthogonal (db4) wavelets. The far-field scattering patterns and the comparison between wavelets transformation and wavelet packet transformation in term number of zeros in impedance matrix and CPU Time reduction are presented. Numerical results are presented to identify which technique is best suited to solve such scattering electromagnetic problems and compared with published results.

ENHANCING CLOSE-UP IMAGE BASED 3D DIGITISATION WITH FOCUS STACKING

Abstract. The 3D digitisation of small artefacts is a very complicated procedure because of their complex morphological feature structures, concavities, rich decorations, high frequency of colour changes in texture, increased accuracy requirements etc. Image-based methods present a low cost, fast and effective alternative because laser scanning does not meet the accuracy requirements in general. A shallow Depth of Field (DoF) affects the image-based 3D reconstruction and especially the point matching procedure. This is visible not only in the total number of corresponding points but also in the resolution of the produced 3D model. The extension of the DoF is a very important task that should be incorporated in the data collection to attain a better quality of the image set and a better 3D model. An extension of the DoF can be achieved with many methods and especially with the use of the focus stacking technique. In this paper, the focus stacking technique was tested in a real-world experiment to digitise a museum artefact in 3D. The experiment conditions include the use of a full frame camera equipped with a normal lens (50mm), with the camera being placed close to the object. The artefact has already been digitised with a structured light system and that model served as the reference model in which 3D models were compared and the results were presented.

Proximity effect in a shielded symmetrical three-phase line

In this paper we present an approximate analysis of the proximity effect in a shielded symmetrical three-phase line with conductors of circular cross section. The system of two integral equations for current densities is solved approximately by assuming them in the form of two finite series with properly chosen basic functions. The unknown coefficients in these series are found by applying the point matching procedure. Numerical results are given for the AC to DC resistance ratio of the line conductors and for the power loss in the shield.

CONTOURS BASED APPROACH FOR THERMAL IMAGE AND TERRESTRIAL POINT CLOUD REGISTRATION

Abstract. Building energetic performances strongly depend on the thermal insulation. However the performance of the insulation materials tends to decrease over time which necessitates the continuous monitoring of the building in order to detect and repair the anomalous zones. In this paper, it is proposed to couple 2D infrared images representing the surface temperature of the building with 3D point clouds acquired with Terrestrial Laser Scanner (TLS) resulting in a semi-automatic approach allowing the texturation of TLS data with infrared image of buildings. A contour-based algorithm is proposed whose main features are : 1) the extraction of high level primitive is not required 2) the use of projective transform allows to handle perspective effects 3) a point matching refinement procedure allows to cope with approximate control point selection. The procedure is applied to test modules aiming at investigating the thermal properties of material.

Fusion of planning CT and cystoscopy images for bladder tumor delineation: A feasibility study

Bladder tumor delineation and localization during treatment are challenging problems in radiotherapy for bladder cancer. The purpose of this study is to investigate improvement of tumor delineation by the fusion of cystoscopy images with the planning CT-scan using lipiodol markers injected around the visible tumor during cystoscopy. A registration method was developed for the fusion of cystoscopy images with a planning CT-scan and was tested on a phantom and retrospectively on the imaging data of four bladder cancer patients. For the patients, small deposits of lipiodol were injected at the visible margin of the tumor or previous transurethral resection site during cystoscopy. These deposits were clearly visible on the planning CT-scan and served as markers for both tumor delineation and image guidance of the radiotherapy treatment. Here, the markers were used for the registration of cystoscopy images with the planning CT-scan. The registration procedure works as follows: First, coarse registrations were made to orient the cystoscopy image correctly, using the center of gravity of the markers, the center of the CT bladder, and one of N markers as fiducial points in a point matching procedure. Starting from these N orientations, full registrations are performed taking lens deformation into account. Since a cystoscopy image is 2D, each pixel corresponds to a line-of-sight. The distances between the CT markers and the lines-of-sight of the cystoscopy markers were minimized. The final cost function (the root mean square distance between corresponding CT markers and lines-of-sight) was used to quantify the quality of the registration. The registration with the lowest final cost was considered to represent the correct orientation. The CT-based tumor delineation was finally backprojected onto the cystoscopy image. The fusion of cystoscopy images with a planning CT-scan succeeded for the phantom and three out of four patients. The fiducial registration error (FRE) for the phantom image registration based on five markers was 1.1 mm, while the target registration error was 1.2-1.7 mm. The FREs for the patient images were 0.1-3.6 mm. The registration procedure failed for one patient, since it was not possible to indicate unambiguously the corresponding lipiodol marker locations in the cystoscopy image and the planning CT-scan. The difference between the CT and cystoscopy defined tumor outlines clearly exceeded the registration accuracy. Registration of cystoscopy images and planning CT-scan is feasible and allows for improvement of tumor delineation. However, the lipiodol injection protocol needs to be improved to facilitate identification of markers on both cystoscopy images and planning CT-scans.

Near-field scattering by dielectric spheroidal particles with sizes on the order of the illuminating wavelength

We present a theoretical study of electric field scattering by wavelength-sized spheroids. The incident, internal, and scattered fields are computed analytically by a spheroidal coordinate separation-of-variables solution, assuming axially incident monochromatic illumination. The main sources of possible numerical errors are identified and an additional point-matching procedure is implemented to provide a built-in test of the validity of the results. Numerical results were obtained for prolate and oblate particles with particular aspect ratios and sizes, and a refractive index of 1.33 relative to the surrounding medium. Special attention is paid to the characteristics of the near-field in close proximity to the spheroids. It is shown that particles with sizes close to the incident wavelength can produce high field enhancements whose spatial location and extension can be controlled by the particle geometry.

Automated detection and segmentation of cylindrical fragments from calibrated C-arm images for long bone fracture reduction

Long bone fracture belongs to one of the most common injuries encountered in clinical routine trauma surgery. Automated identification, pose and size estimation, and contour extraction of diaphyseal bone fragments can greatly improve the usability of a computer-assisted, fluoroscopy-based navigation system for long bone fracture reduction. In this paper, a two-step solution is proposed. In the first step, the pose and size of a diaphyseal fragment are estimated through a three-dimensional (3D) morphable object-based fitting process using a parametric cylinder model. This fitting process is optimally solved by a hybrid optimization technique coupling a random sample consensus (RANSAC) paradigm and an iterative closest point (ICP) matching procedure. Monte Carlo simulation was used to determine the parameters for the RANSAC paradigm. The results of the fragment detection step are then fed to the second step, where a region information based active contour model is used to extract the fragment contours. We designed and conducted experiments to quantify the accuracy and robustness of the proposed approach. Our experimental results conducted on images of a plastic bone as well as on those of patients demonstrate a promising accuracy and robustness of the proposed approach.

Validation of vessel-based registration for correction of brain shift

The displacement and deformation of brain tissue is a major source of error in image-guided neurosurgery systems. We have designed and implemented a method to detect and correct brain shift using pre-operative MR images and intraoperative Doppler ultrasound data and present its validation with both real and simulated data. The algorithm uses segmented vessels from both modalities, and estimates the deformation using a modified version of the iterative closest point (ICP) algorithm. We use the least trimmed squares (LTS) to reduce the number of outliers in the point matching procedure. These points are used to drive a thin-plate spline transform to achieve non-linear registration. Validation was completed in two parts. First, the technique was tested and validated using realistic simulations where the results were compared to the known deformation. The registration technique recovered 75% of the deformation in the region of interest accounting for deformations as large as 20 mm. Second, we performed a PVA-cryogel phantom study where both MR and ultrasound images of the phantom were obtained for three different deformations. The registration results based on MR data were used as a gold standard to evaluate the performance of the ultrasound based registration. On average, deformations of 7.5 mm magnitude were corrected to within 1.6 mm for the ultrasound based registration and 1.07 mm for the MR based registration.

An Efficient Volume Integral-Equation Approach for Characterization of Lossy Dielectric Materials

An efficient volume integral-equation approach for characterizing lossy dielectric materials in the Courtney holder type of measurement environment is proposed. Utilizing the parallel-plate dyadic Green's functions and the volume equivalence theorem, an effective electric-field integral equation is developed for azimuthally invariant mode analysis of a parallel-plate dielectric resonator. Volumetric cylindrical pulse basis functions and a point-matching moment-method procedure are used to formulate an eigenvalue problem. A novel singularity treatment, which uses a Bessel function identity, is presented. In an iterative permittivity searching process, perturbation of the eigenmatrix equation involves solely recomputing a diagonal matrix, which is a function of permittivity only. Therefore, the efficiency of the searching process is greatly increased. Two numerical examples are provided to illustrate the applicability and validity of the proposed approach to the evaluation of dielectric constant, loss tangent, and surface resistance of the parallel plates.

Wavelet-like bases for thin-wire integral equations in electromagnetics

In this paper, wavelets are used in solving, by the method of moments, a modified version of the thin-wire electric field integral equation, in frequency domain. The time domain electromagnetic quantities, are obtained by using the inverse discrete fast Fourier transform. The retarded scalar electric and vector magnetic potentials are employed in order to obtain the integral formulation. The discretized model generated by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix which have to be solved for each frequency of the Fourier spectrum of the time domain impressed source. Therefore, orthogonal wavelet-like basis transform is used to sparsify the moment matrix. In particular, dyadic and M-band wavelet transforms have been adopted, so generating different sparse matrix structures. This leads to an efficient solution in solving the resulting sparse matrix equation. Moreover, a wavelet preconditioner is used to accelerate the convergence rate of the iterative solver employed. These numerical features are used in analyzing the transient behavior of a lightning protection system. In particular, the transient performance of the earth termination system of a lightning protection system or of the earth electrode of an electric power substation, during its operation is focused. The numerical results, obtained by running a complex structure, are discussed and the features of the used method are underlined.

Analysis of strictly bound modes in photonic crystal fibers by use of a source-model technique.

We describe a source-model technique for the analysis of the strictly bound modes propagating in photonic crystal fibers that have a finite photonic bandgap crystal cladding and are surrounded by an air jacket. In this model the field is simulated by a superposition of fields of fictitious electric and magnetic current filaments, suitably placed near the media interfaces of the fiber. A simple point-matching procedure is subsequently used to enforce the continuity conditions across the interfaces, leading to a homogeneous matrix equation. Nontrivial solutions to this equation yield the mode field patterns and propagation constants. As an example, we analyze a hollow-core photonic crystal fiber. Symmetry characteristics of the modes are discussed and exploited to reduce the computational burden.

An advanced numerical model in solving thin-wire integral equations by using semi-orthogonal compactly supported spline wavelets

In this paper, the semi-orthogonal compactly supported spline wavelets are used as basis functions for the efficient solution of the thin-wire electric field integral equation (EFIE) in frequency domain. The method of moments (MoM) is used via the Galerkin procedure. Conventional MoM directly applied to the EFIE, leads to dense matrix which often becomes computationally intractable when large-scale problems are approached. To overcome these difficulties, wavelets can be used as a basis set so obtaining the generation of a sparse matrix; this is due to the local supports and the vanishing moments properties of the wavelets. In the paper, this technique is applied to analyze electromagnetic transients in a lightning protection systems schematized as a thin-wire structure. The study is carried out in frequency domain; a discrete fast Fourier transform algorithm can be used to compute time profiles of the electromagnetic interesting quantities. The unknown longitudinal currents are expressed by using multiscale wavelet expansions. Thus, the thin-wire EFIE is converted into a matrix equation by the Galerkin method. Results for linear spline wavelets along with their comparison with conventional MoM that uses triangular basis functions and the point matching procedure are presented, for two case studies. Good agreement has been reached with a strong reduction of the computational complexity.

Trefftz finite elements for electromagnetics

It is shown that the method of minimum autonomous blocks (MAB) of Nikol'skii and Nikol'skaia can be reformulated as the Trefftz finite-element method. Solutions of Maxwell's equations in form of plane waves are used to represent fields inside a finite element. Their projections on a set of basis functions on the surface of the element are used to obtain a descriptor of the element in form of an admittance matrix. It is shown that a point-matching projection procedure gives the frequency-domain transmission-line-matrix formulation and Galerkin-type projection leads to the MAB formulation. Admittance matrix representation of the descriptors of the elements makes it possible to use a finite-element-type global matrix assembling procedure and a sparse matrix solver.

Analysis of Electromagnetic Scattering By Infinite Conducting Cylinders of Arbitrary Smooth Cross Section Using a Genetically Optimised Technique (Ga/Mas)

The utilisation of elemental auxiliary sources located inside the scatterer in order to approximately describe the scattered field has proved to be an efficient numerical method for the analysis of electromagnetic (EM) scattering by metallic bodies. In this paper the problem of TM scattering by perfectly conducting cylinders of arbitrary but smooth cross section is treated with the integration of the above technique with the strategy of Genetic Algorithm (GA) optimisation. The GA is employed in order to allocate the auxiliary sources inside the scatterer and minimise the boundary condition error (BCE), which is an endogenous effect of the point matching procedure involved in the numerical solution. For such a case, the trial and error stage usually required for the selection of the source locations is omitted and at the same time GA stochastic search can be potentially conducted in a similar way in complex space. For a predefined accuracy of the BCE, the resulting pleiotropic, GA-optimised allocations of the sources are non-intuitive but notably affected by the geometry of the scatterer. Results are presented for the cases of infinite, perfectly conducting circular, elliptic, and periodically corrugated cylinders, demonstrating sufficient agreement with available solutions.

A parasite-free non-orthogonal frequency-domain finite difference method for the electromagnetic analysis of anisotropic waveguides

A methodology is presented for the development of a discrete vector eigenvalue problem for the dispersive analysis of inhomogeneous, anisotropic waveguiding structures. The methodology is based on the discretization of the the frequency-dependent Maxwell's equations on a non-orthogonal grid using covariant and contravariant representation for the fields and a simple point-matching procedure. The occurrence of spurious modes is avoided by the direct enforcement of Gauss' law in the development of the matrix eigenvalue problem. Results from the application of the proposed method to the dispersive analysis of planar, anisotropic microwave and optical waveguides compare favorably with published data obtained using alternative finite element formulations.

A transport theory of pulse propagation in a strongly forward scattering random medium

The scalar time-dependent equation of radiative transfer is used to develop a theory of pulse propagation in a discrete random medium whose scatter function (phase function) consists of a strong, narrow forward lobe superimposed over an isotropic background. The situation analyzed is that of a periodic sequence of plane-wave pulses, incident from an air half-space, that impinges normally upon the planar boundary surface of a random medium half-space; the medium consists of a random distribution of particles that scatter (and absorb) radiation in accordance with the aforementioned phase function. After splitting the specific intensity into the reduced incident and diffuse intensities, the solution of the transport equation in the random medium half-space is obtained by expanding the angular dependence of both the scatter function and the diffuse intensity in terms of Legendre polynomials, and by using a point matching procedure to satisfy the boundary condition that the forward travelling diffuse intensity be zero at the interface. Curves of received power show that, at small penetration depths, the coherent (reduced incident) intensity dominates, whereas at large depths, the incoherent (diffuse) intensity is the strongest and causes the pulses to broaden and distort. The motivation for this study was to complement a test series, on mm-wave pulse propagation in vegetation, by a theory that provides understanding of overall trends and assistance in the interpretation of measured results. In the mm-wave region, all scatter objects in a forest have large dimensions compared to a wavelength and, therefore, produce strong forward scattering and a phase function of the type assumed in this paper.

Surface integral formulation for calculating conductor and dielectric losses of various transmission structures

The power-loss method, along with a surface integral formulation, has been used to compute the attenuation constant in microstrip and coplanar structures. This method can be used for the analysis of both open and closed structures. Using the surface equivalence principle, the waveguide walls are replaced by equivalent electric surface currents and dielectric surfaces are replaced by equivalent electric and magnetic surface currents. Enforcing the appropriate boundary condition, and E-field integral equation (EFIE) is developed for these currents. Method of moments with pulse expansion and point matching testing procedure is used to transform the integral equation into a matrix one. The relationship between the propagation constant and frequency is found from the minimum eigenvalue of the moment matrix. The eigenvector pertaining to the minimum eigenvalue gives the unknown electric and magnetic surface currents. >

Method for solving eigenvalue problems of the Helmholtz equation with an arbitrarily shaped outer boundary and a number of eccentric inner boundaries of arbitrary shape

This paper presents a method for solving eigenvalue problems of various phenomena that are governed by the Helmholtz equation with an arbitrarily shaped outer boundary and a number of eccentric boundaries of arbitrary shape. In the analysis, the outer boundary condition is satisfied by means of the Fourier expansion collocation method using the exact solution of the equation of motion. To satisfy the inner boundary conditions, the point restraints are added to the equation of motion, and the inner boundary conditions are satisfied by making use of a point matching procedure. The equation for finding the eigenvalues are derived, and numerical calculations are carried out for cases of elliptical outer and inner boundaries and polygonal outer and inner boundaries.

Analysis of eigenvalue problems of the Helmholtz equation with an arbitrarily shaped outer boundary and a number of eccentric inner boundaries of arbitray shape.

This paper presents a method for solving eigenvalue problems of various phenomena which are governed by the Helmholtz equation with an arbitrarily shaped outer boundary and a number of eccentric boundaries of arbitrary shape. In the analysis, the outer boundary condition is satisfied by means of the Fourier expansion collocation methed using the exact solution of the equation of motion. To satisfy the inner boundary conditions, the point restraints are added to the equation of motion, and the inner boundary conditions are satisfied by making use of a point-matching procedure. The equations for finding the eigenvalues are derived, and numerical calculations are carried out for cases of elliptical outer and a number of elliptical inner boundaries, and polygonal outer and a number of elliptical inner boundaries.

Analysis of natural frequencies of cavities and scatterers using an impulsive current model

A recently suggested (see Y. Leviatan et al., ibid., vol.36, p.1722-1734, Dec. 1988) method of moments solution to generalized formulations of electromagnetic scattering from perfectly conducting and material bodies of smooth shape is used to compute the natural frequencies of such bodies. The field inside the body and the field scattered from the body are expanded by means of the field of impulsive current sources (elemental dipoles) situated a distance away from (rather than on) the boundary. The key feature of this approach is the fields anywhere in space can be evaluated analytically, yielding a substantial saving of computation time in comparison with standard on-surface formulations. Impulsive expansion functions are used for the fictitious currents that simulate the source-free fields in the relevant regions, and a point matching procedure is adopted for the enforcement of the boundary conditions. The result is a generalized impedance matrix whose singularities in the complex frequency plane represent the natural frequencies of the body. The numerical solution is simple to execute, computationally efficient, and can be applied to a broad class of bodies of smooth shape. Results demonstrating the excellent accuracy of the procedure are given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>