Graphic Reconstruction Algorithms of the Second-Order Curve, Given by the Imaginary Elements

2016 ◽  
Vol 4 (4) ◽  
pp. 19-30 ◽  
Author(s):  
Короткий ◽  
Viktor Korotkiy ◽  
Гирш ◽  
A. Girsh
Keyword(s):  
Software Package ◽  
Projective Transformation ◽  
Main Property ◽  
Second Order ◽  
Real Point ◽  
Problem Solution ◽  
Reconstruction Algorithms ◽  
Reconstruction Problem ◽  
Curve Reconstruction ◽  
Order Curve

Second-order curves are used as shape-generating elements in the design of technical devices and architectural structures. In such a case, a need for reconstruction task solution may emerge. The reconstruction is called the definition of the main axes and asymptotes of the second-order curve by its incomplete image containing n points and m tangents (n + m = 5). In CAD graphical systems there is no possibility for construction of the second order curve, given by real and imaginary points and tangents. Therefore, the second-order curve reconstruction cannot be made with the standard set of computer graphics tools. In this paper are proposed geometrically accurate algorithms for reconstruction of the secondorder curve, given by a mixed set of real and imaginary elements. A specialized software package has been developed for constructive realization of these algorithms. Imaginary geometric images are pair-conjugated, so there are only seven possible combinations of given data with imaginary elements participation: five points, two of which are imaginary ones; five points, four of which are imaginary ones; three real points, two imaginary tangents; a real point, four imaginary tangents; a real point, two imaginary points, two imaginary tangents; a real point, two imaginary points, two real tangents; two real points, two imaginary points, a real tangent. For reconstruction problem solution is used the main property of polar matching: if P and p are the pole and polar relative to the conic g, the harmonic homology with center P and axis p transforms the curve g in itself. The method of solution based on projective transformation of required conic into a circle. It has been shown that in some cases for reconstruction problem solution its necessary to apply the quadratic involution conversion, resting on plane by a conic beam. The developed technique and software package expand the capabilities of the computer geometric simulation for processes occurring with the second-order curves participation.

scholarly journals X-rays Image reconstruction using Proximal Algorithm and adapted TV Regularization

2021 ◽  
Vol 348 ◽  
pp. 01011
Author(s):  
Aicha Allag ◽  
Redouane Drai ◽  
Tarek Boutkedjirt ◽  
Abdessalam Benammar ◽  
Wahiba Djerir
Keyword(s):  
Structural Information ◽  
X Rays ◽  
Reconstruction Algorithms ◽  
Reconstruction Problem ◽  
Tv Regularization ◽  
Object Based ◽  
Suggested Technique ◽  
Reconstruction Image ◽  
Ill Posed

Computed tomography (CT) aims to reconstruct an internal distribution of an object based on projection measurements. In the case of a limited number of projections, the reconstruction problem becomes significantly ill-posed. Practically, reconstruction algorithms play a crucial role in overcoming this problem. In the case of missing or incomplete data, and in order to improve the quality of the reconstruction image, the choice of a sparse regularisation by adding l1 norm is needed. The reconstruction problem is then based on using proximal operators. We are interested in the Douglas-Rachford method and employ total variation (TV) regularization. An efficient technique based on these concepts is proposed in this study. The primary goal is to achieve high-quality reconstructed images in terms of PSNR parameter and relative error. The numerical simulation results demonstrate that the suggested technique minimizes noise and artifacts while preserving structural information. The results are encouraging and indicate the effectiveness of the proposed strategy.

scholarly journals Optimizing Excitation Coil Currents for Advanced Magnetorelaxometry Imaging

2019 ◽  
Vol 62 (2) ◽  
pp. 238-252 ◽  
Author(s):  
Peter Schier ◽  
Maik Liebl ◽  
Uwe Steinhoff ◽  
Michael Handler ◽  
Frank Wiekhorst ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Magnetic Fields ◽  
Measurement Data ◽  
Quantitative Detection ◽  
Optimization Approach ◽  
Problem Solution ◽  
Reconstruction Algorithms ◽  
System Matrix ◽  
Imaging Quality ◽  
Excitation Coil

AbstractMagnetorelaxometry imaging is a highly sensitive technique enabling noninvasive, quantitative detection of magnetic nanoparticles. Electromagnetic coils are sequentially energized, aligning the nanoparticles’ magnetic moments. Relaxation signals are recorded after turning off the coils. The forward model describing this measurement process is reformulated into a severely ill-posed inverse problem that is solved for estimating the particle distribution. Typically, many activation sequences employing different magnetic fields are required to obtain reasonable imaging quality. We seek to improve the imaging quality and accelerate the imaging process using fewer activation sequences by optimizing the applied magnetic fields. Minimizing the Frobenius condition number of the system matrix, we stabilize the inverse problem solution toward model uncertainties and measurement noise. Furthermore, our sensitivity-weighted reconstruction algorithms improve imaging quality in lowly sensitive areas. The optimization approach is employed to real measurement data and yields improved reconstructions with fewer activation sequences compared to non-optimized measurements.

scholarly journals Numerical Modeling of Self-Consistent Dynamics of Shallow and Ground Waters

2021 ◽  
pp. 45-62
Author(s):  
Sergey Khrapov
Keyword(s):  
Numerical Modeling ◽  
Numerical Solution ◽  
Software Package ◽  
Simulation Software ◽  
Second Order ◽  
Order Of Accuracy ◽  
Ground Waters ◽  
Spatially Inhomogeneous ◽  
Tvd Method ◽  
Joint Dynamics

A mathematical and numerical model of the joint dynamics of shallow and ground waters has been built, which takes into account the nonlinear dynamics of a liquid, water absorption from the surface into the ground, filtration currents in the ground, and water seepage from the ground back to the surface. The dynamics of shallow waters is described by the Saint-Venant equations, taking into account the spatially inhomogeneous distributions of the terrain, the coefficients of bottom friction and infiltration, as well as non-stationary sources and flows of water. For the numerical integration of Saint-Venant’s equations, the well-tested CSPH-TVD method of the second order of accuracy is used, the parallel CUDA algorithm of which is implemented as a software package “EcoGIS-Simulation” for high-performance computing on supercomputers with graphic coprocessors (GPU). The dynamics of groundwater is described by the nonlinear Bussensk equation, generalized to the case of a spatially inhomogeneous distribution of the parameters of the porous medium and the surface of the aquiclude (the boundary between water-permeable and low-permeable soils). The numerical solution of this equation is built on the basis of a finite-difference scheme of the second order of accuracy, the CUDA algorithm of which is integrated into the calculation module of the “EcoGIS-Simulation” software package and is consistent with the main stages of the CSPH-TVD method. The relative deviation of the numerical solution from the exact solution of the nonlinear Boussinesq equation does not exceed 10−4–10−5. The paper compares the results of numerical modeling of the dynamics of groundwater with analytical solutions of the linearized Bussensk equation used as calculation formulas in the methods for predicting the level of groundwater in the vicinity of water bodies. It is shown that the error of these methods is several percent even for the simplest case of a plane-parallel flow of groundwater with a constant backwater. Based on the results obtained, it was concluded that the proposed method for numerical modeling of the joint dynamics of surface and ground waters can be more versatile and efficient (it has significantly better accuracy and productivity) in comparison with the existing methods for calculating flooding zones, especially for hydrodynamic flows with complex geometry and nonlinear interaction of counter fluid flows arising during seasonal floods during flooding of vast land areas.

Frequency Response for MEMS Circular Plate Resonators Under Superharmonic Resonance of the Second Order

2018 ◽  
Author(s):  
Martin Botello ◽  
Julio Beatriz ◽  
Dumitru I. Caruntu
Keyword(s):  
Circular Plate ◽  
Software Package ◽  
Multiple Scales ◽  
Electrostatic Force ◽  
Micro Electro Mechanical System ◽  
Second Order ◽  
Mode Shapes ◽  
Amplitude Response ◽  
Superharmonic Resonance ◽  
Mems Resonator

A nonlinear dynamics investigation is conducted on the frequency-amplitude response of electrostatically actuated micro-electro-mechanical system (MEMS) clamped plate resonators. The Alternating Current (AC) voltage is operating in the realm of superharmonic resonance of second order. This is given by an AC frequency near one-fourth of the natural frequency of the resonator. The magnitude of the AC voltage is large enough to be considered as hard excitation. The external forces acting on the MEMS resonator are viscous air damping and electrostatic force. Two proven mathematical models are utilized to obtain a predicted frequency-amplitude response for the MEMS resonator. Method of Multiple Scales (MMS) allows the transformation of a partial differential equation of motion into zero-order and first-order problems. Hence, MMS can be directly applied to obtain the frequency-amplitude response. Reduced Order Model (ROM), based on the Galerkin procedure, uses mode shapes of vibration for undamped circular plate resonator as a basis of functions. ROM is numerically integrated using MATLAB software package to obtain time responses. Also, ROM is used to conduct a continuation and bifurcation analysis utilizing AUTO 07P software package in order to obtain the frequency-amplitude response. The time responses show the movement of the center of the MEMS circular plate as a function of time. The frequency-amplitude response allows one to observe bifurcation and pull-in instabilities within the nonlinear system over a range of frequencies. The influences of parameters (i.e. damping and voltage) are also included in this investigation.

scholarly journals XDesign: an open-source software package for designing X-ray imaging phantoms and experiments

2017 ◽  
Vol 24 (2) ◽  
pp. 537-544 ◽  
Author(s):  
Daniel J. Ching ◽  
Dogˇa Gürsoy
Keyword(s):  
Computed Tomography ◽  
Data Acquisition ◽  
Software Package ◽  
Reconstruction Algorithms ◽  
X Ray ◽  
X Ray Imaging ◽  
Imaging Phantoms ◽  
Open Source Software Package ◽  
X Ray Computed ◽  
Image Reconstruction Algorithms

The development of new methods or utilization of current X-ray computed tomography methods is impeded by the substantial amount of expertise required to design an X-ray computed tomography experiment from beginning to end. In an attempt to make material models, data acquisition schemes and reconstruction algorithms more accessible to researchers lacking expertise in some of these areas, a software package is described here which can generate complex simulated phantoms and quantitatively evaluate new or existing data acquisition schemes and image reconstruction algorithms for targeted applications.

scholarly journals Reconstruction Algorithms for DNA-Storage Systems

2020 ◽  
Author(s):  
Omer Sabary ◽  
Alexander Yucovich ◽  
Guy Shapira ◽  
Eitan Yaakobi
Keyword(s):  
Simulated Data ◽  
Reconstruction Algorithm ◽  
Longest Common Subsequence ◽  
Levenshtein Distance ◽  
Reconstruction Algorithms ◽  
Reconstruction Problem ◽  
Common Subsequence ◽  
Minimum Number ◽  
Entire Sequence ◽  
Error Probabilities

AbstractIn the trace reconstruction problem a length-n string x yields a collection of noisy copies, called traces, y1, …, yt where each yi is independently obtained from x by passing through a deletion channel, which deletes every symbol with some fixed probability. The main goal under this paradigm is to determine the required minimum number of i.i.d traces in order to reconstruct x with high probability. The trace reconstruction problem can be extended to the model where each trace is a result of x passing through a deletion-insertion-substitution channel, which introduces also insertions and substitutions. Motivated by the storage channel of DNA, this work is focused on another variation of the trace reconstruction problem, which is referred by the DNA reconstruction problem. A DNA reconstruction algorithm is a mapping which receives t traces y1, …, yt as an input and produces , an estimation of x. The goal in the DNA reconstruction problem is to minimize the edit distance between the original string and the algorithm’s estimation. For the deletion channel case, the problem is referred by the deletion DNA reconstruction problem and the goal is to minimize the Levenshtein distance .In this work, we present several new algorithms for these reconstruction problems. Our algorithms look globally on the entire sequence of the traces and use dynamic programming algorithms, which are used for the shortest common supersequence and the longest common subsequence problems, in order to decode the original sequence. Our algorithms do not require any limitations on the input and the number of traces, and more than that, they perform well even for error probabilities as high as 0.27. The algorithms have been tested on simulated data as well as on data from previous DNA experiments and are shown to outperform all previous algorithms.

Imaging of small penetrable obstacles based on the topological derivative method

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Lucas Fernandez ◽  
Ravi Prakash
Keyword(s):  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Second Order ◽  
Reconstruction Method ◽  
Reconstruction Algorithms ◽  
Content Type ◽  
Topology Optimization Problem ◽  
Order Reconstruction ◽  
Topological Derivatives

PurposeThe purpose of this paper is to present topological derivatives-based reconstruction algorithms to solve an inverse scattering problem for penetrable obstacles.Design/methodology/approachThe method consists in rewriting the inverse reconstruction problem as a topology optimization problem and then to use the concept of topological derivatives to seek a higher-order asymptotic expansion for the topologically perturbed cost functional. Such expansion is truncated and then minimized with respect to the parameters under consideration, which leads to noniterative second-order reconstruction algorithms.FindingsIn this paper, the authors develop two different classes of noniterative second-order reconstruction algorithms that are able to accurately recover the unknown penetrable obstacles from partial measurements of a field generated by incident waves.Originality/valueThe current paper is a pioneer work in developing a reconstruction method entirely based on topological derivatives for solving an inverse scattering problem with penetrable obstacles. Both algorithms proposed here are able to return the number, location and size of multiple hidden and unknown obstacles in just one step. In summary, the main features of these algorithms lie in the fact that they are noniterative and thus, very robust with respect to noisy data as well as independent of initial guesses.

Properties Features of Parabola at Its Simulation

2018 ◽  
Vol 6 (2) ◽  
pp. 63-77 ◽  
Author(s):  
О. Графский ◽  
O. Grafskiy ◽  
Ю. Пономарчук ◽  
Yu. Ponomarchuk ◽  
В. Суриц ◽  
...  
Keyword(s):  
Computer Aided Design ◽  
Educational Program ◽  
Second Order ◽  
Construction Methods ◽  
Order Curve ◽  
Straight Line ◽  
Applied Informatics ◽  
Design Systems ◽  
Aided Design ◽  
Graphic Task

When studying the theory of contour construction in “Affine and Projective Geometry” course on educational program specializations “Computer-Aided Design Systems” and “Applied Informatics in Design” a unit of computational and graphic task "Contour Construction" is carrying out in structural design. In this computational and graphic task the contour constructions are carrying out by second-order curves (a circle — by the radius and graphical method; a hyperbola, an ellipse, a parabola — by means of Pascal curves, taking into account positions of engineering discriminant). The constructions of an arc of ellipse, hyperbola, and parabola are carried out based on Pascal theorem: in any hexagon, which vertices belong to a second-order series, three points of the opposite sides’ intersection lie on one straight line — the Pascal line. However, in construction of a conic (a second-order curve), it is necessary to draw students’ attention to the fact that the points belonging to a second-order series (a second-order curve, or a conic) make a geometrical locus of intersection of Pascal hexagon’s adjacent opposite sides. By this method students successfully construct conjugate arcs of an ellipse and a hyperbola with other conics. The construction of a parabola arc, conjugated with other conics, is carried out by the method of engineering discriminant (it is more convenient to divide line segments in halves: a median and a triangle side, which is opposite to its vertex lying on a parabola arc). It should be noted that theoretical and practical material on this subject corresponds to the assimilation of Study Plan’s necessary competences (in accordance with each educational program), however, some aspects of this subject are accepted by students simply by trust. The aim of this paper is research of construction methods for parabola, applied to contour simulation.

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