Frequency dependence on image reconstruction for a buried imperfectly conducting cylinder

Frequency dependence on image reconstruction for a buried imperfectly conducting cylinder is investigated. A conducting cylinder of unknown shape and conductivity is buried in one half‐space and the incident wave is scattered from another half‐space. By using measured scattered field, the image problem is reformulated into an optimization problem and solved by the genetic algorithm. Frequency dependence on image reconstruction is investigated and numerical results show that the reconstruction is well in the resonant frequency range. On the contrary, if the frequency is too high or too low, then the reconstruction becomes bad. This work provides both comparative and quantitative information. © 2002 Wiley Periodicals, Inc. Int J RF and Microwave CAE 12: 144–147, 2002.     

Comparison of image reconstruction by using near‐field and far‐field data for an imperfect conductor

Image reconstruction by using near‐field and far‐field data for an imperfectly conducting cylinder is investigated. A conducting cylinder of unknown shape and conductivity scatters the incident wave in free space and the scattered near and far fields are measured. By using measured fields, the imaging problem is reformulated into an optimization problem and solved by the genetic algorithm. Numerical results show that the convergence speed and final reconstructed results by using near‐field data are better than those obtained by using far‐field data. This work provides both comparative and quantitative information. © 2001 John Wiley & Sons, Inc. Int J RF and Microwave CAE 11: 69–73, 2001.     

A study of microwave imaging for a metallic cylinder

This article presents the studies of time‐domain inverse scattering for a metallic cylinder which based on the finite‐difference time‐domain (FDTD) method and the dynamic differential evolution (DDE). For this study, the FDTD is used for the analysis of the forward scattering part, while for the DDE is applied for the reconstruction of the two‐dimensional metallic cylinder. For the forward scattering, the FDTD method is used to calculate the scattered E fields. Based on the scattering fields, these inverse scattering problems are transformed into optimization problem. By comparing the simulated scattered fields and the calculated scattered fields, the shape and location of the metallic cylinder are reconstructed. Numerical results demonstrate that, even when the initial guess is far away from the exact one, good reconstruction can be obtained. In addition, the effects of Gaussian noise on the reconstruction results are investigated. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE , 2012.     

Solving time domain microwave imaging for two‐dimensional inhomogeneous dielectric cylinder

This article presents the studies of time domain inverse scattering for a two‐dimensional (2D) inhomogeneous dielectric cylinder buried in a slab medium by the asynchronous particle swarm optimization (APSO) and dynamic differential evolution (DDE) method. The method of finite‐difference time‐domain is employed for the analysis of the forward scattering part, while the inverse scattering problem is transformed into optimization one. The DDE algorithm and the APSO are applied to reconstruct the permittivities distribution of a 2D inhomogeneous dielectric cylinder. Both techniques have been tested in the case of simulated measurements contaminated by additive white Gaussian noise. Numerical results indicate that the APSO algorithm outperforms the DDE in terms of reconstruction accuracy and convergence speed. © 2013 Wiley Periodicals, Inc. Int J RF and Microwave CAE 24:147–154, 2014.     

Electromagnetic imaging for shape and variable conductivity

We consider the inverse problem of determining both the shape and the conductivity of a two-dimensional (2D) conducting scatterer from the knowledge of the far-field pattern of TM waves by solving the ill-posed nonlinear equation. Based on the boundary condition and measured scattered field, a set of nonlinear integral equations is derived and the imaging problem is reformulated into an optimization problem. Satisfactory reconstructions are achieved by the genetic algorithm. Numerical results demonstrate that, even when the initial guess is far away from the exact one, good reconstruction can be obtained. In addition, the effect of Gaussian noise on the reconstruction results is investigated. The numerical results show that multiple incident directions permit good reconstruction of shape and, to a lesser extent, conductivity in the presence of noise in measured data. © 2004 Wiley Periodicals, Inc. Int J RF and Microwave CAE 14, 433–440, 2004.     

Inverse scattering of dielectric cylindrical target using dynamic differential evolution and self‐adaptive dynamic differential evolution

The inverse problem under consideration is to reconstruct the characteristic of scatterer from the scattering E field. Dynamic differential evolution (DDE) and self‐adaptive dynamic differential evolution (SADDE) are stochastic‐type optimization approach that aims to minimize a cost function between measurements and computer‐simulated data. These algorithms are capable of retrieving the location, shape, and permittivity of the dielectric cylinder in a slab medium made of lossless materials. The finite‐difference time‐domain (FDTD) is employed for the analysis of the forward scattering. The comparison is carried out under the same conditions of initial population of candidate solutions and number of iterations. Numerical results indicate that SADDE outperforms the DDE a little in terms of reconstruction accuracy. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2013.     

Electromagnetic scattered field time series from finite difference time domain trained time delay neural network

This paper uses time delay neural network (TDNN) for predicting electromagnetic (EM) fields scattered from dielectric objects (cylinder, cylinder‐hemisphere, and cylinder‐cone) using: (a) FDTD generated initial field data for similar conducting objects and (b) Statistical information for the nature of fields. Statistical data indicated that the scattered field nature is close to deterministic. The TDNN structure determination uses statistical data for fixing the number of delays and tabular technique to obtain the number of hidden neurons. The TDNN training uses the Levenberg‐Marquardt (LM) algorithm. The model outputs follow standard FDTD results closely.     

基于混合粒子群算法的二维导体柱目标识别

从电磁场的积分方程出发,采用矩量法（ＭＯＭ）计算导体柱电磁散射的过程;以实际测量的散射场与计算散射场的偏差程度作为目标函数;将带优化变量设置为描述导体柱轮廓的形状函数的傅里叶展开式系数,通过混合粒子群算法（HPSO）对带优化变量进行优化,使目标函数的最小值用来进行电磁成像。仿真结果表明：HPSO简单、通用,具有较强的抗随机噪声干扰的能力。     

散乱数据拟合的自适应分片逆尺度空间算法

散乱数据拟合(逼近)是在信号处理、计算机图形学等领域中被广泛研究的问题, 近些年,利用优化方法获得散乱数据的稀疏表示逼近解也成为了优化和曲面重构交叉领域的热 点。基于由B 样条生成的PSI 空间中的散乱点曲面拟合问题和分片稀疏的联系,将分片稀疏性 引入到Bregman 逆尺度空间算法(ISS)中,提出一种自适应的分片逆尺度空间(aP_ISS)算法,处 理散乱数据的曲面拟合问题。通过对逆尺度空间系统分片符号一致性分析,得到了自适应分片 逆尺度空间系统的性能保证定理和避免了aP_ISS 参数的选取。应用到散乱点曲面重构问题上 的数值实验结果表明,该算法不仅可以有效拟合曲面,还能够较好保护分片稀疏性。     

Surface Reconstruction Based on Hierarchical Floating Radial Basis Functions

In this paper we address the problem of optimal centre placement for scattered data approximation using radial basis functions (RBFs) by introducing the concept of floating centres. Given an initial least‐squares solution, we optimize the positions and the weights of the RBF centres by minimizing a non‐linear error function. By optimizing the centre positions, we obtain better approximations with a lower number of centres, which improves the numerical stability of the fitting procedure. We combine the non‐linear RBF fitting with a hierarchical domain decomposition technique. This provides a powerful tool for surface reconstruction from oriented point samples. By directly incorporating point normal vectors into the optimization process, we avoid the use of off‐surface points which results in less computational overhead and reduces undesired surface artefacts. We demonstrate that the proposed surface reconstruction technique is as robust as recent methods, which compute the indicator function of the solid described by the point samples. In contrast to indicator function based methods, our method computes a global distance field that can directly be used for shape registration.     

Shape‐from‐Operator: Recovering Shapes from Intrinsic Operators

We formulate the problem of shape‐from‐operator (SfO), recovering an embedding of a mesh from intrinsic operators defined through the discrete metric (edge lengths). Particularly interesting instances of our SfO problem include: shape‐from‐Laplacian, allowing to transfer style between shapes; shape‐from‐difference operator, used to synthesize shape analogies; and shape‐from‐eigenvectors, allowing to generate ‘intrinsic averages’ of shape collections. Numerically, we approach the SfO problem by splitting it into two optimization sub‐problems: metric‐from‐operator (reconstruction of the discrete metric from the intrinsic operator) and embedding‐from‐metric (finding a shape embedding that would realize a given metric, a setting of the multidimensional scaling problem). We study numerical properties of our problem, exemplify it on several applications, and discuss its imitations.     

A Time Domain Point Source Method for Inverse Scattering by Rough Surfaces

In this paper we propose a new method to determine the location and shape of an unbounded rough surface from measurements of scattered electromagnetic waves. The proposed method is based on the point source method of Potthast (IMA J. Appl. Math. 61, 119–140, 1998) for inverse scattering by bounded obstacles. We propose a version for inverse rough surface scattering which can reconstruct the total field when the incident field is not necessarily time harmonic. We present numerical results for the case of a perfectly conducting surface in TE polarization, in which case a homogeneous Dirichlet condition applies on the boundary. The results show great accuracy of reconstruction of the total field and of the prediction of the surface location.     

基于L1/2正则化的三维人体姿态重构

针对从给定2D特征点的单目图像中重构对象的3D形状问题,本文在形状空间模型的基础上,结合L_1/2正则化和谱范数的性质提出一种基于L_1/2正则化的凸松弛方法,将形状空间模型的非凸求解问题通过凸松弛方法转化为凸规划问题;在采用ADMM算法对凸规划问题进行优化求解过程中,提出谱范数近端梯度算法保证解的正交性与稀疏性.利用所提的优化方法,基于形状空间模型和3D可变形状模型在卡内基梅隆大学运动捕获数据库上进行3D人体姿态重构,定性和定量对比实验结果表明本文方法均优于现有的优化方法,验证了所提方法的有效性.     

Data‐Driven Sparse Priors of 3D Shapes

We present a sparse optimization framework for extracting sparse shape priors from a collection of 3D models. Shape priors are defined as point‐set neighborhoods sampled from shape surfaces which convey important information encompassing normals and local shape characterization. A 3D shape model can be considered to be formed with a set of 3D local shape priors, while most of them are likely to have similar geometry. Our key observation is that the local priors extracted from a family of 3D shapes lie in a very low‐dimensional manifold. Consequently, a compact and informative subset of priors can be learned to efficiently encode all shapes of the same family. A comprehensive library of local shape priors is first built with the given collection of 3D models of the same family. We then formulate a global, sparse optimization problem which enforces selecting representative priors while minimizing the reconstruction error. To solve the optimization problem, we design an efficient solver based on the Augmented Lagrangian Multipliers method (ALM). Extensive experiments exhibit the power of our data‐driven sparse priors in elegantly solving several high‐level shape analysis applications and geometry processing tasks, such as shape retrieval, style analysis and symmetry detection.     

Inverse scattering from phaseless data in the freespace

In this paper a new approach for microwave imaging of unknown objects embedded in the freespace from phaseless data is presented. Firstly a cost functional is constructed by using the measured amplitude of the total field, which is the norm of the discrepancy between the measured amplitude and the calculated one. Then both the amplitude and phase of the scattered field are retrieved by minimizing the above cost functional. Finally, the geometrical and electrical parameters are reconstructed by using the retrieved scattered field. The phase retrieval process can be achieved in a very short time without adding any burden to the whole inverse scattering problem. The equivalent current density is introduced to reduce the nonlinearity of the inverse problem. The reconstruction of the non-radiating component of the equivalent current density improves the imaging quality. Experimental results are presented for the first time to show the feasibility of inverse scattering from phaseless data. The experimental results also show the validity and stability of the proposed method. Supported by the National Natural Science Foundation of China (Grant Nos. 60701010, 40774093), and the Knowledge Innovation Program of Chinese Academy of Sciences     

Divergence‐Free Shape Correspondence by Deformation

We present a novel approach for solving the correspondence problem between a given pair of input shapes with non‐rigid, nearly isometric pose difference. Our method alternates between calculating a deformation field and a sparse correspondence. The deformation field is constructed with a low rank Fourier basis which allows for a compact representation. Furthermore, we restrict the deformation fields to be divergence‐free which makes our morphings volume preserving. This can be used to extract a correspondence between the inputs by deforming one of them along the deformation field using a second order Runge‐Kutta method and resulting in an alignment of the inputs. The advantages of using our basis are that there is no need to discretize the embedding space and the deformation is volume preserving. The optimization of the deformation field is done efficiently using only a subsampling of the orginal shapes but the correspondence can be extracted for any mesh resolution with close to linear increase in runtime. We show 3D correspondence results on several known data sets and examples of natural intermediate shape sequences that appear as a by‐product of our method.     

柔性结构形态重构的感知网络优化配置研究

以航天结构健康监测为研究背景,针对柔性板状结构形态重构的感知网络进行优化配置研究.在基于应变模态的结构形态重构算法中,以应变位移转换矩阵的条件数作为传感器优化配置的优化准则,以结构形态重构误差作为优化效果评价指标,采用一种改进的模拟退火算法对传感器优化配置进行了研究.针对传感器优化配置中的传感器数量、位置、方向以及多个目标的综合进行了传感器配置优化设计,仿真结果显示通过传感器配置的优化设计,可以有效地提高柔性结构的形态重构效果.最后,通过实验验证了传感器优化配置的有效性,为结构形态重构的感知网络优化配置提供了一定的理论依据.     

散乱数据点集曲线重构的最短路逼近算法

给出了散乱数据点集曲线重构的最短路逼近算法．算法根据数据点的分布构造带权连通图,通过求解带权连通图的最短路径,将散乱数据点集的曲线重构问题转化为有序数据点集的曲线重构问题．算法可以对单连通、多连通和封闭的数据点集进行重构．重构曲线较好地保持了数据点集的形状和走向,尤其是带尖点的数据点集的形状特征．最后给出不同拓扑结构的数据点集的重构曲线实例．     

Space–time blending

Shape transformation between objects of different topology and positions in space is an open modelling problem. We propose a new approach to solving this problem for two given 2D or 3D shapes. The key steps of the proposed algorithm are: increase dimension by converting two input kD shapes into half‐cylinders in (k+1)D space–time, applying bounded blending with added material to the half‐cylinders, and making cross‐sections for getting intermediate shapes under the transformation. The additional dimension is considered as a time coordinate for making animation. We use the bounded blending set operations in space–time defined using R‐functions and displacement functions with the localized area of influence applied to the functionally defined half‐cylinders. The proposed approach is general enough to handle input shapes with arbitrary topology defined as polygonal objects with holes and disjoint components, set‐theoretic objects, or analytically defined implicit surfaces. The obtained unusual amoeba‐like behaviour of the shape combines metamorphosis with the non‐linear motion. Copyright © 2004 John Wiley & Sons, Ltd.     

Real‐Time Symmetry‐Preserving Deformation

In this paper, we address the problem of structure‐aware shape deformation: We specifically consider deformations that preserve symmetries of the shape being edited. While this is an elegant approach for obtaining plausible shape variations from minimal assumptions, a straightforward optimization is numerically expensive and poorly conditioned. Our paper introduces an explicit construction of bases of linear spaces of shape deformations that exactly preserve symmetries for any user‐defined level of detail. This permits the construction of low‐dimensional spaces of low‐frequency deformations that preserve the symmetries. We obtain substantial speed‐ups over alternative approaches for symmetry‐preserving shape editing due to (i) the sub‐space approach, which permits low‐res editing, (ii) the removal of redundant, symmetric information, and (iii) the simplification of the numerical formulation due to hard‐coded symmetry preservation. We demonstrate the utility in practice by applying our framework to symmetry‐preserving co‐rotated iterative Laplace surface editing of models with complex symmetry structure, including partial and nested symmetry.