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.     

A Multibody Factorization Method for Independently Moving Objects

The structure-from-motion problem has been extensively studied in the field of computer vision. Yet, the bulk of the existing work assumes that the scene contains only a single moving object. The more realistic case where an unknown number of objects move in the scene has received little attention, especially for its theoretical treatment. In this paper we present a new method for separating and recovering the motion and shape of multiple independently moving objects in a sequence of images. The method does not require prior knowledge of the number of objects, nor is dependent on any grouping of features into an object at the image level. For this purpose, we introduce a mathematical construct of object shapes, called the shape interaction matrix, which is invariant to both the object motions and the selection of coordinate systems. This invariant structure is computable solely from the observed trajectories of image features without grouping them into individual objects. Once the matrix is computed, it allows for segmenting features into objects by the process of transforming it into a canonical form, as well as recovering the shape and motion of each object. The theory works under a broad set of projection models (scaled orthography, paraperspective and affine) but they must be linear, so it excludes projective cameras.     

A Simple Prior-Free Method for Non-rigid Structure-from-Motion Factorization

This paper proposes a simple “prior-free” method for solving the non-rigid structure-from-motion (NRSfM) factorization problem. Other than using the fundamental low-order linear combination model assumption, our method does not assume any extra prior knowledge either about the non-rigid structure or about the camera motions. Yet, it works effectively and reliably, producing optimal results, and not suffering from the inherent basis ambiguity issue which plagued most conventional NRSfM factorization methods. Our method is very simple to implement, which involves solving a very small SDP (semi-definite programming) of fixed size, and a nuclear-norm minimization problem. We also present theoretical analysis on the uniqueness and the relaxation gap of our solutions. Extensive experiments on both synthetic and real motion capture data (assuming following the low-order linear combination model) are conducted, which demonstrate that our method indeed outperforms most of the existing non-rigid factorization methods. This work offers not only new theoretical insight, but also a practical, everyday solution to NRSfM.     

一种隐式曲面交互调整的新方法

提出了一种对隐式曲面形状进行交互调整的新方法,为隐式曲面的调整提供了两种交互工具,分别是对曲面上点的位置调整和法向调整.该方法以调整后的位置和法向为新曲面的插值条件建立目标函数,极小化该目标函数求解曲面参数的变化量,从而确定新的隐式曲面.文中采用拟牛顿法和序列二次规划法(SQP)求解该非线性优化问题.在调整过程中用粒子的方法对隐式曲面进行绘制,实现了对隐式曲面形状的实时交互调整.最后用实例说明了新方法的有效性.     

A Discontinuous Galerkin Method for the Subjective Surfaces Problem

The work formulates and evaluates the local discontinuous Galerkin method for the subjective surfaces problem based on the curvature driven level set equation. A new mixed formulation simplifying the treatment of nonlinearities is proposed. The numerical algorithm is evaluated using several artificial and realistic test cases.     

基于投影梯度法的非负矩阵分解稀疏算法

文章提出了一种基于投影梯度法的非负矩阵分解稀疏算法,该算法通过引入基于投影梯度的迭代方法,来解决加向量1-范数约束以及加向量2-范数约束的非负矩阵分解问题,得到了局部最优解。通过实验表明该算法在分解时间以及基矩阵的稀疏度表达能力上优于NMF算法和SNMF算法。     

High-Order Mixed Current Basis Functions for Electromagnetic Scattering of Curved Surfaces

We construct high-order mixed current vector basis (unctions on an arbitrary curved surface which can be subdivided as a union of curved triangles and quadrilaterals. The objective is to construct vector basis (a) which consists of high-order polynomials of the surface parameterization variables on triangles and quadrilaterals, (b) part of the basis will have vanishing moments on the triangles and quadrilaterals. The first property will enable us to represent the current distribution over scatter surface with much less number of unknowns and larger patches of either triangular or quadrilateral shapes. The second property will achieve what wavelet basis does on an interval, but on a more general domain, namely, a sparse matrix representation for some integral operators.     

A Parallel Elimination Method for "Periodic" Tridiagonal Systems

We extend the elimination method of Chawla and Khazal [1] to uncouple partitioned blocks of "periodic" tridiagonal linear systems. At each step of the elimination stage, we now need three simultaneous eliminations: within each block, one usual forward elimination and one backward elimination from across the succeeding block, and one elimination in the last row of the last block. An interesting feature of the present elimination procedure is that at the end of it, the property of periodicity of the original system is now passed on to the core system . Once the core system is solved, the blocks uncouple and the solution is obtained in parallel from each block by back substitution. For a system of size N , the classical elimination has an arithmetical operations count of 17N . A best serial algorithm, based on the Sherman-Morrison formula, has an operations count of 0 14N . The present parallel elimination algorithm, employing p partition blocks, has an operations count of O 17N p and, in comparison with the Sherman-Morrison algorithm, it can achieve an efficiency of nearly 82% on a p -processor machine.     

A Semi‐Lagrangian Closest Point Method for Deforming Surfaces

We present an Eulerian method for the real‐time simulation of intrinsic fluid dynamics effects on deforming surfaces. Our method is based on a novel semi‐Lagrangian closest point method for the solution of partial differential equations on animated triangle meshes. We describe this method and demonstrate its use to compute and visualize flow and wave propagation along such meshes at high resolution and speed. Underlying our technique is the efficient conversion of an animated triangle mesh into a time‐dependent implicit representation based on closest surface points. The proposed technique is unconditionally stable with respect to the surface deformation and, in contrast to comparable Lagrangian techniques, its precision does not depend on the level of detail of the surface triangulation.     

A High-Order Kernel Method for Diffusion and Reaction-Diffusion Equations on Surfaces

In this paper we present a high-order kernel method for numerically solving diffusion and reaction-diffusion partial differential equations (PDEs) on smooth, closed surfaces embedded in $\mathbb{R }^d$ . For two-dimensional surfaces embedded in $\mathbb{R }^3$ , these types of problems have received growing interest in biology, chemistry, and computer graphics to model such things as diffusion of chemicals on biological cells or membranes, pattern formations in biology, nonlinear chemical oscillators in excitable media, and texture mappings. Our kernel method is based on radial basis functions and uses a semi-discrete approach (or the method-of-lines) in which the surface derivative operators that appear in the PDEs are approximated using collocation. The method only requires nodes at “scattered” locations on the surface and the corresponding normal vectors to the surface. Additionally, it does not rely on any surface-based metrics and avoids any intrinsic coordinate systems, and thus does not suffer from any coordinate distortions or singularities. We provide error estimates for the kernel-based approximate surface derivative operators and numerically study the accuracy and stability of the method. Applications to different non-linear systems of PDEs that arise in biology and chemistry are also presented.     

A Practical Method for High‐Resolution Embedded Liquid Surfaces

Combining high‐resolution level set surface tracking with lower resolution physics is an inexpensive method for achieving highly detailed liquid animations. Unfortunately, the inherent resolution mismatch introduces several types of disturbing visual artifacts. We identify the primary sources of these artifacts and present simple, efficient, and practical solutions to address them. First, we propose an unconditionally stable filtering method that selectively removes sub‐grid surface artifacts not seen by the fluid physics, while preserving fine detail in dynamic splashing regions. It provides comparable results to recent error‐correction techniques at lower cost, without substepping, and with better scaling behavior. Second, we show how a modified narrow‐band scheme can ensure accurate free surface boundary conditions in the presence of large resolution mismatches. Our scheme preserves the efficiency of the narrow‐band methodology, while eliminating objectionable stairstep artifacts observed in prior work. Third, we demonstrate that the use of linear interpolation of velocity during advection of the high‐resolution level set surface is responsible for visible grid‐aligned kinks; we therefore advocate higher‐order velocity interpolation, and show that it dramatically reduces this artifact. While these three contributions are orthogonal, our results demonstrate that taken together they efficiently address the dominant sources of visual artifacts arising with high‐resolution embedded liquid surfaces; the proposed approach offers improved visual quality, a straightforward implementation, and substantially greater scalability than competing methods.     

Doo-Sabin曲面NC刀具的并行轨迹计算

Doo—Sabin曲面是对多边形控制网格进行递归细分的极限曲面．利用Doo—Sabin曲面具有的逐步逼近的多分辨率特性和误差公式,根据加工误差确定控制网格的细分次数,并以此代替目标曲面进行粗加工刀具轨迹计算,从而合理简化了加工细节,提高了粗加工效率．另外,改进了传统的G—Buffer技术,提出了能统一应用于大型工件粗加工和精加工的S—Buffer算法．进一步分析了S—Buffer数据的相关性,采用平均加权响应时间为性能指标,设计了抢先式的动态负载平衡策略,基于MPI实现了S—Buffer的并行化．     

移动机器人全覆盖路径规划优化方法

从全局优化的角度出发,提出一种基于子区域分割的环境建模方法,将各个子区域缩成节点、子区域重心间距离缩成节点间连线,建立起含障区域的全连通图——广义距离矩阵模型,对Hopfield神经网络求解旅行商问题的动态规划方法进行改进后,将其用于求该模型的最优有向连通图。机器人沿最短路径完成覆盖,就是按最优顺序走过连通图中所有节点并依次覆盖各节点所代表的子区域,从而完成移动机器人在含障区域内的全覆盖路径规划问题的优化解决方案。     

A FPGA-Based Systolic Array Prototype Implementing the Quadrant Interlocking Factorization Method

The systolic processing offers the possibility of solving a large number of standard problems on multicellular computing devices with autonomous cells (Processing Elements—PEs). The resulting systolic arrays exploit the underlying parallelism of many computationally intensive problems and offer a vital and effective way of handling them. Advances in technology and especially in VLSI and FPGA have an ongoing contribution to the evolution of systolic arrays. Herein, a FPGA-based Systolic array prototype implementing the Factorization stage of the Quadrant Interlocking Factorization—QIF (Butterfly) method is presented and the corresponding time-complexities achieved are discussed.     

非正弦周期函数的谐波分析的一种简捷方法

谐波分析是研究非正弦周期函数的重点之一,在数学理论上通过傅里叶变换可以求出周期函数的各次谐波,但是在工程实际中是很难获得非正弦周期函数的解析式,或者函数的解析式过于复杂不便于求积分,因此也就无法直接应用傅里叶变换。通过对畸变周期函数的波形进行等分采样获取数据序列,再以简短的三句指令对序列进行换算,获得畸变函数的各次谐波的幅值,结果证明了该方法能够简捷有效地进行非正弦周期函数的谐波分析。     

电磁逆散射成像的一种混合正则化方法

电磁逆散射成像问题数值求解中,非线性逆散射方程及其对应的离散方程组具有明显的不适定性,针对求解通常所用Tikhonov正则化方法的参数选择在先验选取时缺乏有效的误差信息,而后验选取时需要更多计算量求解有关参数的方程的困难,本文中将小参数Tikhonov正则化方法与共轭梯度法结合,提出了不适定方程组的混合正则化方法。数据仿真表明,该方法既可保证正则化效果,也减少了计算量。     

A Computer Vision Method for 3D Reconstruction of Curves-Marked Free-Form Surfaces

Visual method is now broadly used in reverse engineering for 3D reconstruction. The traditional computer vision methods are feature-based, i.e., they require that the objects must reveal features owing to geometry or textures. For textureless free-form surfaces, dense feature points are added artificially. In this paper, a new method is put forward combining computer vision with CAGD. The surface is subdivided into N-side Gregory patches using marked curves, and a stereo algorithm is used to reconstruct the curves. Then, the cross boundary tangent vector is computed through reflectance analysis. At last, the whole surface can be reconstructed by jointing these patches with 1Gcontinuity.     

一种基于周期能量的基音检测方法

文章对语音信号的能量呈现周期性变化的现象进行了研究,提出了一种基于周期能量变化的基音检测方法。采用一个长帧语音信号平均能量作为基准参考能量,用一个短帧语音信号平均能量来表示瞬时能量。由二者可算出瞬时能量测度(InstantEnergyMeasure,IEM)序列。对瞬时能量测度序列进行自相关计算后,得到基音周期。实验分析表明,该方法在干净和噪声环境下,基音周期提取和清浊判决具有令人满意的效果。