基于多结点样条磨光函数的几何迭代法

几何迭代法在计算机辅助几何设计(CAGD)中有广泛地应用,为了提高传统的 B-样 条曲线插值在几何迭代中的收敛速度和迭代精度,提出了基于多结点样条磨光函数的几何迭代 法,引入多结点样条磨光函数,在曲线拟合时把多结点样条磨光方法和几何迭代方法结合,经过 磨光和迭代,在 L-BFGS 迭代算法的最优解下构造具有高逼近性的曲线拟合方法。实验结果表明, 在相同精度下,该方法不仅减少了迭代次数,且提高了迭代速度,可以用于飞机、汽车等外形设 计上,亦可用于文物、房屋等外形重构和重建,以及卫星图形图像的处理中。     

A new fast multipole boundary element method for two dimensional acoustic problems

A new fast multipole boundary element method (BEM) is presented in this paper for solving large-scale two dimensional (2D) acoustic problems based on the improved Burton–Miller formulation. This algorithm has several important improvements. The fast multipole BEM employs the improved Burton–Miller formulation, and successfully overcomes the non-uniqueness difficulty associated with the conventional BEM for exterior acoustic problems. The improved Burton–Miller formulation contains only weakly singular integrals, and avoids the numerical difficulties associated to the evaluation of the hypersingular integral, it leads to the numerical implementations more efficient and straightforward. Furthermore, the fast multipole method (FMM) and the approximate inverse preconditioned generalized minimum residual method (GMRES) iterative solver are adopted to greatly improve the overall computational efficiency. The numerical examples with Neumann boundary conditions are presented that clearly demonstrate the accuracy and efficiency of the developed fast multipole BEM for solving large-scale 2D acoustic problems in a wide range of frequencies.     

Application of rational function approximation technique to hybrid FE/BI/MLFMA for 3D scattering

In this article, the rational function approximation technique (RFAT) is applied to the hybrid finite‐element/boundary‐integral/multilevel fast multipole algorithm (FE/BI/MLFMA) to acquire wide‐band and wide‐angle backscatter radar‐cross‐section (RCS) by complex targets. The two approaches of using the rational function approximation technique, asymptotic waveform evaluation (AWE) and model‐based parameter estimation (MBPE), both have been investigated and compared by theoretical analysis and numerical experiments. The numerical results acquired by the developed computing algorithm of integrating the hybrid FE/BI/MLFMA with the RFAT are presented in the article, demonstrating that the rational function approximation technique can greatly speed up the hybrid FE/BI/MLFMA to acquire wide‐band and wide‐angle backscatter RCS by complex targets. © 2007 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2007.     

Multi-resolution analysis on the interval with natural spline projection and uniform two-scale relation

The aim of this paper is to present a modification to the Chui and Quak (1992) spline multiresolution analysis for the finite interval. Boundary scaling functions with multipole nodes at interval endpoints are rejected, in favor of the classical B-spline scaling function restricted to the interval. This necessitates derivation of revised boundary wavelets. In addition, a direct method of decomposition results in bandwidth reduction on solving some associated linear systems, and image distortion is reduced by employing natural spline projection. Finally, a hybrid projection scheme is proposed, which particularly for large systems further lowers operation count. Numerical experiments proving the algorithm are indicated.     

低码率图像的快速SV拟合及其最优码流结构的描述方法

给出了一个在低码率图像描述中应用最优支持向量(SV)描述的编码算法,提出一个训练样本集缩减策略,在支持向量机(SVM)模型中用于快速拟合重要的交流(AC)系数,它能够在基本保持原有精度的前提下,有效地提高SVM的回归速度,减少输出参数;提出了直流(DC)系数的按位差分预测编码方法和压缩性能更好的码流产生方法。实验结果表明,该方法不仅缩减了编码时间,而且在相同码率下能获得更好的图像质量。以往基于SV的编码未提及码流结构的描述方法,而快速SV拟合和数据组织方法克服了以往算法可行性差的缺点。     

双天线测向信息辅助捷联惯导快速对准算法

为解决捷联惯导的快速高精度对准问题,给出了一种双天线测向信息辅助的惯导快速对准算法.介绍了双天线测向的基本原理,在此基础上给出了双天线基线安装误差的补偿方法.基于速度、位置、航向观测量,设计了快速对准卡尔曼滤波器,给出了具体航向量测方程.根据实测双天线测向误差特性进行了仿真分析.仿真结果验证了方法的有效性,4 min航...     

Multipole-accelerated capacitance computation for 3-D structures in a stratified dielectric medium using a closed-form Green's function

In this article, the capacitance matrices of three-dimensional conducting structures embedded in a stratified dielectric medium are computed by using the fast muitipole method in conjunction with a closed-form approximation of the appropriate Green's function. Image charges that result from the employment of this Green's function are incorporated into the fast multipole method. This technique is used to accelerate the iterative generalized minimal residual-based solution of the system of equations generated by the method of moments. This yields the charge distributions on the conductors and thereby the required capacitance matrix. It is shown that the use of this technique typically results in a speedup of more than an order of magnitude over iterative and direct methods without a compromise of the numerical accuracy.     

Knot calculation for spline fitting via sparse optimization

Curve fitting with splines is a fundamental problem in computer-aided design and engineering. However, how to choose the number of knots and how to place the knots in spline fitting remain a difficult issue. This paper presents a framework for computing knots (including the number and positions) in curve fitting based on a sparse optimization model. The framework consists of two steps: first, from a dense initial knot vector, a set of active knots is selected at which certain order derivative of the spline is discontinuous by solving a sparse optimization problem; second, we further remove redundant knots and adjust the positions of active knots to obtain the final knot vector. Our experiments show that the approximation spline curve obtained by our approach has less number of knots compared to existing methods. Particularly, when the data points are sampled dense enough from a spline, our algorithm can recover the ground truth knot vector and reproduce the spline.     

基于四次B样条的曲线逼近算法

考虑到插值算法增减节点困难,传统逼近算法精度不够等缺点,有文献提出一种基于三次B样条的曲线逼近算法。该算法通过迭代逼近,提高了计算速度与精度。在系统研究此算法的基础上,将该算法推广到四次B样条,使其具有三阶可导性,并给出该算法收敛性的理论证明。最后用该算法对常用函数进行逼近效果实验。结果表明,所提出的四次B样条的曲线逼近算法收敛速度更快,且能够满足更高精度的实际工业生产需要。     

图像插值的多结点样条技术

为了获得质量更好的插值图像,提出了用具有紧支集的多结点样条基函数来进行图像插值的新技术,并首先将1维的多结点样条插值算法推广到2维,建立了用于图像数据的插值公式;然后分析了多结点样条插值方法的逼近精度、正则性、插值核函数的频域特性.对逼近精度、正则性、插值核函数频域特性的比较表明,该插值方法优于传统的三次卷积插值方法,实验结果也证实了用多结点样条插值算法重建的图像具有更高的质量.     

BH算法的几点注记

N-Body问题的直接计算方法的时间复杂度是O（n2）,BH算法的时间复杂度为O（nlogn）.BH算法利用质心近似计算降低了时间复杂度,但同时也降低了计算结果的准确度.为把与判断足够远的参数θ（θ=l/d）密切相关的计算结果的近似准确度控制在要求的范围内,应用多极扩展和Gauss数值积分方法给出了BH算法质心近似的数学解释以及误差ε与参数θ的关系,得出BH算法是FMM算法和Gauss数值积分的一个特例,并指出Gauss积分法中隐含的正交多项式较FMM中常用的chebyshev正交多项式更与求解的问题相关.     

离散Fourier变换并行算法综述

本文详细介绍了1－D DFT精确计算的六步框架并行算法和按位并行计算法,以及按位计算法在2－D Mesh和Torus上的模拟实现,同时介绍了近似计算中的基于奇异值分解的算法和基于快速多极方法的算法。对于2－D DFT,本文介绍了并行行列算法和并行多项式变换算法,并分析了其优缺点。     

Real-time stereo using approximated joint bilateral filtering and dynamic programming

We present a stereo algorithm that is capable of estimating scene depth information with high accuracy and in real time. The key idea is to employ an adaptive cost-volume filtering stage in a dynamic programming optimization framework. The per-pixel matching costs are aggregated via a separable implementation of the bilateral filtering technique. Our separable approximation offers comparable edge-preserving filtering capability and leads to a significant reduction in computational complexity compared to the traditional 2D filter. This cost aggregation step resolves the disparity inconsistency between scanlines, which are the typical problem for conventional dynamic programming based stereo approaches. Our algorithm is driven by two design goals: real-time performance and high accuracy depth estimation. For computational efficiency, we utilize the vector processing capability and parallelism in commodity graphics hardware to speed up this aggregation process over two orders of magnitude. Over 90 million disparity evaluations per second [the number of disparity evaluations per seconds (MDE/s) corresponds to the product of the number of pixels and the disparity range and the obtained frame rate and, therefore, captures the performance of a stereo algorithm in a single number] are achieved in our current implementation. In terms of quality, quantitative evaluation using data sets with ground truth disparities shows that our approach is one of the state-of-the-art real-time stereo algorithms.     

Fast Evaluation of the Room Transfer Function Using Multipole Expansion

Reverberation in rooms is often simulated with the image method due to Allen and Berkley (1979). This method has an asymptotic complexity that is cubic in terms of the simulated reverberation length. When employed in the frequency domain, it is relatively computationally expensive if there are many receivers in the room or if the source or receiver positions are changing with time. The computational complexity of the image method is due to the repeated summation of the fields generated by a large number of image sources. In this paper, a fast method to perform such summations is presented. The method is based on multipole expansion of the monopole source potential. For offline computation of the room transfer function for N image sources and M receiver points, use of the Allen-Berkley algorithm requires O(NM) operations, whereas use of the proposed method requires only O(N+M) operations, resulting in significantly faster computation of reverberant sound fields. The proposed method also has a considerable speed advantage in situations where the room transfer function must be rapidly updated online in response to source/receiver location changes. Simulation results are presented, and algorithm accuracy, speed, and implementation details are discussed. For problems that require frequency-domain computations, the algorithm is found to generate sound fields identical to the ones obtained with the frequency-domain version of the Allen-Berkley algorithm at a fraction of computational cost     

模拟电路故障诊断新方法

提出了一种新颖的基于多小波神经网络的模拟电路故障诊断方法。介绍了多小波的原理,分析了多小波神经网络的结构、逼近性质及多小波神经网络的算法,提出了用多小波来处理故障信号,提取故障特征向量输入给神经网络,从而进行模拟电路故障诊断。由于多小波函数具有连续、对称性及支撑集短等一系列优点,所以用多小波神经网络来进行模拟电路故障诊断比一般的小波神经网络具有诊断精度高、诊断速度快的优点。给出了仿真诊断实例,验证了该方法的有效性。     

粗糙集和支持向量机的表具识别算法研究

针对量子粒子群算法具有陷入局部值缺点,提出了一种基于改进量子粒子群算法优化的粗糙集和支持向量机相结合的表具识别算法,引入人工蜂群算法和免疫算法,来提高算法搜索空间、收敛速度。首先通过改进量子粒子群算法优化的粗糙集对得到的特征向量进行属性约简,然后经过改进量子粒子群算法优化支持向量机参数。最后通过实验仿真表明,改进的算法能有效地减少决策属性的个数,提高了粗糙集属性约简能力,优化了支持向量机的参数,算法收敛速度快,识别准确率高。     

Fast high-quality volume ray-casting with virtual samplings

Volume ray-casting with a higher order reconstruction filter and/or a higher sampling rate has been adopted in direct volume rendering frameworks to provide a smooth reconstruction of the volume scalar and/or to reduce artifacts when the combined frequency of the volume and transfer function is high. While it enables high-quality volume rendering, it cannot support interactive rendering due to its high computational cost. In this paper, we propose a fast high-quality volume ray-casting algorithm which effectively increases the sampling rate. While a ray traverses the volume, intensity values are uniformly reconstructed using a high-order convolution filter. Additional samplings, referred to as virtual samplings, are carried out within a ray segment from a cubic spline curve interpolating those uniformly reconstructed intensities. These virtual samplings are performed by evaluating the polynomial function of the cubic spline curve via simple arithmetic operations. The min max blocks are refined accordingly for accurate empty space skipping in the proposed method. Experimental results demonstrate that the proposed algorithm, also exploiting fast cubic texture filtering supported by programmable GPUs, offers renderings as good as a conventional ray-casting algorithm using high-order reconstruction filtering at the same sampling rate, while delivering 2.5x to 3.3x rendering speed-up.     

半透明物体的PRT绘制算法

将传统的PRT(Pre-com puted Radiance Transfer)算法应用到半透明的物体上,提出了一种在任意复杂的环境光条件下使用非线性小波绘制半透明物体的快速算法。算法首先对场景中的每一个顶点计算一个转换向量,并且对每一个向量进行小波变换,保存量化后的小波系数;然后用相同的小波基对给定的环境光做小波变换,只保留其中绝对值较大的系数,从而得到环境光的非线性逼近。文章的算法可以将绘制物体的复杂的积分运算简化为N个稀疏向量间的乘积(N是场景中顶点的数目),从而达到实时的绘制速度。论文通过实验验证了算法的有效性。     

Fast additive quantization for vector compression in nearest neighbor search

Vector quantization has been widely employed in nearest neighbor search because it can approximate the Euclidean distance of two vectors with the table look-up way that can be precomputed. Additive quantization (AQ) algorithm validated that low approximation error can be achieved by representing each input vector with a sum of dependent codewords, each of which is from its own codebook. However, the AQ algorithm relies on computational expensive beam search algorithm to encode each vector, which is prohibitive for the efficiency of the approximate nearest neighbor search. In this paper, we propose a fast AQ algorithm that significantly accelerates the encoding phase. We formulate the beam search algorithm as an optimization of codebook selection orders. According to the optimal order, we learn the codebooks with hierarchical construction, in which the search width can be set very small. Specifically, the codewords are firstly exchanged into proper codebooks by the indexed frequency in each step. Then the codebooks are updated successively to adapt the quantization residual of previous quantization level. In coding phase, the vectors are compressed with learned codebooks via the best order, where the search range is considerably reduced. The proposed method achieves almost the same performance as AQ, while the speed for the vector encoding phase can be accelerated dozens of times. The experiments are implemented on two benchmark datasets and the results verify our conclusion.     

基于局部特征过滤的快速火焰图像识别方法

传统的基于物理信号的火焰识别方法易被外部环境干扰,且现有火焰图像特征提取方法对于火焰和场景的区分度较低,从而导致火焰种类或场景改变时识别精度降低。针对这一问题,提出一种基于局部特征过滤和极限学习机的快速火焰识别方法,将颜色空间信息引入尺度不变特征变换（SIFT）算法。首先,将视频文件转化成帧图像,利用SIFT算法对所有图像提取特征描述符;其次,通过火焰在颜色空间上的信息特性进一步过滤局部噪声特征点,并借助关键点词袋（BOK）方法,将特征描述符转换成对应的特征向量;最后放入极限学习机进行训练,从而快速得到火焰识别模型。在火焰公开数据集及真实火灾场景图像进行的实验结果表明：所提方法对不同场景和火焰类型均具有较高的识别率和较快的检测速度,实验识别精度达97%以上;对于包含4301张图片数据的测试集,模型识别时间仅需2.19 s;与基于信息熵、纹理特征、火焰蔓延率的支持向量机模型,基于SIFT、火焰颜色空间特性的支持向量机模型,基于SIFT的极限学习机模型三种方法相比,所提方法在测试集精度、模型构建时间上均占有优势。