基于傅里叶变换轮廓术的钢轨三维面型复原

随着现代化轨道交通的飞速发展,在线非接触式检测技术已成为钢轨面型检测的趋势.本文基于傅里叶变换轮廓术（FTP）提出实现钢轨的三维面型复原的新方法.通过生成虚拟光栅,再将其投影在被测钢轨上,得到被测钢轨的变形光场图.再由滤波和相位展开等步骤成功恢复出被测钢轨的三维面型,为控制钢轨的外形尺寸,提高外观质量提供了新的方法.     

2维载频条纹2维窗口傅里叶变换轮廓术

为了解决3维形貌测量中单一频率光栅条纹的测量信息少、1维双频光栅两个同方向载频容易产生频率混叠及两个载频条纹测量精度不同、连续相位解包法在复杂物体相位解包所存在的问题,提出采用2维网格光栅作为空间载频光栅条纹联合2维窗口傅里叶变换的傅里叶变换轮廓术。两个载频相互垂直,减少可能的频谱混叠;应用2维窗口傅里叶变换进行频谱分析和设计带宽自动调整的滤波器分离出两个1维变形光栅条纹,在一幅变形网格光栅图像中得到两个方向光栅各自所对应的包裹相位分布;并且应用查表法解包得到真实调制相位分布。与1维单频和1维双频比较,这种技术可以获得两倍相同精度的测量信息,并能对复杂物体的相位分布进行解包。给出了详细的理论推导、计算机模拟和实验结果,证实了该方法的可行性。     

基于FPGA的位相测量轮廓术设计与实现

在介绍位相测量轮廓术原理的基础上,提出了基于FPGA的位相测量轮廓术的设计方法;由LCD投影仪、CCD摄像头、FPGA开发板(DE2)等组成硬件装置,研究PMP系统定标的数学模型,提出了直接定标的方法,得出高度和相位之间的映射关系,并且研究了相位展开算法和光栅图像的投影、采集及预处理方法,最后对三维物体的重建方法进行了讨论;该系统实现了同时控制投影和采集光栅图像,具有系统标定、图像处理和分析等多种功能。     

利用傅里叶变换边缘曲线法进行W型轮廓的快速匹配

W型轮廓标靶是一种用于汽车四轮定位的定位标靶,在一幅定位图像中能够快速地检索出与其一致的目标轮廓非常重要。传统的Hu矩、成对几何直方图算法运算速度慢,鲁棒性差。而一些适用于商标图像检索的傅里叶描述子却可以很好地适用于快速轮廓匹配,但是由于在一幅图像中进行目标轮廓的检索引入了过多的轮廓干扰,因此利用形状图像的傅里叶变换提取出轮廓的频谱特征,通过检查目标轮廓对模板轮廓频谱特征的干扰性大小来进行轮廓的相似性度量,并进行算法简化,从而达到轮廓快速匹配的目的。并且其抗干扰能力强,轮廓查找效率高。这说明利用傅里叶变换边缘曲线法进行轮廓形状匹配具有很好的适用性。     

一种三维快速傅里叶变换并行算法

三维快速傅里叶变换在物理计算领域中被广泛地使用.传统并行算法所使用的面划分和块划分方法并不适合稀疏三维向量的傅里叶变换.提出了一种新三维快速傅里叶变换的并行算法,针对稀疏三维向量的傅里叶变换,新算法通过重新调整x,Y,z三个方向的计算顺序,能最大限度地减少计算量以及进程间的通信量,从而减少计算时间,提高并行加速比.详尽的理论分析以及多个高性能计算平台上的实验结果证明:在对稀疏三维向量作傅里叶变换时,新算法优于传统算法.     

基于连续傅里叶变换计算离散傅里叶变换的一种算法

介绍一种利用连续信号的傅里叶变换计算离散序列离散傅里叶变换的算法,给出了这种算法的应用实例,并对此算法的有效性进行了验证.     

基于改进的离散傅里叶变换图像分割算法研究

研究图像分割特征提取优化问题。由于外界信号噪声等问题而引起图像分割分辨率低,清晰度不高,提取图像的主要特征目标是图像分割中关键的技术,针对传统的图像特征提取分割算法无法完成对图像关键特征信息适度提取,另外图像分割计算复杂,为了有效的对图像进行分割,提出了一种改进的离散傅里叶变换的图像分割算法。采用傅里叶变换算法对图像中感兴趣的区域进行分割出来后,对各个分割区域特点进行描述并组成一定的结构,从而获得最优图像分割结果。仿真结果表明,改进的算法可以有效地提取复杂图像区域中的特征信息,分割效果明显,提高了图像分割的分辨率和清晰度。     

基于两重快速傅里叶变换的三维芯片热仿真

为了解决三维芯片设计中的发热问题,针对三维芯片物理模型提出一种快速、准确的热仿真方法.该方法基于三维有限差分法,利用嵌套的两重快速傅里叶变换对有限差分方程进行求解,从而得到芯片温度分布;通过矩阵的特征值分解与快速傅里叶变换,使得只需求解一系列小规模的三对角线性方程组,即可在不损失精度的前提下有效地提升计算速度.数值实验结果表明,文中方法比稀疏矩阵直接求解算法快几十倍,并且由于占用内存少,能有效地求解变量数多达6×107的三维芯片热仿真问题;该方法具有O(nlogn)的时间复杂度与O(n)的空间复杂度,其中n为离散变量数.     

基于傅里叶变换的红外热波图像拼接*

红外热波无损检测中,红外热波空间序列图像间的变化主要是位移和小幅度旋转。针对该特点,在可能的旋转角度范围内,利用傅里叶变换的相位相关技术判定旋转的角度和平移量,实现图像的配准,然后实现图像的拼接。实验结果表明,该方法能够对重叠面积较小的图像序列实现快速拼接。     

基于轮廓端点的一维快速傅里叶变换图形识别

模式识别和机器学习在实际应用中的领域已经越来越广泛,其中图形识别部分十分适合用于算量软件中对柱等异形构件的识别处理计算。2-范数描述子计算简单,易于理解,但是采点数目要求较大,点数少时在实际应用中发挥的作用有限。一维离散快速傅里叶变换有一定的旋转不变性,计算效率和识别效果更理想。轮廓特征与其它特征表示相比更容易获取、计算,配合实际数据特点通常能起到较理想的效果。在对轮廓特征的处理中,取轮廓点时,一般都是按等步长取点,容易错过拐点（轮廓端点）。     

基于IBM量子计算云服务的量子傅里叶变换实现

Shor算法能够相对经典大整数分解算法实现指数加速,从而直接威胁到了RSA密码体制,而量子傅里叶变换是Shor算法中的一个关键变换,也能够相对经典离散傅里叶变换实现指数加速,从而引起了广泛关注。主要针对量子傅里叶变换的实现方案进行研究。首先介绍了IBM公司量子计算云服务的编程基础,随后设计了3比特量子傅里叶变换的量子线路,最后在IBM公司5超导量子比特的量子计算芯片上进行了实验验证。     

姿态特征结合2维傅里叶变换的步态识别

目的 针对现有步态识别方法易受携带物品、衣服变化等影响的问题,提出了将无肩姿态能量图、步态参数等姿态特征与步态参数的2维傅里叶变换相结合的步态识别算法。方法 基于姿态关节点序列提出忽略肩膀宽度信息的无肩姿态能量图,用以减弱衣服变化的影响;由于下肢受衣物及背包影响较小,提取3个或3个以上的下肢关节点局部结构参数,即提取中臀点与左右膝关节点、中臀点与左右踝关节点构成的两个三角形面积以及所有下肢关节点构成的多边形面积作为步态参数,增强下肢参数在步态识别中的作用;人在行走时,单肢体的运动具有一定的周期性,且肢体之间运动具有一定的协调性,用步态参数的2维幅度谱来表示单肢体运动的周期性与肢体之间运动的协调性,以提高步态参数的可区别性;在现有典型步态特征的基础上,融合本文提出的无肩姿态能量图、步态参数及其2维傅里叶变换幅度谱,采用多特征表示步态的方法,充分利用各特征的优点,提出加权平均与最大池化相结合的两层分数融合策略进行步态识别,提高了步态识别算法在携带物品、衣服变化和跨视角等条件下的正确率。结果 实验结果表明,在中国科学院自动化研究所发布的步态数据集CASIA-B上,本文方法在相同视角条件下,正常状态、背包状态和穿大衣状态的平均识别率分别为99.56%、99.23%和94.25%;在跨视角条件下,正常状态、背包状态和穿大衣状态的平均识别率分别为91.32%、85.34%和69.51%。与典型算法相比,穿大衣状态的识别率有显著提升。结论 本文方法采用加权平均与最大池化相结合的两层分数融合策略,综合利用各特征的优点及其适用场景,有效提高了步态识别的准确率,特别是减弱了衣服厚度、样式等变化对步态识别的影响。     

3D deep X-ray lithography for producing a multi-channel Fourier transform interferometer

We introduce a modified LIGA process architecture to manufacture a static lamellar grating Fourier-transform spectrometer invented by Moser and Möller (European patent EP 0 765 488 B1, 1994). Such spectrometers hold unique advantages over common Michelson-type FTIRs including high time resolution, speed, compactness, and robustness. To cope with the spectrometer’s demand for precise high-aspect-ratio micro-fabrication, we present a modified LIGA process which enhances the X-ray lithography by means of a moving mask technique (Heussler and Moser Lithography method and apparatus PCT/SG2011/000376, 2011). The technique relies on independently moving multiple masks stacked on top of each other during the lithographic step and thus allows to locally vary the deposited dose in a positive tone photoresist. First manufacturing results as well as a performance test of a prototype spectrometer are reported.     

Calculation of Fourier transform using symmetrical properties

A matrix method which computes discrete Fourier transforms using a digital computer program is presented in this paper. The proposed technique takes advantage of symmetry of the complex functions about the real and imaginary axes to reduce the number of calculations necessary in a given Fourier transform. Computationally the method described is not as efficient, especially for a large N, as the well-known Cooley-Tukey method. However, it differs from the Cooley-Tukey formulation in two notable respects: first, the present method is not as restrictive in the selection of values of N as the Cooley-Tukey method; and second, the calculations can proceed with the first value of the time function, thus eliminating the need for storing data before beginning with the transform calculations as is the case with the Cooley-Tukey method. In a number of applications, realizing these two conditions is more important than computational efficiency.The logic of a computer program which calculates the Fourier transform using the symmetry properties is described by a flow chart. This paper also includes numerical examples, using the computer program, of a Fourier transform from the time domain to the frequency domain. In addition, the program calculates the inverse Fourier transform, reconstructing the original time function from its frequency contents.     

傅里叶变换的多视角步态识别

步态识别作为一种全新的生物特征识别技术,通过人走路的姿势实现对个人身份的识别和认证。步态能量图将一个周期的步态组合在一起,增强了各帧的相关性,减少了噪声的干扰。对步态能量图进行傅里叶变换,利用傅里叶变换的低频分量对多个视角的步态进行识别。在CASIA数据库中进行实验,结果表明算法简单快速,取得了较好的识别效果。     

A robust 3D point cloud watermarking method based on the graph Fourier transform

Many modern applications make use of 3D modeling and / or reconstruction of complex objects, such as historical monuments and entire urban centers. One of the most common representations of these 3D models is by point clouds, which are a dense set of points irregularly organized in a 3D coordinate system. Usually, the acquisition methods are highly expensive due to the necessary equipment and size of these models. This factor motivates the proposal of watermarking techniques to guarantee the copyright protection as well as to detect illegal copies. This paper presents a non-blind watermarking method for 3D point clouds. The method is based on the graph Fourier transform, a recently introduced signal processing tool which has been applied to signals lying over arbitrarily irregular domains. Unlike other published works regarding point cloud watermarking, instead of inserting the bit sequence in the models’ spatial coordinates, in this work the bits are embedded in the color information attributed in each point of a cloud. Simulation results show high imperceptibility and robustness against several attacks, such as affine transformations, reordering, noise addition and cropping.

     

3DComplete: Efficient completeness inspection using a 2.5D color scanner

In this paper, we present a low-cost and highly configurable quality inspection system capable of capturing 2.5D color data, created using off-the-shelf machine vision components, open-source software libraries, and a combination of standard and novel algorithms for 2.5D data processing. The system uses laser triangulation to capture 3D depth, in parallel with a color camera and a line light projector to capture color texture, which are then combined into a color 2.5D model in real-time.     

3D edge detection using recursive filtering: Application to scanner images

This paper proposes a new algorithm for three-dimensional edge detection. This method is an extension to the 3D case of the optimal 2D edge detector recently introduced by R. Deriche (Int. J. Comput. Vison 1, 1987). It presents better theoretical and experimental performances than some classical approachs used at this date. Experimental results obtained on magnetic resonance images and on echographic images are shown. We stress that this approach can be used to detect edges in other multidimensional data, for instance 2D − t or 3D − t images.     

Computation of Fourier transform integrals using Chebyshev series expansions

In this paper, we extend the Clenshaw-Curtis integration method for the computation of Fourier transform integrals. In particular, we examine the numerical stability of a recurrence relation occurring in this method.