在重构相空间选取样本的时间序列分形预测

提出一种基于相空间重构原理进行样本选取的改进分形预测算法。该算法将时间序列在相空间重构中得到的嵌入维数和时间延迟作为分形预测中数据样本的选择依据,结合分形理论的拼贴定理和插值迭代算法,实现时间序列的分形预测,建立时间序列的分形预测模型。利用此改进算法对低压电力线噪声序列进行预测的结果表明,与现有分形算法相比,改进算法提高了数据样本间的相似度,优化了数据样本的选取,明显提高了预测的精度,适合于对自相似性和周期性不明确的时间序列的预测。     

分形插值曲面

研究一类迭代函数系统和分形插值曲面的构造，得到分形插值曲面面连续的充分必要条件，由此给出了简单的分形超限插值方法和新的网格点插值方法；从而利用网格曲线或网格点上的特征生成连续的分形插值曲面，这种简单有效的方法可广泛地用于分形造型和数据拟合。     

分形插值在风速时间序列中的应用

针对风电场风速数据中大量连续缺失数据的插值问题，提出了一种基于自适应变异粒子群优化（PSO）的分形插值算法。首先，在粒子群优化算法中引入变异因子，增强粒子的多样性，提高算法搜索精度；其次，通过自适应变异粒子群优化算法来得到分形插值算法中垂直比例因子参数的最佳取值；最后，对两组不同趋势和变化特征的数据集进行分形插值计算分析，并把所提算法与Lagrange插值和三次样条插值方法进行对比。结果表明：分形插值不仅可以保持风速曲线的整体波动特性和局部特征，而且比传统插值方法的精度更高；在基于Dataset A的实验中，分形插值的均方根误差（RMSE）分别比Lagrange插值和三次样条插值减小了66.52%和58.57%；在基于Dataset B的实验中，分形插值的RMSE分别比Lagrange插值和三次样条插值减小了76.72%和67.33%。证明分形插值更适合连续缺失且波动强烈的风速时间序列的插值。     

基于医学体数据场的大脑皮层重构

研究如何基于一组连续脑部医学切片重构大脑皮层,介绍体数据场和大脑皮层三维重构系统流程。针对插值后的脑部图像提出一种有效的脑灰质分割算法,通过图像预处理和阈值分割方法获取脑灰质图像。针对分割后的体数据,采用改进的Marching Cubes方法重构大脑皮层三维模型,避免提取脑灰质轮廓线。实验结果验证了该算法的可行性和实用性。     

自适应的三维分形地形重建算法研究*

针对常规三维分形地形重建算法具有的速度慢、插值点分布不均匀、参数设置复杂等缺点,提出自适应的三维分形地形重建算法。该算法根据地形的起伏特征自动确定垂直压缩因子,根据子域面积进行均匀插值。实验结果表明,该方法插值效率更高,所获得的插值曲面更加真实,与常规分形插值相比具有一定的优越性。     

基于函数迭代系统的3-D分形插值算法

提出了一种新的分形插值算法,通过矩形剖分上的采样数据点构建分形插值曲面。该算法保证分形插值时的边界连续性,而且对于初始数据集没有任何对称性限制。所构建的分形插值曲面整体上保持原始数据的主要特征,局部上具备自相似的特点。实验结果表明算法的有效性和低时间复杂度,有利于分形插值的实际应用。     

从点集重构曲面网络方法综述

本文主要对三维数据点重构曲面网格模型方法进行了综述。从三维数据点集重构曲面一般遵循以下三个步骤：1）重构曲面网格模型；2）网格简化；3）拟合曲面（通常为Bezier,NURBS),其中重构曲面网格为关键的一点，三维数据点集由三维数字化仪采集得到，不同的数字化设备，得到的三维数据点集可能会有差别，重构曲面网格的算法也不尽相同，本文介绍了几种对于不同数据形式，有代表性的重构曲面网格算法。     

分形插值在风速时间序列中的应用

针对风电场风速数据中大量连续缺失数据的插值问题,提出了一种基于自适应变异粒子群优化（PSO）的分形插值算法。首先,在粒子群优化算法中引入变异因子,增强粒子的多样性,提高算法搜索精度;其次,通过自适应变异粒子群优化算法来得到分形插值算法中垂直比例因子参数的最佳取值;最后,对两组不同趋势和变化特征的数据集进行分形插值计算分析,并把所提算法与Lagrange插值和三次样条插值方法进行对比。结果表明：分形插值不仅可以保持风速曲线的整体波动特性和局部特征,而且比传统插值方法的精度更高;在基于Dataset A的实验中,分形插值的均方根误差（RMSE）分别比Lagrange插值和三次样条插值减小了66.52%和58.57%;在基于Dataset B的实验中,分形插值的RMSE分别比Lagrange插值和三次样条插值减小了76.72%和67.33%。证明分形插值更适合连续缺失且波动强烈的风速时间序列的插值。     

基于B样条插值的医学图像三维重构技术

传统的三维重构方法不适用于旋转式切片，该文针对旋转式切片提出了一种可行的三维重构方法，即基于B样条插值的重构方法，解决了旋转式切片的实体建模问题，在绘制时利用OpenGL的NURBS接口编程，比三角面片逼近等方法的重构时曲面的绘制质量有了显著提高。另外，该方法也适合于平行式切片的重构。     

三维地形可视化的MATLAB实现

阐述运用二维插值和分形插值方法,基于MATLAB进行三维地形数据的可视化;并给出利用该法在三维地形可视化中的应用实例,说明了三维地形的制作以及可视化实现步骤.结果表明,算法处理数据效率高、效果好.     

Fast distance transformation on irregular two-dimensional grids

In this article, we propose a new fast algorithm to compute the squared Euclidean distance transform (E²DT) on every two-dimensional (2-D) irregular isothetic grids (regular square grids, quadtree based grids, etc.). Our new fast algorithm is an extension of the E²DT method proposed by Breu et al. [3]. It is based on the implicit order of the cells in the grid, and builds a partial Voronoi diagram of the centers of background cells thanks to a data structure of lists. We compare the execution time of our method with the ones of others approaches we developed in previous works. In those experiments, we consider various kinds of classical 2-D grids in imagery to show the interest of our methodology, and to point out its robustness. We also show that our method may be interesting regarding an application where we extract an adaptive medial axis construction based on a quadtree decomposition scheme.     

DLSLA 3-D SAR imaging algorithm for off-grid targets based on pseudo-polar formatting and atomic norm minimization基于伪极坐标变换和原子范数最小化的网格偏离目标DLSLA 3-D SAR成像方法

This paper concerns the imaging problem for downward looking sparse linear array three-dimensional synthetic aperture radar (DLSLA 3-D SAR) under the circumstance of sparse and non-uniform cross-track dimensional virtual phase centers configuration. Since the 3-D imaging scene behaves typical sparsity in a certain domain, sparse recovery approaches hold the potential to achieve a better reconstruction performance. However, most of the existing compressive sensing (CS) algorithms assume the scatterers located on the pre-discretized grids, which is often violated by the off-grid effect. By contrast, atomic norm minimization (ANM) deals with sparse recovery problem directly on continuous space instead of discrete grids. This paper firstly analyzes the off-grid effect in DLSLA 3-D SAR sparse image reconstruction, and then introduces an imaging method applied to off-gird targets reconstruction which combines 3-D pseudo-polar formatting algorithm (pseudo-PFA) with ANM. With the proposed method, wave propagation and along-track image reconstruction are operated with pseudo-PFA, then the cross-track reconstruction is implemented with semidefinite programming (SDP) based on the ANM model. The proposed method holds the advantage of avoiding the off-grid effect and managing to locate the off-grid targets to accurate locations in different imaging scenes. The performance of the proposed method is verified and evaluated by the 3-D image reconstruction of different scenes, i.e., point targets and distributed scene.     

无权重多重网格的最小二乘相位解缠研究

相位解缠是干涉合成孔径雷达（InSAR）测量地形高程、重建三维地形模型的重要步骤之一。介绍了最小二乘的相位解缠原理,提出了一种基于无权重的多重网格算法求解离散泊松方程。该算法是在较大网格基础上解决偏微分方程（PDE）的快速方法,将误差的低频成分转换为高频成分,这样就可以使用高斯-塞德尔松弛法去除多种频率的误差分量。实验结果证明：该方法具有收敛速度快,解缠精度高等优点。     

Particle host cell determination in unstructured grids

An algorithm has been developed to efficiently determine the correct particle host cell for unstructured grids with multiple element types (e.g. tetrahedrons, prisms, hexahedrons, etc.) and large particle movements (e.g. movement across single or multiple cells). The algorithm utilizes a “dot product” searching technique where a direction vector connecting a face centroid and the particle location is dotted with an outwardly-positive face normal to facilitate the host cell search. The algorithm is investigated for particles moving a distance of one or several cell lengths on a variety of two-dimensional (2-D) and three-dimensional (3-D) meshes. Two variations of this approach are introduced and tested, each focusing on different strategies (cell-searching vs. face-searching minimization) to optimize the use of computational resources. Finally, in order to increase the efficiency of each algorithm in the case of large problems where the previous host cell is not known, a “coarse-grain” search is introduced, whereby a small sampling of the total cells are inspected, after which the adjoining-faces search is completed in the host sub-domain.     

Continuous scatterplots

Scatterplots are well established means of visualizing discrete data values with two data variables as a collection of discrete points. We aim at generalizing the concept of scatterplots to the visualization of spatially continuous input data by a continuous and dense plot. An example of a continuous input field is data defined on an n-D spatial grid with respective interpolation or reconstruction of in-between values. We propose a rigorous, accurate, and generic mathematical model of continuous scatterplots that considers an arbitrary density defined on an input field on an n-D domain and that maps this density to m-D scatterplots. Special cases are derived from this generic model and discussed in detail: scatterplots where the n-D spatial domain and the m-D data attribute domain have identical dimension, 1-D scatterplots as a way to define continuous histograms, and 2-D scatterplots of data on 3-D spatial grids. We show how continuous histograms are related to traditional discrete histograms and to the histograms of isosurface statistics. Based on the mathematical model of continuous scatterplots, respective visualization algorithms are derived, in particular for 2-D scatterplots of data from 3-D tetrahedral grids. For several visualization tasks, we show the applicability of continuous scatterplots. Since continuous scatterplots do not only sample data at grid points but interpolate data values within cells, a dense and complete visualization of the data set is achieved that scales well with increasing data set size. Especially for irregular grids with varying cell size, improved results are obtained when compared to conventional scatterplots. Therefore, continuous scatterplots are a suitable extension of a statistics visualization technique to be applied to typical data from scientific computation.     

Interactive scientific visualization of fluid flow

Examples of scientific visualization techniques used for the interactive exploration of very large data sets from supercomputer simulations of fluid flow are presented. Interactive rendering of images from simulations of grids of 2 million or more computational zones are required to drive high-end graphics workstations to their limits with 2-D data. The author presents one such image and discusses interactive steering of 2-D flow simulations, a phenomenon now possible with grids of half a million computational zones. He uses a simulation of compressible turbulence on a grid of 134 million computational zones to set the scale for discussing interactive 3-D visualization techniques. A concept for a gigapixel-per-second video wall, or gigawall, which could be built with present technology to meet the demands of interactive visualization of the data sets that will be produced by the next generation of supercomputers, is discussed     

A review and comparative study of upwind biased schemes for compressible flow computation. Part II: 1-D higher-order schemes

Summary Higher-order upwind biased procedures for solving the equations of 1-D compressible unsteady flow are surveyed. Approaches based upon the use of either switched artificial viscosity, flux-limiting or slopelimiting are considered and described within a unified framework. The approaches are implemented within the context of an edge-based finite element solution algorithm, which represents the basis for a future multi-dimensional extension on general grids. The performance of the different approaches is illustrated by application to the solution of the shock tube problem in different flow regimes.     

基于开关3-D中值滤波的视频序列去噪算法

为提高含噪视频序列的质量和效果,提出一种基于开关噪声检测与三维中值滤波相结合的开关3-D中值滤波算法。该算法通过判断视频序列的每一个像素点,对噪声点用3-D中值滤波处理,再对其进行二次判断,如果判为噪声点,则采用变型3-D中值滤波处理,直到去除所有噪声点为止。仿真实验表明,该算法对“雪花”噪声有较好的滤波效果,当处理加入25%的“雪花”噪声时,3-D开关中值滤波比三维中值滤波的信噪比平均提高了10 dB左右。     

三维矢量场的流动拓扑结构抽取

提出一种基于关键点分类的三维矢量场流动拓扑结构抽取算法,可应用于三维曲线网格、结构化网格和分块网格中.在许多计算流体力学计算中,存在非滑移边界,这种边界上流体的速度为0.通过分析流场边界的表面摩擦场的拓扑,展示绕壁面流体的流动结构;使用图标定位关键点,可交互式地标记和显示涡核区域,并通过选择暗示螺旋流动的图标,沿着该关键点的实特征值对应的特征矢量方向积分流线来完成.测试结果清晰地展示了关键特征区域的流体流动特征.     

Efficient Parallelization of a Three-Dimensional Navier-Stokes Solver on MIMD Multiprocessors

We present an efficient parallelization strategy for speeding up the computation of a high-accuracy 3-dimensional serial Navier-Stokes solver that treats turbulent transonic high-Reynolds flows. The code solves the full compressible Navier-Stokes equations and is applicable to realistic large size aerodynamic configurations and as such requires huge computational resources in terms of computer memory and execution time. The solver can resolve the flow properly on relatively coarse grids. Since the serial code contains a complex infrastructure typical for industrial code (which ensures its flexibility and applicability to complex configurations), then the parallelization task is not straightforward. We get scalable implementation on massively parallel machines by maintaining efficiency at a fixed value by simultaneously increasing the number of processors and the size of the problem.The 3-D Navier-Stokes solver was implemented on three MIMD message-passing multiprocessors (a 64-processors IBM SP2, a 20-processors MOSIX, and a 64-processors Origin 2000). The same code written with PVM and MPI software packages was executed on all the above distinct computational platforms. The examples in the paper demonstrate that we can achieve efficiency of about 60% for as many as 64 processors on Origin 2000 on a full-size 3-D aerodynamic problem which is solved on realistic computational grids.