扰动引力快速确定的替代算法

扰动引力的点质量表达方法使得扰动引力的计算模式具有最为简单的结构 ,但它本身也具有计算量大的缺点 ,与实时计算的目标相矛盾。为解决这一矛盾 ,文中用三次等距B样条函数进行试验。结果表明 ,在已知预设弹道坐标的条件下 ,三次等距B样条函数方法是适于进行快速精确逼近弹道扰动引力的数值算法     

卫星导航系统中轮循式时频测量的数据预处理方法

针对时间频率系统中轮循式测量多通道信号与标准1PPS信号时差的记录错误通道数据问题,对阿伦方差等计算带来的不利影响,提出了一种结合Baarda算法和三次样条插值算法的数据预处理方法,有效地探测数据记录异常点,并计算异常点的三次样条内插值以替换,提高了原始数据可利用率和计算精确度。     

Interpolation of Point Values From Isoline Maps

A Bidirectional Hermitian Spline (BHS) method for the estimation of point values from isoline maps is presented and compared to three other methods. Hermitian splines are used and first derivatives are estimated by either Akima's method or by a clamped cubic spline, if Akima's method returns a zero first derivative. Every desired point value is interpolated twice, once by each of two orthogonally-directed splines. The two spline estimates are then averaged using the error formula for Hermitian splines. In addition, a periodic Hermitian spline is constructed around the study-area perimeter (representing a cross-sectional profile of the edge) to damp undesirable edge effects. Point values can be estimated from small-scale isoline maps drawn in spherical coordinates or from large-scale isoline maps drawn in Cartesian coordinates.     

用样条函数和小波变换进行正射影像图的拼接

介绍了基于匹配的方法, 在拼接影像重叠区找出部分点的同名点, 按同名点的坐标建立样条内插函数, 根据样条函数关系在局部范围内进行几何改正和色调调整, 并在小波变换空间中选取拼接点进行正射影像拼接, 达到了较好效果。     

GIS中曲线误差带模型的一种算法

针对ＧＩＳ中对曲线位置不确定性分析的要求,提出了一种采用数值方法计算拟合曲线点位误差的算法,给出了确定ＧＩＳ中任意曲线误差带模型的具体计算步骤与计算公式,并结合实例,绘制了三次样条拟合曲线的误差带。     

The Discontinuous Nature of Kriging Interpolation for Digital Terrain Modeling

Kriging is a widely employed method for interpolating and estimating elevations from digital elevation data. Its place of prominence is due to its elegant theoretical foundation and its convenient practical implementation. From an interpolation point of view, kriging is equivalent to a thin-plate spline and is one species among the many in the genus of weighted inverse distance methods, albeit with attractive properties. However, from a statistical point of view, kriging is a best linear unbiased estimator and, consequently, has a place of distinction among all spatial estimators because any other linear estimator that performs as well as kriging (in the least squares sense) must be equivalent to kriging, assuming that the parameters of the semivariogram are known. Therefore, kriging is often held to be the gold standard of digital terrain model elevation estimation. However, I prove that, when used with local support, kriging creates discontinuous digital terrain models, which is to say, surfaces with "rips" and "tears" throughout them. This result is general; it is true for ordinary kriging, kriging with a trend, and other forms. A U.S. Geological Survey (USGS) digital elevation model was analyzed to characterize the distribution of the discontinuities. I show that the magnitude of the discontinuity does not depend on surface gradient but is strongly dependent on the size of the kriging neighborhood.     

Spatial Interpolation of Elevation Data With Variable Density: A New Methodology to Derive Quality DEMs

A new methodology for spatial interpolation of elevation data with variable density is proposed. The method is based on two-step interpolation and data processing to minimize interpolation artifacts caused by variable data density. In the first step, the parameterization of the spline interpolation method is focused on areas with sparse data that need smoother interpolation. Then, the resulting surface in these areas is randomly sampled to densify the original data set. In the second step, the parameterization of the interpolation method is focused on areas with a required high level of detail. The final resulting surface contains the properties of surfaces optimized for different data densities and levels of detail     

车载激光扫描数据的道路边界线提取方法

鉴于城市道路两侧具有路坎这一特点,结合车载激光扫描系统的轨迹数据将整体点云进行分块处理,从每一块点云中截取部分数据投影到相应的截面上;然后,对获取的截面数据进行分割处理提取伪扫描线,根据路坎的坡度以及高差特点从伪扫描线中识别出路坎点;最后,利用三次样条插值的方法对提取的道路路坎点进行插值处理,得到道路边界线。实验证明了该方法的可行性和有效性。     

利用 LiDAR 点云提取有地形约束的光滑海岸线

针对传统海岸线提取算法误差大、在地形突变区域形变大的缺点,提出了一种基于离散 LiDAR 点云提取有地形约束海岸线的方法.首先,通过离散点云构建约束三角网,减少内插规则格网的误差并且保证海岸线不穿越地形结构;其次,进行顾及地形结构的点云高程修正,在数据源上缓解海岸线的平滑问题;最后采取二次多项式法消除毛刺,利用动态阈值张力样条函数内插生成光滑海岸线.     

基于二元样条函数的DEM传递误差模型

根据两点数值微分公式建立了基于二元样条函数的规则格网数字高程模型(DEM)的表面表达模型,得出了基于二元样条函数的传递误差公式。公式表明,二元样条函数的DEM传递误差与双线性多项式的传递误差相同。但由于样条函数的DEM表面建模误差低于线性多项式的DEM表面建模误差,因此,基于样条函数的DEM表面模型具有更高的精度。     

B样条与磨光样条在基于矩形格网的DEM内插中的应用

本文研究了Ｂ样条和磨光样条应用在基于矩形格网的ＤＥＭ内插中的思想、方法及实现过程。并从逼真性,保凸性,光滑性,运算速度等方面对Ｂ样条、磨光样条与双线性内插算法做了实验比较。理论和实验表明,所述方法具有较好的效果。     

Triangulated spherical splines for geopotential reconstruction

We present an alternate mathematical technique than contemporary spherical harmonics to approximate the geopotential based on triangulated spherical spline functions, which are smooth piecewise spherical harmonic polynomials over spherical triangulations. The new method is capable of multi-spatial resolution modeling and could thus enhance spatial resolutions for regional gravity field inversion using data from space gravimetry missions such as CHAMP, GRACE or GOCE. First, we propose to use the minimal energy spherical spline interpolation to find a good approximation of the geopotential at the orbital altitude of the satellite. Then we explain how to solve Laplace’s equation on the Earth’s exterior to compute a spherical spline to approximate the geopotential at the Earth’s surface. We propose a domain decomposition technique, which can compute an approximation of the minimal energy spherical spline interpolation on the orbital altitude and a multiple star technique to compute the spherical spline approximation by the collocation method. We prove that the spherical spline constructed by means of the domain decomposition technique converges to the minimal energy spline interpolation. We also prove that the modeled spline geopotential is continuous from the satellite altitude down to the Earth’s surface. We have implemented the two computational algorithms and applied them in a numerical experiment using simulated CHAMP geopotential observations computed at satellite altitude (450 km) assuming EGM96 (n _max = 90) is the truth model. We then validate our approach by comparing the computed geopotential values using the resulting spherical spline model down to the Earth’s surface, with the truth EGM96 values over several study regions. Our numerical evidence demonstrates that the algorithms produce a viable alternative of regional gravity field solution potentially exploiting the full accuracy of data from space gravimetry missions. The major advantage of our method is that it allows us to compute the geopotential over the regions of interest as well as enhancing the spatial resolution commensurable with the characteristics of satellite coverage, which could not be done using a global spherical harmonic representation. The results in this paper are based on the research supported by the National Science Foundation under the grant no. 0327577.     

薄板样条函数及复杂曲面的数学表示

介绍了自然样条函数的计算方法,并在此基础上将一维样条函数推广到多维。讨论了用薄板样条函数表示光滑三维曲面问题,提出了相应的曲面数字模型的计算方法。     

自然样条半参数模型与系统误差估计

采用自然样条逼近的数据处理方法 ,探讨了自然样条半参数回归分析方法。在补偿最小二乘的原则下 ,利用三次样条函数构造补偿项 ,通过广义交叉核实函数自动选取光滑参数。自编程序进行计算 ,得到了回归参数向量和样条函数的补偿最小二乘估计。模拟计算表明 ,该方法适合于回归函数模型误差与测量系统误差的估计     

A multiresolution hierarchical classification algorithm for filtering airborne LiDAR data

We presented a multiresolution hierarchical classification (MHC) algorithm for differentiating ground from non-ground LiDAR point cloud based on point residuals from the interpolated raster surface. MHC includes three levels of hierarchy, with the simultaneous increase of cell resolution and residual threshold from the low to the high level of the hierarchy. At each level, the surface is iteratively interpolated towards the ground using thin plate spline (TPS) until no ground points are classified, and the classified ground points are used to update the surface in the next iteration. 15 groups of benchmark dataset, provided by the International Society for Photogrammetry and Remote Sensing (ISPRS) commission, were used to compare the performance of MHC with those of the 17 other publicized filtering methods. Results indicated that MHC with the average total error and average Cohen’s kappa coefficient of 4.11% and 86.27% performs better than all other filtering methods.     

Storage-efficient reconstruction framework for planar contours

A storage-efficient reconstruction framework for cartographic planar contours is developed. With a smaller number of control points, we aim to calculate the area and perimeter as well as to reconstruct a smooth curve. The input data forms an oriented contour, each control point of which consists of three values: the Cartesian coordinates (x, y) and tangent angle θ. Two types of interpolation methods are developed, one of which is based on an arc spline while the other one is on a cubic Hermite spline. The arc spline-based method reconstructs a G¹ continuous curve, with which the exact area and perimeter can be calculated. The benefit of using the Hermite spline-based method is that it can achieve G² continuity on most control points and can obtain the exact area, whereas the resulting perimeter is approximate. In a numerical experiment for analytically defined curves, more accurate computation of the area and perimeter was achieved with a smaller number of control points. In another experiment using a digital elevation model data, the reconstructed contours were smoother than those by a conventional method.     

对渐进三角网点云数据滤波算法的改进

针对渐进三角网滤波算法（PTD）进行拓普康LiDAR点云数据处理过程中易将地物点误判为地面点的缺陷,本文提出两种改进方法。一种是采用局部坡度拟合法对PDT算法进行改进,将点云数据按高程值与拟合坡面法求解的拟合高程值的差由小到大进行排序,将为地面点可能性更大的点优先判定,从而获取更加精确的TIN;另一种是引入薄板样条曲线（TPS）插值法,对PTD算法进行改进,将PTD中候选点判断参数改为TPS法中的弯曲能量增长值,从而减少误判。结果表明,使用以上两种改进算法,综合考虑第1类误差和第2类误差影响,在大部分地形特征下比传统PTD算法表现更优,对低矮植被、桥、斜坡等特殊地物的滤波效果更佳。     

三次参数样条曲线在等高线矢量化中的应用

主要阐述了如何应用参数样条曲线在AutoCAD中快速准确地矢量化等高线。通过对三次参数样条曲线不同边界条件所绘线形的分析,最终选定了用夹持端样条曲线来矢量化等高线,并在AutoCAD平台上和VC 6.0开发环境下,用Object ARX开发工具包开发完成该矢量化程序。实践证明,该法切实可行,提高了工作效率。     

一种面向CPU/GPU异构环境的协同并行空间插值算法

CPU/GPU异构混合系统是一种新型高性能计算平台,但现有并行空间插值算法仅依赖CPU或GPU进行加速,迫切需要研究协同并行空间插值算法以充分利用异构计算资源,进一步提升插值效率。以薄板样条函数插值为例,提出一种CPU/GPU协同并行插值算法以加速海量激光雷达（light detector & ranger,LiDAR）点云生成数字高程模型（DEM）。通过插值任务的分解与抽象封装以屏蔽底层硬件执行模式的差异性,同时在多级协同并行框架基础上设计了Greedy-SET动态调度策略,策略顾及底层硬件能力的差异性,以实现异构并行资源的充分利用和良好负载均衡。实验表明,协同并行插值算法在高性能工作站上取得19.6倍的加速比,相比单一CPU或GPU并行算法,其效率提升分别达到54%和44%,实现了高效的协同并行处理。