一种混合曲面散乱点云曲率计算方法

针对局部点云曲面拟合过程中系数矩阵容易出现病态等问题,本文利用局部点云与切平面的夹角特性,对曲面拟合方程的权阵进行修正,并在此基础上,提出了基于三次曲面和四次曲面拟合的混合曲面散乱点云曲率计算方法,同时通过统计分析圆环面和球面的曲率计算值和真值差别,证实了该算法不仅精度高,且错误率低。     

基于主成分回归的GPS高程曲面拟合

本文阐述了多项式曲面拟合GPS高程中参数数目对法方程条件数和结果的影响,当过度参数化时,观测方程的法方程会病态,传统的最小二乘无法得到可靠的结果,岭估计到目前为止仍然没有一种很好的确定岭参数的方法,主成分估计可以在保持原始数据信息损失最少的前提下,实现数据的降维避免法方程病态,从而得到参数的精确估值。并且把该方法运用于某测区,通过比较不同方法和不同参数数目时的计算结果,得出主成分估计在不同参数时都可以取得比较满意的结果,同时计算结果表明中心化和标准化对于多项式曲面拟合GPS高程的必要性。     

自然地貌的计算机晕渲表示

本文给出了在投影平面上计算地形曲面灰度的公式以及自然地貌的晕渲表示算法。地形曲面的逼近利用了微小曲面可近似地被看作极小曲面的原理。同时，本文还给出了在地形原图上沿X和Y方向进行数据采集的算法，相应的X和Y方向构成微小地形曲面的四个边界断面，通过应用有理式样条插值函数，可在曲面求解前确定相应边界断面曲线，从而得出边界点画数值作为曲面方程求解的已知条件。作为计算机地貌晕渲表示方法的一个实例文末给出了利用X-Y绘图仪和TEKTRO-NIX 4006-Ⅰ图形显示仪作图的结果，并且表明在高分辨率图像显示仪的条件下，可获得更为细腻的晕渲表示。     

基于两步解法的似大地水准面拟合

基于最小二乘估计(LS估计)的曲面拟合,作为似大地水准面拟合的一种方法,巳广泛应用在GPS高程转换中.然而,如果曲面拟合方程中存在病态问题,LS估计方法往往不能解算出稳定且准确的参数估值.在LS估计的基础上,探讨了基于两步解法的似大地水准面拟合方法.该方法能够减弱病态方程对拟合结果的影响,提高GPS高程转换的质量.最后...     

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。     

基于DEM的地形曲率计算模型误差分析

地形曲率是地形表面几何形态和地学建模的基本变量之一。本文首先对曲率计算模型进行了归纳,然后通过数据独立的DEM误差分析方法和实际DEM的分析验证,对目前九种曲率计算的三类曲率计算模型进行了量化分析比较。研究结果表明,当DEM数据精度比较高时,高次曲面(四次曲面)能给出较高精度的曲率计算结果,而当DEM误差较大时,低次曲面(二次曲面)由于具有误差的平滑作用而能产生较高精度的曲率值。     

运用GPS曲面拟合高程精化锦州市区似大地水准面

利用已完成的锦州市区基础控制成果对锦州市似大地水准面精化进行了研究。介绍了GPS高程的应用理论,大地水准高的计算方法以及利用曲面拟合法计算大地水准面高,并对结果进行了分析,绘制出高程异常等值线图。     

高精度曲面建模的三维地形可视化研究

根据高精度曲面建模理论(HASM)中曲面单元算法的特点,提出基于视点的多分辨率LOD实时生成算法。该方法通过对规则格网的DEM数据进行划分,以单元分片为基本单位对DEM数据进行组织。根据各曲面单元与视点的相对关系,以不同间距对曲面单元进行内插,实时重建视景内的三维地形。在实时显示过程中,对硬盘中的数据进行实时读取,采用多线程技术对图像渲染操作进行处理,实现了对DEM数据的实时计算、动态显示。该方法无需对规则格网DEM数据建立空间层次组织结构,在对虚拟地形进行实时漫游过程中,存储空间占用少,不受数据规模的影响。     

青藏高原中部似大地水准面精化的应用研究

介绍了精化似大地水准面的常用方法。采用青海和西藏三级GPS大地控制网测量数据,利用移动曲面法、改进的移动曲面法、二次曲面拟合法和改进的二次曲面拟合法对青藏高原中部似大地水准面进行了拟合计算。结果表明,利用改进的移动曲面法和改进的二次曲面法能有效地提高本地区似大地水准面的精化效果,精度优于0.5 m。     

多级移动曲面拟合的自适应阈值点云滤波方法

为了提高机载激光雷达点云滤波算法的精度、效率以及自适应性,提出了一种多级移动曲面拟合的自适应阈值点云滤波方法。首先,对点云数据进行预处理即剔除粗差,然后通过格网化分割建立格网索引,利用每个格网的邻域格网中的最低点建立曲面方程,计算真实高程与拟合高程的差值并设置自适应性阈值进行滤波,最后采用多级滤波策略,即逐级改变格网大小并自动设置邻域和阈值,直到滤波结果达到精度要求。使用国际摄影测量与遥感学会（ISPRS）提供的测试数据对算法进行验证,第1、2类误差和总误差平均值分别为7.33%、10.64%、6.34%。将该算法与ISPRS公布的8大经典滤波算法进行比较,结果表明该方法的适应性强,滤波结果具有较高的准确性。     

HASM-AD algorithm based on the sequential least squares

The HASM(high accuracy surface modeling) technique is based on the fundamental theory of surfaces,which has been proved to improve the interpolation accuracy in surface fitting.However,the integral iterative solution in previous studies resulted in high temporal complexity in computation and huge memory usage so that it became difficult to put the technique into application,especially for large-scale datasets.In the study,an innovative model(HASM-AD) is developed according to the sequential least squares on...     

高精度曲面模型的解算

为了提高Gass-Seidel(GS)算法的收敛速度,提出了改进的GS算法(MGS),用于解算高精度曲面模型(HASM)(HASM-MGS)。以高斯合成曲面为研究对象,将HASM-MGS与HASM-GS和Matlab提供的函数进行对比,结果表明,达到相同的模拟中误差,HASM-MGS计算时间远小于HASM-GS和Matlab提供的函数;HASM-MGS计算时间与模拟区域的网格数呈非常好的线性关系,时间复杂度比传统的方法降低两个数量级。     

Method of reducing HASM boundary error

High accuracy surface modeling (HASM) constructed based on the fundamental theorem of surface is more accurate than the classical methods. However, because of boundary error, location error, etc, HASM has a big accuracy loss in real-world examples. In former researches we solved the location error with Taylor expansion. In order to reduce the HASM boundary error and improve its accuracy further, this paper presents a new method of Laplace interpolation to compute the region boundary value. Gaussian synthetic surface and the real world test region are employed to validate the efficiency of this method. Results show that the boundary value computed with Laplace interpolation is more accurate than the classical methods, which can be regarded as an alternative for boundary value computation.     

A high accuracy surface modeling method based on GPU accelerated multi‐grid method

A high accuracy surface modeling method (HASM) has been developed to provide a solution to many surface modeling problems such as DEM construction, surface estimation and spatial prediction. Although HASM is able to model surfaces with a higher accuracy, its low computing speed limits its popularity in constructing large scale surfaces. Hence, the research described in this article aims to improve the computing efficiency of HASM with a graphic processor unit (GPU) accelerated multi‐grid method (HASM‐GMG). HASM‐GMG was tested with two types of surfaces: a Gauss synthetic surface and a real‐world example. Results indicate that HASM‐GMG can gain significant speedups compared with CPU‐based HASM without acceleration on GPU. Moreover, both the accuracy and speed of HASM‐GMG are superior to the classical interpolation methods including Kriging, Spline and IDW.     

An Adaptive Method of High Accuracy Surface Modeling and Its Application to Simulating Elevation Surfaces

An adaptive method is employed to speed up computation of high accuracy surface modeling (HASM), for which an error indicator and an error estimator are developed. Root mean‐square error (RMSE) is used as the error estimator that is formulated as a function of gully density and grid cell size. The error indicator is developed on the basis of error surfaces for different spatial resolutions, which are interpolated in terms of the absolute errors calculated at sampled points while paying attention to the landform characteristics. The error surfaces indicate the magnitude and distribution of errors in each step of adaptive refinement and make spatial changes to the errors in the simulation process visualized. The adaptive method of high accuracy surface modeling (HASM‐AM) is applied to simulating elevation surface of the Dong‐Zhi tableland with 27.24 million pixels at a spatial resolution of 10 m × 10 m. Test results show that HASM‐AM has greatly speeded up computation by avoiding unnecessary calculations and saving memory. In addition, HASM‐AM improves simulation accuracy.     

A Multi‐Grid Method of High Accuracy Surface Modeling and Its Validation

A method of high accuracy surface modeling (HASM) has been constructed to find a solution for error problems that had long troubled surface modeling in geographical information systems (GIS). It is found that when a preconditioned conjugate gradient (PCG) algorithm is used to solve the large sparse linear system, which HASM can be transferred into, HASM performs best in terms of simulation compared with all other algorithms. But its computing speed is not fast enough for all applications. A multi‐grid method is introduced into HASM to try to shorten its computing time. Both numerical and real‐world tests demonstrate that there is a range of stop error (SE). The multi‐grid method of HASM (HASM‐MG) greatly increases computing speed when SEs are within this range, compared with the PCG algorithm of HASM (HASM‐PCG). HASM‐MG is suitable for applications with a need for less accuracy and a shorter computing time. HASM‐PCG is appropriate for issues needing higher accuracy. HASM‐MG performs better than HASM‐PCG in flat areas, while HASM‐PCG does better in complex terrainm in terms of accuracy and computing time.     

基于高精度曲面模型的DEM构建与误差分析

引入地形表达误差(terrain representation error,Etr),选择标准曲面和甘肃省董志塬地区作为研究对象,利用窗口分析法实现Etr的提取;用统计分析法得出Etr随网格分辨率变化的回归方程;根据误差传播定律计算DEM中误差。数值结果表明,该方法能更准确的计算HASM生成的DEM精度;相同的采样数下,HASM较传统方法(IDW,Spline和Kriging)能生成更高精度和分辨率的DEM。在难以获取已知数据的地区,HASM提供了生成相对准确DEM的高效工具。     

HASM解算的2维双连续投影方法

基于曲面论原理的高精度曲面建模方法（HASM）解决了长期困扰地理信息系统界的误差问题,但使用该方法需要求解大规模线性方程系统导致其计算效率较低并限制了其广泛应用。为提高HASM线性系统的解算速度和精度,本文基于二维双连续投影提出了一种解算HASM的新方法（HASM-DSPM）。为了提高收敛速度和解算精度,该方法采用选取优化的投影空间和两次校正策略。理论分析表明,使用该方法比使用高斯赛尔方法（Gauss-Seidel, GS）和改进的高斯赛德尔方法(Modified Gauss-Seidel, MGS)效率明显提高。分别用本文引入的方法、高斯赛德尔方法和效率较高的MGS方法分别进行了HASM方程组的解算,并对高斯合成曲面和实际项目区模拟进行了模拟试验。结果表明,和GS、MGS方法相比,本文提出的HASM-DSPM解算方法无论收敛速度和计算时间都有明显改善。     

一种由等高线构建DEM的新方法

基于HASM,提出了一种由等高线建立DEM的新方法HASM-OC。HASM—OC方法保证地形曲面的整体光滑性,保证DEM最大程度上忠实于原始等高线数据。实际等高线案例结果表明,HASM—OC方法与基于薄板样条原理的Hutchinson方法的DEM模拟结果及其回放的等高线差相比,前者比后者保留更多的地形特征信息,前者的回放等高线比后者回放等高线更忠实于原始数据。