顾及地形梯度变化特征的DEM构建方法及其应用实例研究

以高精度曲面建模(HASM)方法为基础,提出了一种顾及变量梯度变化特征的DEM构建方法,将地表高程的梯度变化方向融入到HASM方法中的高斯方程构建中。实验结果表明,构建的DEM无论是从高程精度还是形态精度都优于对比方法。构建的DEM高程数值误差的绝对值最大值、平均绝对值误差、均方根误差等指标均低于对比方法,同时该方法构建的DEM高程误差的空间分布更为随机,表明该方法具有更好地稳健性,受数据质量、地形复杂程度等因素的影响较小。此外,构建的DEM生成的等高线与原始等高线偏差最小,生成的山体阴影与参照DEM生成的山体阴影相似度最好,表明构建的DEM具有更好的形态精度。本研究对复杂地形区域的DEM构建及应用分析具有一定参考价值。     

优化的高精度曲面建模方法在江南微丘DEM构建中的应用研究

微丘是我国江南地区一类常见的地表形态,该地形的精确模拟是构建江南地区高精度DEM的重要组成部分。在分析HASM方法原理的基础上,结合地表在局部区域的变化特征,提出了HASM空间插值方法的一种优化思路。通过局部计算区域的坐标系旋转,重新构建了计算格网点周围点的高程之间的约束方程关系。选择南京市栖霞区某处的微丘地形作为实验区域,对比分析了优化HASM方法和反距离加权插值(IDW),普通克里格插值(OK),和样条插值(Spline)等经典插值方法构建DEM的精度,结果表明优化后的HASM方法精度显著优于IDW、OK等经典插值方法,而通过生成不同实验方法的山体阴影图,表明与Spline等经典插值方法相比,优化后的HASM方法所构建的DEM与实际地表形态一致性更好。     

顾及DEM误差自相关的坡度计算模型精度分析

基于DEM的坡度计算,其误差来源于DEM误差、DEM结构和坡度计算模型。在顾及DEM误差自相关的前提下,对四种DEM坡度计算模型进行了分析和评价。研究表明,三阶不带权差分能给出较高的坡度计算精度;在局部窗口中,格网点数量越多,坡度计算越准确;等权比不等权的坡度计算模型更准确;DEM误差自相关结构形式对坡度计算无影响。进一步的理论分析和试验分析还表明：DEM误差自相关性的存在,不仅能够改善地形分析的精度,也能改善DEM自身精度。     

二、P21 普通测量学、地形测量学

CH20082004顾及DEM误差自相关的坡度计算模型精度分析=The Accuracy Assessment on Slope Algorithms with DEM Error Spatial Autocorrelation/刘学军,卞璐,卢华兴,朱莹(南京师范大学虚拟地理环境教育部重点实验室)//测绘学报.-2008,37(2).-200～206基于DEM的坡度计算,其误差来源于DEM误差、DEM结构和坡度计算模型.在顾及DEM误差自相关的前提下,对4种DEM坡度计算模型进行了分析和评价。研究表明,三阶不带权差分能给出较高的坡度计算精度;在局部窗口中,格网点数量越多,坡度计算越准确;等权比不等权的坡度计算模型更准确;DEM误差自相关结构形     

高精度曲面模型解算改进的Gauss-Seidel法

为了降低HASM的时间复杂度,采用一种改进Gauss-Seidel(GS)算法(MGS)解算HASM方程组。首先,从理论上分析了MGS算法收敛速度快于GS算法,然后以高斯合成曲面作为研究对象,用四组模拟试验表明,相同的网格数、达到相同的计算精度,MGS算法计算时间小于GS算法,且两种算法时间差与模拟区域网格数呈二次线性相关;固定网格数,使用相同的内迭代或者外迭代次数,MGS算法精度高于GS算法,但增加内迭代或者外迭代次数,GS算法同样收敛;MGS算法计算时间与网格数呈线性相关。MGS算法能够有效解决HASM模拟大区域的计算时间瓶颈,提高HASM运算速度。以甘肃省董志塬某测区SRTM3作为研究对象,基于MGS的HASM用于模拟DEM表明,HASM精度要高于传统的插值方法。     

ASTER立体像对提取玛尔挡坝区DEM及精度评价

ASTER立体像对提取DEM已经成为近年来DEM提取研究的热点问题。本文基于ENVI软件,利用AS-TER立体像对提取青藏高原玛尔挡坝区DEM,并对其进行精度评价和误差来源分析。结果表明,利用ENVI软件提取ASTER-DEM方法可行,提取的DEM效果较好,能与地形图重叠,高程精度可达30m,而且地形较平坦地区精度高于地形陡峭地区;控制点的多少及精度、成像时的环境和气象条件、波段特性、影像空间分辨率等都影响着DEM的精度。     

基于重构等高线的格网细化模型

以规则格网DEM为基础,利用回放等高线与原等高线进行比较,提出两个误差指标和一种格网细化模型,以生成多分辨率的格网DEM,并提高DEM的等高线精度。针对该模型的两个关键步骤,进行了较为详细的论述。通过对一幅实际地形数据进行试验,比较不同方法得出的DEM等高线精度,为DEM精度研究,特别是多分辨率DEM精度研究,提供了一种新的方法和思路。     

最佳DEM分辨率的确定及其验证分析

在玛尔挡地区格网DEM的数据上选择实验样区,以不同分辨率情况下DEM数据对地表模拟表达的逼近程度为研究对象,最优逼近时的栅格单元大小的临界值就是所求的最佳分辨率。在分析坡度中误差法和公式法等常见方法的基础上,借鉴坡度中误差的思想,选取区域地形粗糙度K、剖面线长度SL两个定量指标来综合分析确定该地区格网DEM的最佳分辨率。在ArcGIS平台上对方法进行了实验验证,得出分别以2m和8m作为玛尔挡地区1∶10 000和1∶50 000 DEM生产时是最佳分辨率的结论。研究表明这种解决办法不仅可以克服GIS空间分析中DEM分辨率确定的盲目性和随意性,而且能确保基于DEM的各种空间分析的精度,为相关研究提供重要的参考价值。     

基于填挖方分析的DEM精度评价模型

针对DEM高程中误差评价指标的不足,提出了一种基于填挖方分析的DEM精度评价模型以及计算方法,将DEM填挖方误差E_c定义为待评价DEM与参考DEM在同一区域的三维体积差异和与该区域面积之商。探究了DEM填挖方误差和DEM分辨率R以及地形平均坡度S之间的关系,得到DEM填挖方误差的定量估算模型为E_c=0.004 8·R·S。实验表明,模型估算精度达95.85%以上。该模型为在不同地形条件下,确定满足限差要求的DEM分辨率提供了依据。     

小波派生多尺度DEM的精度分析

利用陕北5 m分辨率DEM数据为基本数据,对Haar小波派生出一系列更低分辨率DEM进行复合精度分析。通过等高线套合、数据中误差以及表面重合指数等方法,分析其高程采样误差与空间分布;通过分析对比其在所提取的地面坡度、沟谷网络等地形因子上的差异,分析其地形描述误差。研究结果显示:小波派生多尺度DEM在精度的颓减上呈现指数形的变异规律,当达到三级重构DEM(40 m分辨率)时,其精度仍优于1:5万(25 m分辨率)DEM。该结果对于实现地形的有效简化与掌握多尺度DEM不确定性规律具有一定的意义。     

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.     

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。     

A total error-based multiquadric method for surface modeling of digital elevation models

Digital elevation model (DEM) source data are subject to both horizontal and vertical errors owing to improper instrument operation, physical limitations of sensors, and bad weather conditions. These factors may bring a negative effect on some DEM-based applications requiring low levels of positional errors. Although classical smoothing interpolation methods have the ability to handle vertical errors, they are prone to omit horizontal errors. Based on the statistical concept of the total least squares method, a total error-based multiquadric (MQ-T) method is proposed in this paper to reduce the effects of both horizontal and vertical errors in the context of DEM construction. In nature, the classical multiquadric (MQ) method is a vertical error regression procedure, whereas MQ-T is an orthogonal error regression model. Two examples, including a numerical test and a real-world example, are employed in a comparative performance analysis of MQ-T for surface modeling of DEMs. The numerical test indicates that MQ-T performs better than the classical MQ in terms of root mean square error. The real-world example of DEM construction with sample points derived from a total station instrument demonstrates that regardless of the sample interval and DEM resolution, MQ-T is more accurate than classical interpolation methods including inverse distance weighting, ordinary kriging, and Australian National University DEM. Therefore, MQ-T can be considered as an alternative interpolator for surface modeling with sample points subject to both horizontal and vertical errors.     

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.     

DEM地表坡向变率的向量几何计算法

作为计算坡向变率的数据基础,坡向矩阵具有方向性,以标量的方式计算带有方向属性的数据,将带来计算方式的误区及计算结果的偏差。本文以数学高斯曲面和不同黄土地貌样区5 m分辨率DEM数据为基础,针对坡向数据具有方向性的特点,设计基于数学向量的坡向变率计算方法。首先针对坡向数据进行极坐标转换,形成坡向矩阵的向量几何表达;然后以该坡向向量数据为基础来计算坡向变率;最后将本文方法的计算结果与传统标量方法的计算结果展开对比分析。试验结果显示,本文方法的坡向变率计算有效地避免了正北方向产生的极大偏差以及坡向差超过180°时的不准确现象,同时其他大部分区域也得出更为合理准确的坡向变率计算结果。在不同分辨率DEM下,本文方法能得到较为稳定的结果。本文所提出的基于向量几何的坡向变率计算方法可为精准数字地形分析提供参考,也是借鉴数学向量几何的方法解决数字地形分析问题的重要实践。     

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。     

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.     

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。     

Noisy Data Smoothing in DEM Construction Using Least Squares Support Vector Machines

Since spatial datasets are subject to sampling errors, a smoothing interpolation method should be employed to remove noise during DEM construction. Although least squares support vector machines (LSSVM) have been widely accepted as a classifier, their effect on smoothing noisy data is almost unknown. In this article, the smoothness of LSSVM was explored, and its effect on smoothing noisy data in DEM construction was tested. In order to improve the ability to deal with large datasets, a local method of LSSVM has been developed, where only the neighboring sampling points around the one to be estimated are used for computation. A numerical test indicated that LSSVM is more accurate than the classical smoothing methods including TPS and kriging, and its error surfaces are more evenly distributed. The real‐world example of smoothing noise inherent in lidar‐derived DEMs also showed that LSSVM has a positive smoothing effect, which is approximately as accurate as TPS. In short, LSSVM with a high efficiency can be considered as an alternative smoothing method for smoothing noisy data in DEM construction.