基于双三次Hermite插值方法的DEM误差传播分析

针对由双三次Hermite插值所生成的DEM数据,提出了一种新的传播误差估计方法。传播误差估计模型所适用的空间对象包括:线、不规则三角网(TIN)和规则格网等DEM数据。基于统计学中的误差传播定律,推导出了由非线性插值方法所生成DEM的误差传播公式。最后,将由双三次Hermite插值方法所生成DEM的传播误差与先前研究中采用线性插值所生成DEM的传播误差进行对比分析,由此可以更加全面地掌握通过线性插值或者非线性插值方法所生成DEM的误差传播规律。该成果可用于指导对实际生产DEM产品过程中插值方法的选择。     

基于双二次插值多项式的DEM传递误差模型

基于函数插值方法,得出了基于不完全双二次插值多项式的规则格网数字高程模型(DEM)的表面表达模型,并推导了相应的传递误差公式。公式表明,不完全双二次多项式的DEM传递误差与双线性多项式的传递误差相同。但由于不完全双二次多项式的DEM表面建模误差低于线性多项式的DEM表面建模误差,因此基于不完全双二次多项式的DEM表面模型具有更高的精度。     

基于双二次插值多项式的DEM传递误差模型

基于函数插值方法,得出了基于不完全双二次插值多项式的规则格网数字高程模型(DEM)的表面表达模型,并推导了相应的传递误差公式.公式表明,不完全双二次多项式的DEM传递误差与双线性多项式的传递误差相同.但由于不完全双二次多项式的DEM表面建模误差低于线性多项式的DEM表面建模误差,因此基于不完全双二次多项式的DEM表面模型具有更高的精度.     

插值条件下格网DEM坡度计算模型的噪声误差分析

针对目前DEM（Digital Elevation Model, DEM）数字地形分析的精度评价多数不考虑DEM误差的空间自相关性或仅仅采用经验的自相关性模型问题,本文从DEM插值入手,从理论上推导了插值条件下格网DEM邻域窗口内坡度噪声误差的空间自相关性模型以及坡度精度模型,并选取典型的插值方法和坡度差分算法,从实验角度分析了在顾及和不顾及空间自相关性两种情况下的格网DEM坡度计算模型的噪声精度,实验结果表明：坡度精度受DEM噪声误差的空间自相关性影响较大,并与DEM插值方法和坡度计算模型中的差分算法有关。     

基于随机过程的格网DEM精度场模型

针对目前DEM格网精度从理论上难于统一量化描述问题,提出一种基于随机过程的格网DEM（grid digital elevation model, grid DEM）精度场模型,该模型从随机过程理论入手,借助DEM的统一插值模型,建立了DEM两类误差（噪声误差和逼近误差）的数学表达,并分析了构成DEM误差的各个分量的数学意义。与已有的模型相比,该模型实现了传统DEM两类误差的统一描述,此外,该模型适用任意插值方式生成的格网DEM的精度评价。     

一种改进的双线性规则格网DEM内插算法

在构建高精度规则格网DEM过程中,针对双线性内插模型对地形表面的线性描述所产生的误差问题,提出了一种误差校正的方法。该方法依据待插值点邻域内的坡形以及坡度与R因子的值对双线性内插中间结果进行校正。实验结果表明,在4种不同地貌类型区域,基于误差校正的双线性内插方法精度均高于传统的双线性内插方法,在丘陵、低山、高山地区内插精度也高于自然邻近内插、反距离加权内插与普通克里格内插方法。     

基于Coons曲面的格网DEM传递误差

构造了基于边界曲线的Coons曲面DEM;研究了Coons曲面DEM的传递误差,推导出不同边界曲线构成的Coons曲面DEM模型的传递误差;得到了Coons曲面DEM的传递误差大于双线性DEM的传递误差的结论,并分析了传递误差与格网点数目的关系.     

应用地统计学和径向基函数的DEM插值

为了解决紧支撑径向基函数(CSRBF)内插生成DEM中合理设置紧支撑半径的问题,文章提出了基于地统计学和CSRBF的DEM插值方法,采用地统计学中变程的倍数来度量空间相关性的强弱,取变程的倍数设为CSRBF紧支撑半径,使得CSRBF插值矩阵呈稀疏带状分布,保证插值矩阵稳定求解,最终生成较高精度的DEM。最后以实测高程数据为例,使用交叉验证对插值方法进行实验,根据最大误差、最小误差、平均误差和均方根误差等指标进行精度分析,结果表明该插值方法精度高,插值结果可靠,可作为一种有效的DEM插值方法。     

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。     

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.     

DEM线性建模过程中的高程误差传播

在建立数字高程模型(DEM)时,基于规则格网数据和基于三角形网数据的线性建模是常用的方法。在建模过程中,结点的高程误差会随之传播。研究了DEM在基于规则格网数据和基于三角形网数据的线性建模过程中的高程误差传播问题,推导出了在结点高程误差相关情形下的高程误差传播公式,求出了在规则格网和不规则格网面上的平均高程传播误差。平均高程传播误差可以作为DEM线性插值过程中高程误差传播的度量指标。     

Robust methods for assessing the accuracy of linear interpolated DEM

Methods for assessing the accuracy of a digital elevation model (DEM) with emphasis on robust methods have been studied in this paper. Based on the squared DEM residual population generated by the bi-linear interpolation method, three average-error statistics including (a) mean, (b) median, and (c) M-estimator are thoroughly investigated for measuring the interpolated DEM accuracy. Correspondingly, their confidence intervals are also constructed for each average error statistic to further evaluate the DEM quality. The first method mainly utilizes the student distribution while the second and third are derived from the robust theories. These innovative robust methods possess the capability of counteracting the outlier effects or even the skew distributed residuals in DEM accuracy assessment. Experimental studies using Monte Carlo simulation have commendably investigated the asymptotic convergence behavior of confidence intervals constructed by these three methods with the increase of sample size. It is demonstrated that the robust methods can produce more reliable DEM accuracy assessment results compared with those by the classical t-distribution-based method. Consequently, these proposed robust methods are strongly recommended for assessing DEM accuracy, particularly for those cases where the DEM residual population is evidently non-normal or heavily contaminated with outliers.     

用等高线内插DEM的不同算法的误差分析

本文以南方丘陵地区为研究区域,利用ARCG IS软件平台,对不同的DEM内插算法的误差进行了对比研究,研究表明:不同的算法内查高程误差总体符合正态分布,且较大误差主要分布在地形结构线附近;研究还表明:在南方丘陵地区,与人们通常采用的TIN方法建立的DEM相比,ANUDEM插值生成的DEM更能够精确地模拟真实的地形。     

A causal analysis of error in viewsheds from USGS digital elevation models

Users of GIS are faced with the ongoing and difficult problem of estimating the validity of a GIS output given the uncertainty of the quality of digital mapped data. This research project examines the manner in which error from a digital elevation model (DEM) results in error in an estimate of a viewshed. The data set includes two DEMs for the same study area. A 10-metre DEM serves as the control model to test a United States Geological Survey (USGS) DEM. The amount and spatial pattern of the error in the test DEM is determined by comparing it to the control DEM. A viewshed analysis is then performed at a set of 61 sites. After determining the relative accuracy of the viewsheds thus estimated, a causal model of viewshed error is developed, which links the sources of the DEM error with the error in the viewshed. The most important factor in DEM error is terrain roughness. The error in the viewsheds is a result of the error being propagated from the DEM, with landscape characteristics of the viewpoinr playing a role due to their effect on the error in the DEM. The conceptual path model developed sets the stage for a quancitative approach that will attempt to predict viewshed error from the landscape characteristics without direct knowledge of the error in the DEM.     

Developing a Fine-Resolution Digital Elevation Model to Support Hydrological Modeling and Ecological Studies in the Northern Everglades

Accurate high-resolution terrain data are essential for hydrological modeling in lowlands. This study integrates elevation survey data and vegetation data at the point and 50 m scales to develop a fine-resolution digital elevation model (DEM) for the northern Everglades of Florida. The terrain was divided into two vertical strata (lowland and highland) based on a 50 m scale vegetation map. The DEM in highlands was interpolated with all the survey points and later adjusted using an association between vegetation and hydroperiod (the number of days per year that land is flooded). The DEM in lowlands was interpolated with elevation surveys tagged as lowland types. The two DEMs were then combined, forming a new DEM with a 7.7 cm mean absolute validation error—a significant (2.3 cm) improvement over the previous DEM.     

基于Coons曲面的规则格网DEM表面模型

内插是数字高程模型的核心问题。目前的内插模型主要是由离散的格网数据构建的连续曲面,直接以点推面,可能存在较大的地形误差。本文建立的Coons曲面DEM表面模型,首先利用离散的格网数据构造与格网边界相对应的地形剖面曲线的拟合曲线,再基于拟合曲线构建DEM表面模型。实验表明：Coons曲面DEM表面模型是一种高精度的DEM表面模型,其地形模拟误差比直接基于格网数据建立的双线性内插、样条函数内插和移动曲面拟合法的误差都小,实际地形模拟误差与双线性模型相比减少15％-28％,且精度随着构建边界拟合曲线所用格网点的增多而逐渐提高。     

A measure of average error variance of line features

This article presents a new development in measuring the positional error of line features in Geographic Information Systems (GIS), in the form of a new measure for estimating the average error variance of line features, including line segment, polyline, polygon, and curved lines. This average error measure is represented in the form of a covariance matrix derived by an analytical approach. Corresponding error indicators are derived from this matrix. The error of line features mainly results from two factors: (1) an error propagated from the original component points of line features and (2) a model error of interpolation between these points. In this study, a method of average error estimation has been derived regarding the first type error of line features that are interpolated by either linear or cubic interpolation methods. The main contribution of the research is the provision of an error measure to assess the quality of spatial data in application settings. The proposed error models for estimating average error variance of line features in a GIS are illustrated by both simulated and practical experiments. The results show that the line accuracy from a linear interpolation is better than a line interpolated using a cubic model.     

基于多方向剖面线Douglas-Pucker算法简化的DEM综合方法

文中提出一种基于多方向剖面线Douglas-Pucker(DP)算法简化的数字高程模型(DEM)综合方法,首先通过一定角度间隔旋转DEM,获得不同方向的剖面线;然后通过剖面线DP算法的简化获得特征;在此基础上,通过抑制局部极值,融合多方向的特征点,同时消除冗余;最后利用这些点构建三角网,再内插成规则DEM获得保持特征的DEM综合结果。利用两组2m格网的DEM数据进行实验,通过结果的定量和定性分析可以发现,文中方法比传统两个方向的简化方法可以获得更高精度的综合结果。     

规则格网数字高程模型的建立

基于规则格网的数字高程模型和基于不规则三角网的数字高程模型是目前数字高程模型的2种主要结构。研究了基于规则格网数字高程模型(DEM)的建模原理和方法,分析了建立DEM的精度影响,并建立了模型,实现了算法。结果表明,逐点内插法十分灵活,内插效率较高,精度较高。