DEM若干理论问题思考

对用中误差描述和评价DEM整体精度的DEM随机误差观提出质疑,认为DEM是由带随机误差的原始数据内插而成,DEM误差就应由性质不同的两部分误差组成,即测绘所产生的随机误差和内插所产生的对地表曲面的逼近误差,二者可分别进行质量控制,对于内插误差,应采用定义域内的全部点是否符合最大绝对偏差的一次性否决法进行检验.通过讨论三维地面概念模型和DEM高保真问题等概念,说明DEM误差以随机误差概而论之的实质是漠视了DEM高保真这一质量要求;并结合地图代数研究,论述等高线族和地形结构线族的空间几何对偶关系———后者是前者的广义Voronoi界线,因此,当利用等高线数据生产DEM时,并不存在选择性采样F-S数据的必要.

Some problems of DEM error theory

DEM precision is almost expressed and accessed in form of random error.This paper argues against it and expounds that DEM error should consist of two parts: one part is the random error of DEM original data,which is inevitably caused by survey and mapping.The other part is approximation error produced by DEM interpolation.These two types of error request the totally different check-up standards and improving approaches and they should be treated respectively.DEM interpolation error should be accessed by the standard that the errors of all DEM points are less than the maximal absolute deviation.Concretely,by introducing the concept model of landform surface and discussing the problem of high fidelity DEM,the paper points out that the error analysis method in which DEM error is discussed as the random error only disregards the quality demand about high fidelity DEM.In addition,combining map algebra research,the paper explains that there is a determinate spatial geometry relation between contour family and terrain structure line family,and the later is the broad sense Voronoi borderlines of the former.Therefore,F-S data is unnecessary when using contour data to produce DEM.