引用本文: 杨海, 王船海, 马腾飞, 郭伟建. 方差-尺度规律在DEM插值方法评价中的应用[J]. 武汉大学学报 ( 信息科学版), 2016, 41(12): 1605-1612.
YANG Hai, WANG Chuanhai, MA Tengfei, GUO Weijian. Application in Accuracy Assessment for DEM Interpolation Methods Based on a Variance-scale Law[J]. Geomatics and Information Science of Wuhan University, 2016, 41(12): 1605-1612.
 Citation: YANG Hai, WANG Chuanhai, MA Tengfei, GUO Weijian. Application in Accuracy Assessment for DEM Interpolation Methods Based on a Variance-scale Law[J]. Geomatics and Information Science of Wuhan University, 2016, 41(12): 1605-1612.

Application in Accuracy Assessment for DEM Interpolation Methods Based on a Variance-scale Law

• 摘要: 提出基于方差-尺度规律的新型插值方法评价体系，根据“在给定研究区域内，变量的统计方差随尺度增大而减小”的理论规律，提出三项预设的评价准则。以DEM插值应用为例，选取高精度曲面模型、样条插值、克里金插值、反距离权重插值4种方法进行对比评价。数值实验表明，方差-尺度递变趋势的评价准则值得存疑。两组DEM插值案例表明，地形的复杂特性、插值算子的光滑效应以及尺度的综合效应致使理论的渐变规律无法达到。引入采样方差值后，不同采样密度下仍可以将方差变化趋势及方差的整体大小作为精度评价准则，在对第二、第三条预设评价准则修缮后确立三项评价准则。综合所有案例可知，此评价体系原理简单、操作方便，为DEM插值方法评价提供了一套新的标准和框架，并且可针对不同采样密度条件提出完善的插值方法适用性建议。

Abstract: A new accuracy assessment framework for interpolations, based on a variance-scale law, is proposed in this paper. Based findings in different research areas, it has been shown that the variance of a certain variable decreases with agrowing scale. According to this theoretical law, three presupposed assessment criteria have been proposed. Application cases in DEM interpolation were selected and four common methods, i.e., HASM, Spline, Kriging, and IDW were chosen for comparison in this new framework. The second assessment criterion, regarding changing trends, was found to be questionable in a numerical test. The results of two real-world DEM interpolation cases indicate that the theoretical changing trend in the variance-scale relation cannot be obtained in real terrain cases because of an complicated integrated effects, characteristic of the real-world terrain, and the smoothing effect of interpolators and interpolation scales. However, as the original sampling variance was introduced into the framework, the general changing trend of variances and the overall level of variances at most scales could still be used as accuracy assessment measures even under different sampling densities. After modifying the second and the third criterion, the final three criteria in this assessment framework were established. Both the numerical surface case and real-world DEM examples indicate that this assessment framework is simple in theory, convenient for usie, and is an objective and effective assessment method, widening the field of accuracy assessment in DEM interpolation. Moreover, based on the results of different sampling densities, this framework can also provide valuable application suggestions for choosing suitable interpolation methods in real-world cases.

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