Bias estimation and correction for triangle-based surface area calculations
Bias estimation and correction for triangle-based surface area calculations
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基于三角形的表面积计算的偏差估计和校正
DOI：
10.1080/13658816.2016.1162795
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发表时间：
2016-11
影响因子：
5.7
通讯作者：
Dong Chun
中科院分区：
文献类型：
--
作者：
Xue Shuqiang;Dang Yamin;Liu Jiping;Mi jinzhong;Dong Chun
表面积的计算对于各种各样的空间填充现象，例如在一个土地区域内植物或动物的堆积，都是有意义的。利用数字高程模型（DEM）数据，我们可以使用连续曲面模型（如不规则三角网（TIN））来计算地表面积。然而，正如本文讨论的基于三角形的表面积一样，由于它是对包含测量误差的DEM数据的非线性映射，因此表面积通常是有偏的。为了减少表面的偏置，我们提出了一种二阶偏置校正方法，通过将非线性误差传播到基于三角形的表面。这一过程表明，DEM数据中的随机误差导致了基于三角形的表面积的偏差，而DEM数据中的系统误差可以通过利用高差来减小。偏差在理论上由概率积分给出，该概率积分可以用数值方法逼近，包括数值积分和蒙特卡罗方法；但这些方法需要对DEM测量误差的理论分布假设，且计算成本很高。在大多数情况下，我们只有测量误差的方差信息；因此，提出了一种基于非线性误差传播的偏差估计方法。在二阶偏差估计的基础上，通过去除原始方差估计中的偏差，可以立即改善表面积方差。通过蒙特卡罗方法和数值积分对主要结果进行了验证。他们表明，通过从原始从DEM数据计算的基于三角形的表面积中去除所提出的偏差估计，可以获得无偏表面积。
ABSTRACT The calculation of surface area is meaningful for a variety of space-filling phenomena, e.g., the packing of plants or animals within an area of land. With Digital Elevation Model (DEM) data we can calculate the surface area by using a continuous surface model, such as by the Triangulated Irregular Network (TIN). However, just as the triangle-based surface area discussed in this paper, the surface area is generally biased because it is a nonlinear mapping about the DEM data which contain measurement errors. To reduce the bias in the surface area, we propose a second-order bias correction by applying nonlinear error propagation to the triangle-based surface area. This process reveals that the random errors in the DEM data result in a bias in the triangle-based surface area while the systematic errors in the DEM data can be reduced by using the height differences. The bias is theoretically given by a probability integral which can be approximated by numerical approaches including the numerical integral and the Monte Carlo method; but these approaches need a theoretical distribution assumption about the DEM measurement errors, and have a very high computational cost. In most cases, we only have variance information on the measurement errors; thus, a bias estimation based on nonlinear error propagation is proposed. Based on the second-order bias estimation proposed, the variance of the surface area can be improved immediately by removing the bias from the original variance estimation. The main results are verified by the Monte Carlo method and by the numerical integral. They show that an unbiased surface area can be obtained by removing the proposed bias estimation from the triangle-based surface area originally calculated from the DEM data.
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影响因子：
1.6
作者：
I. Gillissen
通讯作者：
I. Gillissen
影响因子：
1.3
作者：
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通讯作者：
S. Wechsler;C. Kroll
DOI：
--
发表时间：
2009
期刊：
--
影响因子：
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DOI：
10.1111/j.2517-6161.1971.tb00871.x
发表时间：
1971-07
期刊：
Journal of the royal statistical society series b-methodological
影响因子：
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作者：
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通讯作者：
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影响因子：
3.3
作者：
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