A Robust Multiquadric Method for Digital Elevation Model Construction
A Robust Multiquadric Method for Digital Elevation Model Construction
复制标题
数字高程模型构建的鲁棒多重二次方法
DOI：
10.1007/s11004-013-9451-8
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发表时间：
2013-04-01
影响因子：
2.6
通讯作者：
Li, Yanyan
中科院分区：
文献类型：
--
作者：
Chen, Chuanfa;Li, Yanyan
多次二次插值方法具有较高的插值精度，在空间数据插值中得到了广泛的应用。然而，MQ是一种精确插值方法，不适合插值有噪声的采样数据。尽管最小二乘MQ （LSMQ）具有平滑采样误差的能力，但由于在估计采样节点的权重时采用最小二乘准则，因此它对异常值的鲁棒性不足。为了降低异常值对数字高程模型精度的影响，提出了一种鲁棒的MQ （MQ- r）方法。MQ-R包括两个独立的过程：结点选择和线性方程组的求解。这两个独立的过程分别通过空间填充设计和最小的绝对偏差来实现，两者都对异常值具有很强的鲁棒性。利用具有一系列不同分布误差的高斯合成曲面，对MQ-R和LSMQ的性能进行了比较。结果表明，LSMQ算法受到异常点的严重影响，而MQ-R算法具有良好的抗异常点能力，即使数据受到严重异常点的污染，也能构造出令人满意的曲面。以实际的DEM构建为例，对MQ-R、LSMQ和经典插值方法（包括逆距离加权法、薄板样条法和ANUDEM）的鲁棒性进行了评价。结果表明，与经典方法相比，MQ-R在均方根误差方面具有最高的精度。综上所述，当采样数据存在异常值时，MQ-R可以作为DEM构建的替代方法。
The multiquadric method (MQ) with high interpolation accuracy has been widely used for interpolating spatial data. However, MQ is an exact interpolation method, which is improper to interpolate noisy sampling data. Although the least squares MQ (LSMQ) has the ability to smooth out sampling errors, it is inherently not robust to outliers due to the least squares criterion in estimating the weights of sampling knots. In order to reduce the impact of outliers on the accuracy of digital elevation models (DEMs), a robust method of MQ (MQ-R) has been developed. MQ-R includes two independent procedures: knot selection and the solution of the system of linear equations. The two independent procedures were respectively achieved by the space-filling design and the least absolute deviation, both of which are very robust to outliers. Gaussian synthetic surface, which is subject to a series of errors with different distributions, was employed to compare the performance of MQ-R with that of LSMQ. Results indicate that LSMQ is seriously affected by outliers, whereas MQ-R performs well in resisting outliers, and can construct satisfactory surfaces even though the data are contaminated by severe outliers. A real-world example of DEM construction was employed to evaluate the robustness of MQ-R, LSMQ, and the classical interpolation methods including inverse distance weighting method, thin plate spline, and ANUDEM. Results showed that compared with the classical methods, MQ-R has the highest accuracy in terms of root mean square error. In conclusion, when sampling data is subject to outliers, MQ-R can be considered as an alternative method for DEM construction.