引用本文: 高原, 朱娅男, 陈传法, 胡占占, 胡保健. 高精度DEM建模的加权径向基函数插值方法[J]. 武汉大学学报 ( 信息科学版), 2023, 48(8): 1373-1379.
GAO Yuan, ZHU Yanan, CHEN Chuanfa, HU Zhanzhan, HU Baojian. A Weighted Radial Basis Function Interpolation Method for High Accuracy DEM Modeling[J]. Geomatics and Information Science of Wuhan University, 2023, 48(8): 1373-1379.
 Citation: GAO Yuan, ZHU Yanan, CHEN Chuanfa, HU Zhanzhan, HU Baojian. A Weighted Radial Basis Function Interpolation Method for High Accuracy DEM Modeling[J]. Geomatics and Information Science of Wuhan University, 2023, 48(8): 1373-1379.

## A Weighted Radial Basis Function Interpolation Method for High Accuracy DEM Modeling

• 摘要: 在数字高程模型（digital elevation model，DEM）建模过程中，经典空间插值方法均没有考虑断裂线附近的局部地形特征影响，使得断裂线局部区域高程被平滑，从而导致地形特征失真。为了解决该问题，构造了一种顾及断裂地形特征的定权方法，并以径向基函数（radial basis function，RBF）为插值算子，提出了加权径向基函数方法。首先通过捕捉每个采样点的结构张量，自适应计算采样点与待求点的距离，然后利用该距离对每个采样点赋予合适的权重，最后利用加权插值实现DEM建模。以10组国际摄影测量和遥感学会公共数据和1组山体滑坡区域的机载激光雷达点云数据为例，利用所提方法构建样区DEM，并将计算结果与标准RBF及传统插值算法（如反距离加权法、克里金法、约束不规则三角网法）进行比较。精度分析表明，不论采样点数为多少，所提方法计算精度均优于其他插值方法；对DEM山体阴影图分析表明，相较于传统插值方法，所提方法能较好地保持断裂线局部地形特征。

Abstract:
Objectives  In the process of digital elevation model (DEM) modeling, the existing interpolation methods do not take into account the local topographic characteristics near the breaklines, which makes the elevation of the local area of the breakline smoothed, thus leading to topographic distortion. A weight function with respect to considering the characteristics of breaklines is constructed, and a weight radial basis function (RBF) method is proposed. The proposed method makes full use of the gradient and direction information of the sampling points near the fracture line.
Methods  First, the distance between the sampling point and the point to be sought is calculated adaptively by capturing the structure tensor of each sampling point, and then the distance is used to assign a suitable weight to each sampling point, finally the DEM modeling is realized by using weighted interpolation.
Results  Examples on 10 public data and 1 private dataset of DEM construction with airborne light detection and ranging (LiDAR) point clouds indicates that the calculation results of each interpolation method gradually decrease with the decrease of sampling points. Compared to RBF and the classical interpolation methods including inverse distance weighting, ordinary Kriging and constrained triangulated irregular network, our proposed method has a better ability to maintain terriain features in the breakline area. Regardless of sample density, our proposed method is always more accurate than the other methods.
Conclusions  Overall, the proposed method with the merit of terrain feature preservation is helpful for the construction of high-accurate DEMs, which play an important role in some geoscience applications with data quality as the most important factor.

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