Airborne light detection and ranging (lidar) is becoming a widely adopted technique for capturing elevation data, which are mainly used for creating digital terrain models (DTMs). However, the large size of lidar datasets poses a serious computational challenge to the promising radial basis function (RBF) interpolation method. In this work, to reduce the huge computational cost and improve the interpolation accuracy, random Fourier features are first introduced to approximate the Gaussian kernel of RBFs in feature space, then a random features-based weighted RBF interpolation method is developed. Based on randomized Fourier features, the nonlinear kernel-based training and evaluation of the RBF method is transformed into simple linear operations in feature space, and with the help of weighted ridge regression, the negative effect of the non-Gaussian distribution of lidar datasets on DTM production is reduced. In other words, the combination of randomized Fourier features and weighted ridge regression improves the efficiency and accuracy of the RBF interpolation method. Experiments on simulated datasets indicate that the proposed method performs better than the classical or random features-based RBF method for dealing with non-Gaussian distributed samples, with the former being slightly less accurate than the iterative RBF method due to the low-dimensional random features. However, the computational cost of the new method is much lower compared with the classical or iterative RBFs. Interpolation of airborne lidar-derived points demonstrates that the new method has a computational cost similar to the inverse distance weighting and triangulated irregular network (TIN) approaches, and is significantly faster than the ordinary kriging (OK) or thin plate spline (TPS) methods. Quantitatively, for interpolation of 644,433 points, the proposed method is approximately 833 and 21 times faster than OK and TPS, respectively. Moreover, the new method avoids the surface discontinuity artifacts presented by the OK, TPS, and TIN methods.

中文翻译：

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基于随机特征的数字地形模型高效插值方法

机载光检测和测距（激光雷达）正成为捕获高程数据的一种广泛采用的技术，该技术主要用于创建数字地形模型（DTM）。但是，激光雷达数据集的大尺寸给有希望的径向基函数（RBF）插值方法带来了严重的计算挑战。在这项工作中，为了减少巨大的计算成本并提高插值精度，首先引入随机傅立叶特征来逼近特征空间中的RBF的高斯核，然后开发了一种基于随机特征的加权RBF插值方法。基于随机傅立叶特征，基于非线性核的RBF方法训练和评估在特征空间中转化为简单的线性运算，并借助加权岭回归，减少了激光雷达数据集的非高斯分布对DTM产生的负面影响。换句话说，随机傅里叶特征和加权岭回归的组合提高了RBF插值方法的效率和准确性。在模拟数据集上进行的实验表明，该方法在处理非高斯分布样本方面比基于经典或基于随机特征的RBF方法性能更好，由于低维随机特征，前者的精度略低于迭代RBF方法。但是，与经典或迭代RBF相比，新方法的计算成本要低得多。空中激光雷达衍生点的插值表明，该新方法的计算成本与反距离加权和不规则三角网（TIN）方法相似，并且比普通克里金法（OK）或薄板样条（TPS）方法要快得多。从数量上讲，对于644433个点的插值，所提出的方法分别比OK和TPS快833和21倍。而且，新方法避免了由OK，TPS和TIN方法呈现的表面不连续伪影。