[1]王金鑫,秦子龙,曹泽宁,等.基于八叉树的修正克里金空间插值算法[J].郑州大学学报(工学版),2021,42(06):22-28.[doi:10.13705/j.issn.1671-6833.2021.06.004]
　WANG Jinxin,QIN Zilong,CAO Zening,et al.Modified Kriging Spatial Interpolation Algorithm Based on Octree Mechanism[J].Journal of Zhengzhou University (Engineering Science),2021,42(06):22-28.[doi:10.13705/j.issn.1671-6833.2021.06.004]

点击复制

基于八叉树的修正克里金空间插值算法()

分享到：

《郑州大学学报(工学版)》[ISSN:1671-6833/CN:41-1339/T]

卷:

42卷

期数:

2021年06期

页码:

22-28

栏目:

出版日期:

2021-11-10

文章信息/Info

Title:

Modified Kriging Spatial Interpolation Algorithm Based on Octree Mechanism

作者:

王金鑫; 秦子龙; 曹泽宁; 陈艺航; 石焱

郑州大学地球科学与技术学院;郑州大学水利科学与工程学院;

Author(s):

WANG Jinxin1;  QIN Zilong2;  CAO Zening2;  CHEN Yihang2;  SHI Yan2

School of Earth Science and Technology of Zhengzhou University; School of Water Conservancy Science and Engineering, Zhengzhou University;

关键词:

八叉树; 克里金插值; 点密度; 点空间分布; 三维地质建模

Keywords:

octree;  Kriging interpolation;  point density;  point spatial distribution;  3D geological modeling

DOI:

10.13705/j.issn.1671-6833.2021.06.004

文献标志码:

A

摘要:

针对空间插值算法中需合理设置待插值点的邻域搜索，并考虑空间分布问题，本文提出了一种基于八叉树的空间插值邻域搜索策略。首先，构建采样点的最小外包围盒并对其进行八叉树剖分，将采样点各自归于剖分后的包围盒中；然后，对待插值点进行邻域点搜索，并通过定义点密度来约束待插值点的空间分布；最后，对于空间内任意待插点，将上述的邻域搜索策略应用到普通克里金插值模型中进行空间插值，并将本文方法与传统的空间插值方法进行对比实验。结果表明：本文方法在插值精度与效率上均优于传统方法，且能保证插值点在空间分布的均匀性，数据冗余较少，可应用于各类基于离散点的空间插值场景与插值算法中，是一种可靠的空间插值算法。

Abstract:

Neighborhood search is an important step in the spatial interpolation algorithm. Whether the neighborhood range is properly selected has a great impact on the interpolation efficiency and accuracy. Aiming at the problem that there were few studies on neighborhood search of interpolation algorithm, a neighborhood search strategy based on octree considering the spatial distribution of discrete points was proposed in this paper. Firstly, the minimal enclosing box of the sampling points was constructed and divided with octree, and the sampling points were grouped into each divided box. Then, the spatial distribution of the interpolating points was constrained by defining the point density. Finally, the above neighborhood search strategy is applied to the ordinary Kriging interpolation model. In order to verify the feasibility of the proposed method, in true 3D geological modeling, the proposed algorithm of this paper, the conventional Kriging interpolation based on fixed distance and fixed number strategy, and the inverse distance weighted interpolation were all used to calculate respectively, and the geological model was constructed from the data obtained from the interpolation. By comparing the method of this paper with the traditional spatial interpolation methods, it was concluded that the proposed method was superior to the traditional method in interpolation accuracy and efficiency when the same number of points were obtained under the same conditions, except for the fixed number method of 30 sample points. Although the fixed number method of 30 sample points had a slight advantage in accuracy, its calculation time is 6.6 times longer than that of the proposed method. In addition, the proposed method improved the time by 20% compared with the traditional method under the same conditions. Compared with the traditional method, the proposed method reduced the redundancy by nearly 1/3 when using the interpolated data to construct the geological model at the same level, thus improving the efficiency of calculation.

常用功能