顾及特征水深点距离重分配的反距离加权插值算法

Inverse distance weighted interpolation with the consideration of distance redistribution of characteristic depth points

中文关键词:  特征水深点  距离重分配  反距离权重插值  空间内插

英文关键词:feature depth point  distance redistribution  IDW  spatial interpolation

中文摘要:

      水深是反映海底地形地貌的最基础要素，对缺失的水深点进行准确的插值能帮助有效地表达海底地形地貌起伏形态。针对海底地形变化复杂的区域，传统的反距离加权插值法存在只考虑样本水深点与待插值水深点之间的距离，而忽略了样本水深点之间的空间相关性的问题。本文提出了一种顾及特征水深点距离重分配的反距离加权插值算法。该算法首先对离散的水深点构建特征水深线，在特征水深线的基础上，提取特征水深线上的特征点作为特征水深点；然后在所有样本水深点到待插值水深点距离之和不变的约束下，提出距离重分配的量化指标；最后构造出一个顾及特征水深点距离重分配的 IDW插值算法模型。实验结果表明，在海底地形变化复杂的区域，顾及特征水深点距离重分配的反距离加权插值算法与传统的IDW、自然邻域插值、样条函数插值算法等相比，能有效提高水深点的插值精准度。

英文摘要:

      Water depth is the most basic element that reflects the seabed topography, and accurate interpolation of the missing depth points can effectively reflect the undulations of the seabed topography. For areas with complex seabed topography, the traditional inverse distance weighted interpolation method only considers the distance between the sample water depth point and that to be interpolated, and ignores the problem of the spatial correlation between the sample water depth points. This paper proposes an inverse distance weighted interpolation algorithm that takes into account the distance redistribution of feature water depth points. The algorithm first constructs a feature water depth line for discrete water depth points, and extracts the feature points on the feature water depth line as the feature water depth points. Then the sum of the distances from all the sample water depth points to the water depth point to be interpolated remains unchanged under the constraints of the quantitative index of distance redistribution is proposed. Finally, an IDW interpolation algorithm model that takes into account the distance redistribution of feature water depth points is constructed. Experimental results show that in areas with complex seabed terrain changes, the inverse distance weighted interpolation algorithm, which takes into account the distance redistribution of characteristic water depth points, can effectively improve water depth points compared with traditional IDW, natural neighborhood interpolation,and spline function interpolation algorithms.