基于马氏距离的多高斯Voronoi图生成方法

发布时间：2018-02-12 17:07

  本文关键词： 欧氏距离 马氏距离 多高斯 Voronoi图 一对多关系　出处：《地理与地理信息科学》2016年03期 　论文类型：期刊论文

【摘要】：Voronoi图作为一种重要的几何结构,不仅是计算几何研究的重要内容,还是地理空间分析的有力工具,在科学与工程领域应用广泛。针对传统欧氏距离条件下Voronoi图生长元权值大小等同、生长元与Voronoi图数据结构一对一关系的局限性,该文以高斯分布的统计距离为切入点,利用马氏距离作为Voronoi图生成距离测度,提出一种新的Voronoi图,即多高斯Voronoi图(MGVD)。MGVD不但囊括了欧氏距离作用下产生的普通Voronoi图与加权Voronoi图,而且将生长元与Voronoi图数据结构的一对一关系拓展为空间的一对多关系,表现出单个空间生长元的多个Voronoi图存在。最后,通过模拟实验验证了该方法的可行性。
[Abstract]:The Voronoi map is an important geometric structure, is not only an important part of research in computational geometry, is a powerful tool for the analysis of geographic space, widely used in the fields of science and engineering. The traditional Euclidean distance under the condition of Voronoi growth element weights equal growth element and Voronoi graph data structure is a one-to-one relationship limitation. In this paper, the statistical distribution of Gauss distance as the starting point, use the Mahalanobis distance as the distance measure to generate Voronoi diagram, this paper proposes a new Voronoi map, which Gauss Voronoi (MGVD).MGVD not only include the ordinary Voronoi diagram Voronoi diagram and generate Euclidean distance under the action, and the growth of yuan and the relationship between development of one to many relationships for spatial data structures of Voronoi, showing a number of Voronoi yuan in the presence of a single space growth chart. Finally, the simulation results verify the feasibility of the method.

【作者单位】： 中国矿业大学(北京)地球科学与测绘工程学院;
【基金】：中央高校基本科研业务费专项资金项目(2010YD06)
【分类号】：P208
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本文编号：1506134