基于马氏距离的多高斯Voronoi图生成方法  

A Generating Method of Multi-Gaussian Voronoi Diagram Based on Mahalanobis Distance

作　　者：康顺[1] 相诗尧[1] 

机构地区：[1]中国矿业大学(北京)地球科学与测绘工程学院,北京100083

出　　处：《地理与地理信息科学》2016年第3期49-52,共4页Geography and Geo-Information Science

基　　金：中央高校基本科研业务费专项资金项目(2010YD06)

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。Voronoi diagram not only is regarded as one of the most popular data structure in computational geometry,but also an advantageous tool in geospatial analysis,and provided with extensive applications in all fields of science and engineer.In terms of the equal weight values being possessed by each generating cell of Voronoi diagram,and the one-to-one relationship data structure limitation between generating cell and its corresponding Voronoi diagram produced by traditional Euclidean distance,from viewpoint of the statistical distance of Gaussian distribution,a new Voronoi diagram,namely Multi-Gaussian Voronoi Diagram,abbr.MGVD,is proposed in this paper based on Mahalanobis distance,which is utilized as the distance measure.The MGVD includes the generalization method of ordinary Voronoi and weighted Voronoi diagram based on Euclidean distance.Moreover,the MGVD extends the data structure between generating cell and its corresponding Voronoi diagram from one-to-one relationship in space to that one-to-many,which makes the spatial existence of multi-Voronoi diagram which belongs to a single generating cell.Last but not least,the method was proved to be feasible by simulation experiments.

关 键 词：欧氏距离 马氏距离 多高斯 VORONOI图 一对多关系 

分 类 号：P208[天文地球—地图制图学与地理信息工程]