空间点模式是一个2维离散点集,点集中的每一个元素代表地球表面一个点状目标的空间位置.当2维离散点集具有集聚特征时,称其为集聚型空间点模式,它与空间聚类、制图综合和空间分析的许多具体应用紧密相关.如何提取集聚型空间点模式的结构信息(集聚子群的个数和对应的集聚中心)是其中尚未彻底解决的问题.作者以几何概率为理论基础,提出测度正方形区域内2维离散点集分布特征的H函数并推导其解析表达式,运用H函数设计和实现了集聚型2维离散点集结构信息提取的通用算法.利用该算法处理一个由居民地坐标数据得到的具有集聚特征的空间点模式,提取出其结构信息并进行可视表达.分别以该空间点模式中的各离散点为顶点和发生元生成Delaunay三角网和Voronoi图,在Delaunay三角网中保留面积最小的前1/10、前1/100三角形的顶点,在Voronoi图中保留面积最小的前1/10、前1/100邻近多边形的发生元,将可视表达的点集结构信息分别与依据Delaunay三角网和Voronoi图得到的结果进行对比分析.结果表明,运用H函数能够有效地提取出集聚型空间点模式的全局性结构信息,而Delaunay三角网和Voronoi图虽然能够反映其局部密度,但在提取全局结构信息时存在局限性.%Although point patterns have been intensively studied, the problem of how to extract the structure information from a clustered spatial point pattern still remains. The author put forth the H function, which is capable of measuring the distributive characteristics of a two dimension discrete point set in a square, and derives its analytical expression theoretically based on geometric probability. Then a general algorithm to extract the structure information of a two dimension discrete point set is designed and implemented by means of H function. Subsequently the algorithm is employed to process a clustered spatial point pattern consisting of real residential coordinate data. Its structure information is derived and visualized. After that, generate the Delaunay Triangulation and Voronoi Diagram of the same spatial point pattern respectively, keep the vertices of 1/10 and 1/100 Delaunay triangles with the least area in the point set to form two graphs, and keep the generators of 1/10 and 1/100 Voronoi polygons with the least area in the point set to form another two graphs, make a contrast between the result of the algorithm with each of the four graphs. It turns out that although Delaunay Triangulation and Voronoi Diagram are capable of indicating the local point density of a clustered spatial point pattern, they are explicitly limited in terms of extracting its structure information, while the algorithm introduced in this article can effectively perform doing so.
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