面向大规模交互数据空间划分的Voronoi图生成算法及应用

传统Voronoi图对大量点集进行Voronoi划分时会产生Voronoi单元格数过多的现象,导致难以适用于地理信息系统、生物医学等诸多领域。为了解决这个问题,提出一种自适应基于密度的聚类算法(Density-Based Spatial Clustering of Applications with Noise, DBSCAN)的Voronoi图。阐述了Voronoi单元合并的现象,证明了其发生的充要条件,提出该Voronoi图的生成算法并进行仿真。通过显微镜下嗜中性粒细胞、我国地表火点数据对算法进行验证,结果表明,该算法能够有效解决点集规模较大时,Voronoi图划分过于细致的问题,突破了传统Voronoi图单点对单点的划分形式。此外,该算法拓宽了Voronoi图在图形图像处理、生物医学、地理信息系统等领域的应用。

Voronoi diagram generation algorithm and application for large-scale interactive data space partition

When the traditional Voronoi diagram divides a large number of point sets into Voronoi, there are too many Voronoi cells, which makes it difficult to apply to such fields as geographic information systems and biomedicine. In order to solve this problem, a Voronoi diagram based on adaptive DBSCAN (density-based spatial clustering of applications with noise) was proposed. The phenomenon of Voronoi unit merge was explained. The necessary and sufficient conditions for its occurrence were proved. The algorithm for generating the Voronoi diagram was proposed and simulated. In order to verify its effectiveness, the algorithm was applied to neutrophils under the microscope and fire point data on the surface of China. The results show that the algorithm can effectively solve the problem that Voronoi diagram is too meticulous when the point set size is large, which breaks through the single point to single point division form of the traditional Voronoi diagram. In addition,the algorithm broadens the application of Voronoi diagrams in the fields of graphic image processing,biomedicine and geographic information systems.