Integrative Study of Voronoi-Delaunay Spatial Tessellation and Spatial Statistics

Voronoi-Delaunay空间细分与空间统计的综合研究

基本信息

批准号：
17500188
负责人：
TANEMURA Masaharu
金额：
$ 2.37万
依托单位：
The Institute of Statistical Mathematics
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2007
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17500188/
关键词：
Voronoi-Delaunay analysis Aftershock activity Spatial-temporal data Langerhans cell Spatial tessellation of a sphere Morphological analysis Map data of trees Super-computer system 全地球規模余震活動球面ボロノイ・デローネイ分割 MCMCによる近似尤度第k近接距離ポアソン・ボロ

项目摘要

When a number of particles are distributed in a finite region in the space, it is the important role of spatial statistics to extract the information of statistical properties of the given spatial data and to provide an appropriate result which is useful to the scientific field corresponding to the observed data. On the other hand, there is a method of analyzing spatial data, called Voronoi-Delaunay analysis, which produces the spatial information of a given configuration of particles as a statistical distribution of the shape of Voronoi cells or Delaunay cells which are obtained by the tessellation of observed area. But, hitherto, Voronoi-Delaunay analysis was limited as a supplementary tool of the spatial statistics. In this research project, however, we aimed to positively integrate the Voronoi-Delaunay analysis to the spatial statistics by utilizing the former as a tool for extracting detailed information about the spatial data and by utilizing the results of the analysis as means … More of constructing various statistical models.In the study of statistical distribution of Poisson Voronoi cells, we obtained accurate statistical distributions of several characteristics of Poisson Voronoi cells in 4-D and 5-D spaces, and presented them as prototypes of multivariate spatial statistics. Then, we performed computations of Voronoi-Delaunay tessellation of a large scale spatial-temporal data. This is concerned with records of aftershocks of earthquakes in Japan, and the data is composed of latitude, longitude and time (3-dimensional) for each event. Data size is about 560, 000, and in order to perform the computation of 3-D Voronoi-Delaunay tessellation for such a big size of data, we used the Super-Computer system Altix of ISM for main computation and the UNIX workstation which was introduced by this project for implementing and checking computer programs.In order to make a list of Delaunay cells for such a big data, we have developed an efficient program. Further, we have prepared the Voronoi-Delaunay analysis of aftershocks of earthquakes for whole of the earth. For this computation, we need a computer program of Voronoi-Delaunay tessellation on the sphere. We have already devised such a program.Finally, we have performed Voronoi-Delaunay tessellation for spatial point patterns of Langerhans cells in a skin tissue of mouse and for spatial point patterns of pine trees in a wild situation. Less

当多个粒子分布在空间的有限区域时，空间统计学的重要作用是提取给定空间数据的统计特性信息，并提供对相应科学领域有用的适当结果。另一方面，有一种分析空间数据的方法，称为 Voronoi-Delaunay 分析，它产生给定粒子配置的空间信息，作为 Voronoi 单元或 Delaunay 单元形状的统计分布。获得的但是，迄今为止，Voronoi-Delaunay 分析作为空间统计的补充工具受到限制，然而，在本研究项目中，我们的目标是利用前者将 Voronoi-Delaunay 分析积极地整合到空间统计中。一种提取空间数据详细信息的工具，并利用分析结果作为构建各种统计模型的手段。在泊松沃罗努单元的统计分布研究中，我们获得了准确的统计分布泊松沃罗诺单元在 4 维和 5 维空间中的几个特征，并将它们作为多元空间统计的原型，然后，我们对大规模时空数据进行了 Voronoi-Delaunay 曲面细分的计算。日本地震余震的数据由纬度、经度和时间（3维）组成，每个事件的数据大小约为560, 000，为了对如此大的数据量进行3D Voronoi-Delaunay曲面细分的计算，我们使用ISM的超级计算机系统Altix进行主要计算，并使用本项目引入的UNIX工作站来实现和检查计算机为了制作如此大数据的 Delaunay 单元列表，我们开发了一个有效的程序，此外，我们还准备了地震余震的 Voronoi-Delaunay 分析。对于整个地球的计算，我们需要一个在球体上进行 Voronoi-Delaunay 曲面细分的计算机程序。我们已经设计了这样一个程序。最后，我们对皮肤中的朗格汉斯细胞的空间点图案进行了 Voronoi-Delaunay 曲面细分。小鼠组织和野生环境下松树的空间点图案。