基于Voronoi图的空间关系计算研究
摘要
空间关系在地理信息系统(GIS)空间数据建模、空间查询、空间分析、空间推理、制图综合、地图理解等过程中起着重要的作用，因此对空间关系的计算与理解是地理信息科学发展的关键问题之一。目前，国际上主要采用基于点集拓扑学的9交(9-Intersection)方法进行GIS空间关系计算的研究与应用，然而由于该方法却存在着理论与实际方面的缺陷与不足。鉴于此，本文就GIS的空间关系计算这一关键问题进行了探索与尝试。
本文首先系统总结了国内外主要的GIS空间关系计算的方法与模型，对其进行了分类研究，分析了各类方法的主要优点与不足；在此基础之上，本文针对GIS空间数据的特征，以空间认知、拓扑学、集合代数与计算几何为主要理论依据，提出使用空间目标的整体及其Voronoi区域，应用基本的集合算子进行空间关系计算的VW方法。
该方法是利用空间目标整体及其Voronoi区域判断空间关系，以集合运算构造空间关系代数算子，而操作算子之值是空／非空、维数、连通数、面积、长度及其组合。其不仅克服了现有空间关系计算方法理论上的不足，而且可以方便地同时从多个角度量测空间关系的定量与定性信息，具有较强的综合性、可计算性与可操作性，从而为空间关系计算的研究提供了一个新的思路与尝试。
为了利用新的方法进行空间关系计算，首先需要计算空间目标的Voronoi图，为此本文对Voronoi图的生成与维护进行了研究，提出了基于主动生长技术的栅格Voronoi图的动态生成及维护方法，并针对Voronoi图的特点，发展了基于栅格虚拟四边界的Voronoi边界的提取与矢量化方法，为空间关系的进一步计算奠定了基础。
然后本文利用VW方法的基本原理，对拓扑关系、方向关系、邻近关系进行了研究：提出了基于目标整体及其Voronoi图与多项集合算子的拓扑关系四元组计算模型V4T，并利用该模型给出了计算拓扑关系的具体方法与步骤；接着依据VW方法的基本策略，探讨了方向关系中的主方向关系与左右关系的计算问题，通过以观察者作为方向参考系，建立方向区域，利用Voronoi区域的分布建立了两目标之间的主方向分布与主方向关系的计算模型，并通过建立左右Voronoi区域构建了左右关系的计算模型；提出了Voronoi K阶邻近的概念，发展了Voronoi K阶邻近的波浪计算法、对向计算法与穿越计算法，并指出Voronoi K阶邻近的有序性、度量性与局域拓扑性。
最后，作者以VC++作为开发工具，运用面向对象的方法，基于COM技术从底层独立开发研制了基于Voronoi图的空间关系计算工具VTKit，并以实际的空间数据为例对本文所提出的计算方法与模型进行了实验，有力地验证了作者所提出的计算方法与模型的合理性与可行性。
Spatial relations are one of the most distinctive aspects of spatial or geographical information, and thus a better understanding of the cognitive aspects of spatial relations, and their formalization in computational models, is critical to the advancement of geographical information science.
Currently, 9-intersection method is most popular to be used for the studies and applications of spatial relations in CIS field. However, there are some imperfections and deficiencies in theory and practice in this method, such as the paradox of topological definition, linear dependency of three components of an object and worse computability and so on. To overcome the limitations of this method and other related methods and models and improve the current methods and models for spatial relations, a new method, simply called VW method for the computation of spatial relations is presented in this thesis.
In this method, a spatial object is treated as a whole, the Voronoi region of an object is employed to enhance its interaction with its neighbors, and appropriate operators from set operators and several types of values are utilized to compute the spatial relations spatial objects. The new approach can overcome the shortcomings of existing methods and presents a framework for computing different spatial relations.
In order to use this method more efficiently, Voronoi diagrams should be generated and maintained dynamically at first. So a new raster based method is described for generating and maintaining Voronoi diagrams dynamically with active region growing technology, and also a method based on virtual four boundaries for conversion of raster Voronoi regions into vector is presented.
And then three different types of spatial relations are computed using the new method for spatial relations: for topological relations, a formal computational model called V4T model is presented, and the strategies and steps are developed based on this model; for main direction relations, the distribution of Voronoi regions is used to establish a formal model; for left and right relations, the computation is performed by constructing the directed Voronoi regions; for spatial neighboring relations, the concept of neighbor is extended and Voronoi K order neighbor is introduced to define and compute different neighobring relations within one conceptual framework, also three algorithms are presented to compute the order of neighboring relations.
Finally, a tool VTKit for the computation of spatial relations and Voronoi diagram and related applications is developed independently to examine the new method and models for spatial relations using VC++ and COM technology on the platform of Windows 2000. Experimental results with the practical and simulated spatial data show the reasonability and practicability of the new method for spatial relations.
本文首先系统总结了国内外主要的GIS空间关系计算的方法与模型，对其进行了分类研究，分析了各类方法的主要优点与不足；在此基础之上，本文针对GIS空间数据的特征，以空间认知、拓扑学、集合代数与计算几何为主要理论依据，提出使用空间目标的整体及其Voronoi区域，应用基本的集合算子进行空间关系计算的VW方法。
该方法是利用空间目标整体及其Voronoi区域判断空间关系，以集合运算构造空间关系代数算子，而操作算子之值是空／非空、维数、连通数、面积、长度及其组合。其不仅克服了现有空间关系计算方法理论上的不足，而且可以方便地同时从多个角度量测空间关系的定量与定性信息，具有较强的综合性、可计算性与可操作性，从而为空间关系计算的研究提供了一个新的思路与尝试。
为了利用新的方法进行空间关系计算，首先需要计算空间目标的Voronoi图，为此本文对Voronoi图的生成与维护进行了研究，提出了基于主动生长技术的栅格Voronoi图的动态生成及维护方法，并针对Voronoi图的特点，发展了基于栅格虚拟四边界的Voronoi边界的提取与矢量化方法，为空间关系的进一步计算奠定了基础。
然后本文利用VW方法的基本原理，对拓扑关系、方向关系、邻近关系进行了研究：提出了基于目标整体及其Voronoi图与多项集合算子的拓扑关系四元组计算模型V4T，并利用该模型给出了计算拓扑关系的具体方法与步骤；接着依据VW方法的基本策略，探讨了方向关系中的主方向关系与左右关系的计算问题，通过以观察者作为方向参考系，建立方向区域，利用Voronoi区域的分布建立了两目标之间的主方向分布与主方向关系的计算模型，并通过建立左右Voronoi区域构建了左右关系的计算模型；提出了Voronoi K阶邻近的概念，发展了Voronoi K阶邻近的波浪计算法、对向计算法与穿越计算法，并指出Voronoi K阶邻近的有序性、度量性与局域拓扑性。
最后，作者以VC++作为开发工具，运用面向对象的方法，基于COM技术从底层独立开发研制了基于Voronoi图的空间关系计算工具VTKit，并以实际的空间数据为例对本文所提出的计算方法与模型进行了实验，有力地验证了作者所提出的计算方法与模型的合理性与可行性。
Spatial relations are one of the most distinctive aspects of spatial or geographical information, and thus a better understanding of the cognitive aspects of spatial relations, and their formalization in computational models, is critical to the advancement of geographical information science.
Currently, 9-intersection method is most popular to be used for the studies and applications of spatial relations in CIS field. However, there are some imperfections and deficiencies in theory and practice in this method, such as the paradox of topological definition, linear dependency of three components of an object and worse computability and so on. To overcome the limitations of this method and other related methods and models and improve the current methods and models for spatial relations, a new method, simply called VW method for the computation of spatial relations is presented in this thesis.
In this method, a spatial object is treated as a whole, the Voronoi region of an object is employed to enhance its interaction with its neighbors, and appropriate operators from set operators and several types of values are utilized to compute the spatial relations spatial objects. The new approach can overcome the shortcomings of existing methods and presents a framework for computing different spatial relations.
In order to use this method more efficiently, Voronoi diagrams should be generated and maintained dynamically at first. So a new raster based method is described for generating and maintaining Voronoi diagrams dynamically with active region growing technology, and also a method based on virtual four boundaries for conversion of raster Voronoi regions into vector is presented.
And then three different types of spatial relations are computed using the new method for spatial relations: for topological relations, a formal computational model called V4T model is presented, and the strategies and steps are developed based on this model; for main direction relations, the distribution of Voronoi regions is used to establish a formal model; for left and right relations, the computation is performed by constructing the directed Voronoi regions; for spatial neighboring relations, the concept of neighbor is extended and Voronoi K order neighbor is introduced to define and compute different neighobring relations within one conceptual framework, also three algorithms are presented to compute the order of neighboring relations.
Finally, a tool VTKit for the computation of spatial relations and Voronoi diagram and related applications is developed independently to examine the new method and models for spatial relations using VC++ and COM technology on the platform of Windows 2000. Experimental results with the practical and simulated spatial data show the reasonability and practicability of the new method for spatial relations.
引文
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