简单面目标与带孔洞面目标间拓扑关系的层次表达方法

A Hierarchical Approach to Topological Relations between a Simple Area and an Area with Holes

带孔洞的面目标是现实中较为常见的一类复杂目标,它们之间的拓扑关系要比简单面目标复杂得多。本文基于空间划分和目标分解的思想,利用点集(拓扑学)理论中的邻域概念详细分析和描述带孔洞面目标的点集拓扑分量,这种描述方法实质上是简单面目标点集拓扑分量描述的一种自然延展。进而,对简单面目标间拓扑关系的描述和区分方法进行了扩展,层次地分析和区分简单面目标与带孔洞面目标间的拓扑关系。相比于Egenhofer等人提出的代数描述和间接表达方法,本文提出的方法是一种直接描述和层次表达的方法,并且与简单面目标间拓扑关系的表达方法是相统一的。

Topological relations have been a focus of research in many disciplines such as computer science, artificial intelligence, cognitive science, linguistics, robotics and geographic information science. Unfortunately, they have so far only been defined for and applicable to simple objects like single points, continuous lines and simple areas, not involving the design, definition, and description of topological relations operating on the complex objects. This article tries to make an effort to this gap and pays attention to the spatial areas with holes. Based upon the idea of space partition and object decomposition, topological components of an area ob ject with holes are defined by the use of the concept of neighborhood in the point set topology, which is a natu ral extension of the definitions for topological components of a simple area. And then, a hierarchical approach to topological relalions is presented for two simple areas, which is indeed necessary for many practical applica tions. The hierarchical approach is further extended to the topological relations between a simple area and an area with, hole（s）. It can be concluded that the proposed approaches are very general, suitable for topological relations of both simple areas and complex areas.