拓扑关系的闭球模型及复合表的推导

CLOSED BALL MODEL AND COMPOSITION TABLE DERIVATION FOR TOPOLOGICAL RELATIONS

Egenhofer和Franzosa提出的拓扑关系的4-交集模型是定性空间推理中常用的模型，但基于4-交集模型难以推导出拓扑关系的完备集、概念邻域和复合表．本文以拓扑学为基础，提出了（n，n）完备集的概念，建立了拓扑关系的闭球模型．基于闭球模型可以直接推导出拓扑关系的（n，n）完备集和概念邻域以及复合表．结果表明，对定性空间推理来说，闭球模型比4-交集模型更简单有效．

Egenhofer and Franzosa's 4-set model for topological relations is the mostcommon one in qualitative spatial reasoning. However, it is hard to derive the completeset, concept neighborhood, and composition table for topological relations based on 4-setmodel. In this paper, based on fundamental topology theories, the concept of (n,n) complete set is proposed and the closed ball model is constructed. It is easy to get (n,n) com-plete set and concept neighborhood, and possible to derive composition table for topological relations based on closed ball model. It is shown that closed ball model is a valid modelfor topological relations and is simpler than 4-set model.