Refined topological relations play an important role in spatial database quality control. Currently, there is no unified and reasonable method to represent refined line/region and line/line topological relations in two-dimensional (2D) space. In addition, the existing independent line/region and line/line models have some drawbacks such as incomplete type discrimination and too many topological invariants. In this paper, a refined line/region and line/line topological relations are represented uniformly by the sequence, dimension, and topological type of the intersection components. To make the relevant definitions conform to the traditional cognitions in 2D Euclidean space, the (simple) spatial object is defined based on manifold topology, and the spatial intersection components are defined based on the whole-whole object intersection set. Then the topological invariant of node degree is introduced, and the adjacent point kinds (e.g., “Null”, “On”, “In”, and “Out”) are defined to distinguish the intersection component types. Excluding impossible and symmetrical types, 29 types of intersection-lines (including 21 between lines/regions and 8 between lines/lines), and 6 types of intersection-points (including 2 between lines/regions and 4 between lines/lines) are classified. On this basis, a node degree-based whole-whole object intersection sets (N-WWIS) model for refined line/region and line/line topological relations is presented, and it can be combined with the Euler number-based whole object intersection and difference (E-WID) model (coarse level) to form a hierarchical representation method of topological relations. Furthermore, a prototype system based on the N-WWIS model for automatic topological integrity checking is developed and some evaluation experiments are conducted with OpenStreetMap (OSM) data is presented based on the classification of intersection components. The experimental results show that the N-WWIS model will enable the geographic information systems (GIS) community to develop automated topological conflict checking and dealing tools for spatial data updates and quality control.

中文翻译：

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基于全对象相交成分的细线/区域和线/线拓扑关系模型

精细的拓扑关系在空间数据库质量控制中起着重要作用。当前，还没有统一合理的方法来表示二维（2D）空间中的细化线/区域和线/线拓扑关系。另外，现有的独立线/区域和线/线模型具有一些缺点，例如类型识别不完全和拓扑不变量过多。在本文中，细化的线/区域和线/线拓扑关系由相交分量的顺序，维和拓扑类型统一表示。为了使相关定义符合2D欧几里得空间中的传统认知，基于流形拓扑定义（简单）空间对象，并基于整个整体对象相交集定义空间相交分量。然后，引入节点度的拓扑不变量，并定义相邻点的类型（例如“ Null”，“ On”，“ In”和“ Out”）以区分相交分量类型。除不可能和对称类型以外，还对29种相交线（包括线/区域之间的21条和线/线之间的8条）和6种类型的交点（包括线/区域之间的2条和线/线之间的4条）进行了分类。在此基础上，提出了一种基于节点度的全线对象整体交集（N-WWIS）模型，用于精细的线/区域和线/线拓扑关系，可与基于欧拉数的全对象交集和差异（E-WID）模型（粗略级别）以形成拓扑关系的层次表示方法。此外，开发了基于N-WWIS模型的拓扑完整性自动检查原型系统，并基于交叉口组件的分类，利用OpenStreetMap（OSM）数据进行了一些评估实验。实验结果表明，N-WWIS模型将使地理信息系统（GIS）社区能够开发用于空间数据更新和质量控制的自动化拓扑冲突检查和处理工具。