Qualified topological relations between spatial objects with possible vague shape

Abstract

Broad boundary is generally used to replace one‐dimensional boundary for spatial objects with vague shape. For regions with broad boundary, this concept should respect both connectedness and closeness conditions. Therefore, some real configurations, like regions with partially broad boundary (e.g. lake with rocky and swamp banks), are considered invalid. This paper aims to represent different levels of shape vagueness and consider them during the identification of topological relations. Then, an object with vague shape is composed by two crisp components: a minimal extent and a maximal extent. Topological relations are identified by applying the 9‐Intersection model for the subrelations between the minimal and maximal extents of objects involved. Four subrelations are then represented through a 4‐Intersection matrix used to classify the topological relations. For regions with broad boundary, 242 relations are distinguished and classified into 40 clusters. This approach supports an adverbial expression of integrity constraints and spatial queries.

Keywords:

• Spatial objects with vague shape
• Topological relations
• Partial shape vagueness
• Spatial query
• Integrity constraints
• Spatial data integration

Notes

1. The region is defined as the elementary component of the space, i.e. points and lines are not considered.

2. The closure, in point set topology, is the union of the interior and the boundary.

3. The spatial relations (i.e. Equal, Contains, Covers) used in this definition are those defined in Egenhofer and Herring (1990).