A Hierarchical Representation of Line-region Topological Relations

Topological relations have found applications in many fields such as similarity analysis, spatial query, object matching, inconsistency detection, spatial association rule mining, spatial reasoning, and so on. This paper is concentrated on the hierarchical representation of the topological relations between a line and a region in IR. In this study, line-region relations are classified into basic relations and compound relations based on the number of intersections between line and region boundary. The basic relations are further differentiated into 16 types based on the invariants of dimension and local order. These basic relations are then organized into a hierarchy with multiple levels of topological invariants. These invariants are developed from the point of view of set theory, including (a) separation number and dimension at set level, (b) intersection type at element level, and (c) sequence of intersection types at an integrated level. A practical example is provided to illustrate the use of the hierarchical approach presented in this paper.