SOM: A Novel Model for Defining Topological Line-Region Relations

Abstract

Topological line-region relations are generally defined by the Ninth-Intersection Model (9IM) or the Dimensionally Extended Ninth-Intersection Model (DE-9IM) in GIS. In the paper, Segment Operator Model (SOM) is introduced to solve the same problem. Let a simple region R filter a simple curve L and produce a set of curve segments within the exterior, the interior or the borders of R. The topological relations between curve segments and R are mapped into seven categories: across, stabsin, along, bowsto, sticksto, inside and disjoint. SOM is based on counting the curve segments that belong to each of the seven categories. Any topological relations defined in 9IM or DE-9IM can be expressed in SOM. In SOM, L is atomic to R when only a single curve segment is produced, simplex to R when no more than three curve segments are produced, otherwise, L is complex to R. L is uniform to R when only one kind of curve segments are produced.