Multi-level Topological Relations Between Spatial Regions Based Upon Topological Invariants

Abstract

Topological relations have played important roles in spatial query, analysis and reasoning. In a two-dimensional space (IR 2 ), most existing topological models can distinguish the eight basic topological relations between two spatial regions. Due to the arbitrariness and complexity of topological relations between spatial regions, it is difficult for these models to describe the order property of transformations among the topological relations, which is important for detailed analysis of spatial relations. In order to overcome the insufficiency in existing models, a multi-level modeling approach is employed to describe all the necessary details of region-region relations based upon topological invariants. In this approach, a set of hierarchically topological invariants is defined based upon the boundary-boundary intersection set (BBIS) of two involved regions. These topological invariants are classified into three levels based upon spatial set concept proposed, which include content, dimension and separation number at the set level, the element type at the element level, and the sequence at the integrated level. Corresponding to these hierarchical invariants, multi-level formal models of topological relations between spatial regions are built. A practical example is provided to illustrate the use of the approach presented in this paper.

A Combinatorial Reasoning Mechanism with Topological and Metric Relations for Change Detection in River Planforms: An Application to GlobeLand30’s Water Bodies

“…We used the intersection and difference model (IDM) proposed by [53] to express the topological relations between regions. This model can more accurately describe the topological relations between a region and an empty set than can other models.…”

Extension of RCC Topological Relations for 3d Complex Objects Components Extracted From 3d Lidar Point Clouds

“…In this model, topological relationships are grouped into six categories including relations between point-point, point-line, pointregion, line-line, line-region, region-region. Among these relations, region-region relations are the most commonly used to express topological relations between different primitives (Deng, 2007). The existing eight topological relations (RCC-8) are (Randell, 1992): disconnected (DC), partial overlap (PO), equal (EQ), externally connected (EC), tangential proper part (TPP), non-tangential proper part (NTPP) and their inverse relations are TPPi and NTPPi respectively.…”

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