From Quantitative Spatial Operator to Qualitative Spatial Relation Using Constructive Solid Geometry, Logic Rules and Optimized 9-IM Model, A Semantic Based Approach

TL;DR

This paper presents a semantic approach combining Constructive Solid Geometry, logic rules, and an optimized 9-IM model to compute and infer topological spatial relations between 3D objects.

Contribution

It introduces a novel method integrating CSG, semantic definitions, and logic rules to determine and reason about topological relations in 3D spatial data.

Findings

Successfully computed topological relations using CSG operators

Stored relations in an ontology for inference

Defined semantic and logical rules for spatial reasoning

Abstract

The Constructive Solid Geometry (CSG) is a data model providing a set of binary Boolean operators such as Union, Difference and Intersection. In this work, these operators are used to compute topological relations between objects defined by the constraints of the nine Intersection Model (9-IM) from Egenhofer. With the help of these constraints, we define a procedure to compute the topological relations on CSG objects. These topological relations are Disjoint, Contains, Inside, Covers, CoveredBy, Equals and Overlaps, and are defined in a top-level ontology with a specific semantic definition on relation such as Transitive, Symmetric, Asymmetric, Functional, Reflexive, and Irreflexive. The results of topological relations computation are stored in the ontology allowing after what to infer on these topological relationships. In addition, logic rules based on the Semantic Web Language allows the definition of logic programs that define which topological relationships have to be computed on which kind of objects. For instance, a "Building" that overlaps a "Railway" is a "RailStation".