From 9-IM Topological Operators to Qualitative Spatial Relations using 3D Selective Nef Complexes and Logic Rules for bodies

TL;DR

This paper introduces a method combining 3D Selective Nef Complexes and SWRL rules to automatically compute and infer topological spatial relations between 3D objects, enhancing spatial reasoning in ontologies.

Contribution

It presents a novel approach integrating 3D Nef polyhedra, 9-IM topological operators, and SWRL rules for automatic spatial relation computation and inference.

Findings

Successfully computed topological relations like Disjoint, Overlaps, Contains.

Stored relations in OWL-DL ontology for reasoning.

Enabled inference of new object relationships based on topological rules.

Abstract

This paper presents a method to compute automatically topological relations using SWRL rules. The calculation of these rules is based on the definition of a Selective Nef Complexes Nef Polyhedra structure generated from standard Polyhedron. The Selective Nef Complexes is a data model providing a set of binary Boolean operators such as Union, Difference, Intersection and Symmetric difference, and unary operators such as Interior, Closure and Boundary. In this work, these operators are used to compute topological relations between objects defined by the constraints of the 9 Intersection Model (9-IM) from Egenhofer. With the help of these constraints, we defined a procedure to compute the topological relations on Nef polyhedra. These topological relationships are Disjoint, Meets, Contains, Inside, Covers, CoveredBy, Equals and Overlaps, and 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 the computation of topological relationships are stored in an OWL-DL ontology allowing after what to infer on these new relationships between objects. In addition, logic rules based on the Semantic Web Rule Language allows the definition of logic programs that define which topological relationships have to be computed on which kind of objects with specific attributes. For instance, a "Building" that overlaps a "Railway" is a "RailStation".