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Topological relations and direction relations represent two pieces of the qualitative spatial reasoning triumvirate. Researchers have previously attempted to use the direction relation matrix to derive a topological relation, finding that no single direction relation matrix can isolate a particular topological relation. In this paper, the technique of topological augmentation is applied to the same problem, identifying a unique topological relation in 28.6% of all topologically augmented direction relation matrices, and furthermore achieving a reduction in a further 40.4% of topologically augmented direction relation matrices when compared to their vanilla direction relation matrix counterpart.
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This content will become publicly available on April 1, 2026
Conceptual Neighborhood Graphs of Topological Relations in Z2
Topological relations form the backbone of qualitative spatial reasoning and, as such, play a paramount role in geographic information systems. Three decades of research have provided a proliferation of sets of qualitative topological relations in both continuous and discretized spaces, but only in continuous spaces has the concept of organizing these relations into a larger framework (called a conceptual neighborhood graph) been considered. Previous work leveraged matrix differences to derive the anisotropic scaling neighborhood for these relations. In this paper, a simulation protocol is used to derive conceptual neighborhood graphs of qualitative topological relations in Z2 for the operations of translation and isotropic scaling. It is further shown that, when aggregating raster relations into their continuous counterparts and collapsing neighborhood connections within these groups, the familiar conceptual neighborhood structures for continuous regions appear.
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- Award ID(s):
- 2019470
- PAR ID:
- 10655882
- Publisher / Repository:
- MDPI
- Date Published:
- Journal Name:
- ISPRS International Journal of Geo-Information
- Volume:
- 14
- Issue:
- 4
- ISSN:
- 2220-9964
- Page Range / eLocation ID:
- 150
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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