Conceptual Neighborhoods of Topological Relations between Lines

Rui Reis, Max Egenhofer, and João Matos
The 13th International Symposium on Spatial Data Handling (SDH 2008), Montpellier, France
A. Ruas and C. Gold (eds.), Springer, June 2008.


Conceptual neighborhood graphs capture the similarity among qualitative relations. This paper derives the graphs for the thirty-three topological relations between two crisp, undirected lines and for the seventy-seven topological relations between two lines with uncertain boundaries. The analysis of the graphs shows that the normalized node degree increases, from the crisp to the broad-boundary lines, roughly at the same degree as it increases for crisp lines that are transformed from R1 into R2.