A set of topological invariants for relations between lines embedded i
n the 2-dimensional Euclidean space is given. The set of invariants is
proven to be necessary and sufficient to characterize topological equ
ivalence classes of binary relations between simple lines. The topolog
y of arbitrarily complex geometric scenes is described with a variatio
n of the same set of invariants. Polynomial time algorithms are given
to assess topological equivalence of two scenes. The relevance of iden
tifying such a set of invariants and efficient algorithms is due to ap
plication areas of spatial database systems, where a model for describ
ing topological relations between planar features is sought.