The Topology of Spatial Scenes in ℝ2

Spatial scenes are abstractions of some geographic reality, focusing on the spatial objects identified and their spatial relations. Such qualitative models of space enable spatial querying, computational comparisons for similarity, and the generation of verbal descriptions. A specific strength of spatial scenes is that they offer a focus on particular types of spatial relations. While past approaches to representing spatial scenes, by recording exhaustively all binary spatial relations, capture accurately how pairs of objects are related to each other, they may fail to distinguish certain spatial properties that are enabled by an ensemble of objects. This paper overcomes such limitations by introducing a model that considers (1) the topology of potentially complexly structured spatial objects, (2) modeling applicable relations by their boundary contacts, and (3) considering exterior partitions and exterior relations. Such qualitative scene descriptions have all ingredients to generate topologically correct graphical renderings or verbal scene descriptions.