The Direction-Relation Matrix: A Representation for Direction Relations between Extended Spatial Objects

Cardinal directions are an important component of spatial relations, complementing topological relations and approximate distances as qualitative representations of space. They are frequently used as a selection criterion in spatial queries and for assessing similarities of spatial scenes. Past research in geographic information science has focused on the representation of cardinal directions, such as North and North-East, in quadrants or as cone-shaped partitions. Such models for cardinal directions are useful for point-like objects; however, they are insufficient for extended objects, such as regions and lines, because they make cognitively implausible inferences. To represent such situations more appropriately, the Direction-Relation Matrix is introduced. It records for a reference object into which direction partitions an extended target object falls and offers, at a finer level of granularity, the option to record how much of the object falls into each direction partition. This multi-resolution representation provides an improved approximation for direction relations of complexly structured spatial objects, including such shapes as concave regions or objects with holes. A significant advantage over other methods is that the popular, but often error-prone, approximation with minimum bounding rectangles is replaced by reference to the objects’ actual geometric representations. This paper defines formally the Direction-Relation Matrix and demonstrates how it can be compared to determine direction-similar spatial scenes.