What is in a Contour Map

Contours maps such as topographic maps compress the information of a function over a two-dimensional area into a discrete set of closed lines that connect points of equal value isolines, striking a fine balance between expressiveness and cognitive simplicity. They allow humans to perform many common sense reasoning tasks about the underlying function e.g. elevation. This paper analyses and formalizes contour semantics in a first-order logic ontology that forms the basis for enabling computational common sense reasoning about contour information. The elicited contour semantics comprises four key concepts --- contour regions, contour lines, contour values, and contour sets --- and their subclasses and associated relations, which are grounded in an existing qualitative spatial ontology. All concepts and relations are illustrated and motivated by physical-geographic features identifiable on topographic contour maps. The encoding of the semantics of contour concepts in first-order logic and a derived conceptual model as basis for an OWL ontology lay the foundation for fully automated, semantically-aware qualitative and quantitative reasoning about contours.