Metric details for natural-language spatial relations

Spatial relations often are desired answers that a geographic information system (GIS) should generate in response to a user's query. Current GISs provide only rudimentary support for processing and interpreting natural-language-like spatial relations, because their models and representations are primarily quantitative, while natural-language spatial relations are usually dominated by qualitative properties. Studies of the use of spatial relations in natural language showed that topology accounts for a significant portion of the geometric properties. This article develops a formal model that captures metric details for the description of natural-language spatial relations. The metric details are expressed as refinements of the categories identified by the g-intersection, a model for topological spatial relations, and provide a more precise measure than does topology alone as to whether a geometric configuration matches with a spatial term or not. Similarly, these measures help in identifying the spatial term that describes a particular configuration. Two groups of metric details are derived: splitting ratios as the normalized values of lengths and areas of intersections; and closeness measures as the normalized distances between disjoint object parts. The resulting model of topological and metric properties was calibrated for 64 spatial terms in English, providing values for the best fit as well as value ranges for the significant parameters of each term. Three examples demonstrate how the framework and its calibrated values are used to determine the best spatial term for a relationship between two geometric objects.