Metric details for natural-language spatial relations

Spatial relations often are desired answers that a geographic information s ystem (GIS) should generate in response to a user's query. Current GISs pro vide only rudimentary support for processing and interpreting natural-langu age-like spatial relations, because their models and representations are pr imarily quantitative, while natural-language spatial relations are usually dominated by qualitative properties. Studies of the use of spatial relation s in natural language showed that topology accounts for a significant porti on of the geometric properties. This article develops a formal model that c aptures metric details for the description of natural-language spatial rela tions. The metric details are expressed as refinements of the categories id entified 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, the se measures help in identifying the spatial term that describes a particula r configuration. Two groups of metric details are derived: splitting ratios as the normalized values of lengths and areas of intersections; and closen ess 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 val ue ranges for the significant parameters of each term. Three examples demon strate how the framework and its calibrated values are used to determine th e best spatial term for a relationship between two geometric objects.