Defining and Comparing Content Measures of Topological Relations

This work defines and compares three content measures that characterize topological relations between rectangular regions in a two-dimensional space. These content measures use simplified views of spatial objects in order to create an efficient mechanism for capturing the topological content of spatial configurations. The content measures are compared based on the correlation between two similarity rankings: (1) a similarity ranking defined in terms of the distance of content-measure values and (2) a similarity ranking defined in terms of the error of the geometric adjustment between pairs of objects. The correlation between similarity rankings is used as indicator of how well these content measures characterize topological relations. Such content measures provide mechanisms for creating efficient methods to describe and access information on the basis of the topological content of spatial configurations.