A point-set-based approximation for areal objects: A case study of representing localities

Since partonomy knowledge is an important component of human cognition, we propose a point-set-based region (PSBR) model to approximate areal objects, especially vague areal objects. Two major properties of this model are that it is cognition-accordant and that it can represent vague regions easily. Given a point-set-based model, we can estimate the corresponding region using various methods, including convex hull, minimum bounding box, one-class support vector machine, and point density. We can examine the spatial relationships between two PSBRs using the derived areal objects. Additionally, we present a number of methods to compute relationships directly, based on two PSBRs. In the case study, we use a number of localities in China to demonstrate applications of the PSBR model. The proposed model can be implemented easily in an object-relational database management system. Hence, it provides a reasonable representation for vague objects that takes both manageability and approximation into account, especially now that Web 2.0 is making point data more convenient to collect.