A Location-and-Form-Based Distance for Geographical Analysis

Abstract

Location and geometric form constitute a fundamental basis for the characterization of objects in space. The traditional distance-based geographical analysis of objects, however, usually ignores information associated with their forms. In this article, we propose a location-and-form-based distance to simultaneously take into account these basic characteristics. For substantiation, the significance of the proposed distance is examined with respect to its methodological contributions and applicability. In terms of methodology, we use pattern analysis by the L statistic as an example to show the form effect on the conventional geographical analysis, which is based solely on the location-based distance, and show how to generalize point distance–based analyses to the analysis of objects with forms. With respect to applicability, we demonstrate the capability of our proposed distance in improving the performance of matching buildings in OpenStreetMap and the corresponding standard reference of an area. It is also applicable to other real-life problems in which object forms are involved. Generally, the location-and-form-based distance and the associated methods can give us a new perspective on the conceptualization of distance. The proposed distance can be further extended to include other object attributes to study spatial relationships of objects based on a general notion of distance. Therefore, the proposed distance is a powerful concept that can comprehensively reveal the multifaceted nature of geographical relationships. This study advances the frontier of theoretical and applied research in geography where distance plays an important role.