Geo-info Graph Spectrum Analysis for Representing Distance Relations in Gis

Distance is a fundamental concept in spatial sciences. Spatial distance is a very important parameter to measure the relative positions between spatial objects and to indicate the degree of similarity between neighbouring objects. Indeed, spatial distance plays an important role in spatial query, analysis and reasoning. However, how to represent directional relations in a unified form is still an open issue. Indeed, the information of object direction is complicated and relative. It is difficult to describe the directional relations using mathematical method. In this paper, existing representing algorithms for the distance between spatial objects are evaluated and their problems pointed out; then, the concept of Geo-info Graph Spectrum is introduced as a metric indicator for different types of spatial objects. This paper presents a rigorous mathematical methodology that addresses the idea of using directional spectrum for direction analysis between spatial objects. So, the complicatedness can be represented by their spectrums or feature values, and the relatively can be represented by the hierarchies of their spectrums (or feature values). Furthermore, an experiment is given to illustrate the feasibility and advantages of the proposed approach in the paper, explaining how to use Direction Spectrum to do spectrum generation and spectrum analysis as to get the results of directional relationship between spatial objects. Finally, potential applications are discussed. * Corresponding author. [email protected]