Quantitative Expressions of Spatial Similarity in Multi-scale Map Spaces

Spatial similarity plays an important role in automated map generalization, spatial computations, spatial reasoning, spatial retrieval and the construction of multi-scale spatial databases. Nevertheless, the features of spatial similarity relations have never been investigated systematically, yet. To fill the gap, this paper focuses on quantitative expressions of the features of spatial similarity relations in map spaces. It firstly summarizes and analyzes the features of similarity in other fields, such as computer science, psychology and geography; then it proposes a number of features of spatial similarity relations in map spaces, i.e., equality, minimality, auto-similarity, symmetry (reflectivity), non-transitivity, triangle inequality, and scale dependency. Mathematical expressions of the features are presented and explained. Finally, potential research issues in spatial similarity relations are reviewed.