Quantitative expressions of spatial similarity between road networks in multiscale map spaces

Spatial similarity plays a critical role in the perception and cognition in capturing information from maps; it can be used as a constraint to automate map generalization. Although measuring similarities seems natural to humans, it can be challenging to quantify them. This is especially true when it comes to calculating spatial similarity degrees between groups of spatial objects at varying scales and quantitatively expressing the relations between spatial similarity and change of map scale in multiscale map spaces. Taking road networks as an example, this paper proposes an approach to measuring spatial similarity between a road network at a large scale and its generalized counterpart at a smaller scale. By fitting a power function to three typical types of road networks, this paper provides a formula for expressing the change in spatial similarity as the map scale changes. The proposed quantitative method lays a foundation for using spatial similarity as a constraint during road network generalization.