Establishment of the Similarity Metric Model of Multi-scale Spatial Object Using Isometry

From the perspective of metric geometry, this paper proposes an isomorphic model for multi-scale spatial object representation. Firstly, the multi-scale spatial objects are considered as rigid shapes and non-rigid shapes respectively. Then, the shape distances based on geometry similarity and topology similarity are constructed by the concept of isometry invariance. Finally, the two kinds of similarity shape distances are combined to form a two-element set and are used as an evaluated criterion of multi-scale spatial object similarity. Experiments on different complexity levels of spatial line and polygon objects show that, the two similarity metrics can encode both geometrical and topological changes, and be in accord with the abstract principles of multi-scale spatial object representation.