Towards a Formal Model for Multi-Resolution Spatial Maps

Topological and metric aspects of the multiresolution representation of geographic maps are considered. The combinatorial structure of maps is mathematically modelled through abstract cell complexes, and maps at diierent detail are related through continuous functions over such complexes. Metric aspects of multiresolution are controlled through the concept of homotopy. Two alternative multiresolution models are proposed, which are implicitly deened by a sequence of map simpliica-tions that fulll both topological and metric consistency rules.