A symmetry detector for map generalization and urban-space analysis
This article presents an algorithmic approach to the problem of finding symmetries in building footprints, which is motivated by map generalization tasks such as symmetry-preserving building simplification and symmetry-aware grouping and aggregation. Moreover, symmetries in building footprints may be used for landmark selection and building classification. The presented method builds up on existing methods for symmetry detection in vector data that use algorithms for string matching. It detects both mirror symmetries and repetitions of geometric structures. In addition to the existing vector-based methods, the new method finds partial symmetries in polygons while allowing for small geometric errors and, based on a least-squares approach, computes optimally adjusted mirror axes and assesses their quality. Finally, the problem of grouping symmetry relations is addressed with an algorithm that finds mirror axes that are almost collinear. The presented approach was tested on a large building dataset of the metropolitan Boston area and its results were compared with results that were manually generated in an empirical test. The symmetry relations that the participants of the test considered most important were found by the algorithm. Future work will deal with the integration of information on symmetry relations into algorithms for map generalization.
generalization algorithms building gis geometry urban