Smooth Building Footprint Aggregation with Alpha Shapes

Abstract

We propose a method to continuously aggregate building footprints into generalized polygons. This enables smooth zooming that preserves information about dense built-up areas even in coarse-grained views. The goal is to compute a set of polygons for each zoom level that describe the built-up areas well. At the same time, the complexity of the polygons should be low to allow for efficient rendering and easy visual comprehension. Previous approaches for building footprint generalization are quite involved and often come with handcrafted rules for different building shapes and aggregation steps. We show that α-shapes, a generalization of convex hulls, can be elegantly instrumented to retrieve suitable outline polygons for clustered building sets at any desired level of detail. To form clusters, we use the proximity information obtained from a Delaunay triangulation of the buildings exterior. The clusters are then approximated by α-shapes (which are themselves based on Delaunay triangulations). We conduct an experimental evaluation on buildings extracted from OSM up to a country-sized data set containing more than 30 million building footprints. We show that our new method efficiently produces concise polygons for all zoom levels that capture the shape of the built-up areas well.