Delineating urban areas using building density

We develop a new dartboard methodology to delineate urban areas using detailed information about building location, which we implement using a map of all buildings in France. For each pixel, our approach compares actual building density after smoothing to counterfactual smoothed building density computed after randomly redistributing buildings. We define as urban any area with statistically significant excess building density. Within urban areas, extensions to our approach allow us to distinguish 'core' urban pixels and detect centres and subcentres. Finally, we develop novel one-and two-sided tests that provide a statistical basis to compare maps with different delineations, which we use to assess the robustness of our approach and to document large differences between our preferred delineation and the corresponding official one.