ICC Programming


4602.3 - An Area Compactness Metric considering Spatial Context and Topology

Tuesday, July 4
3:30 PM - 3:50 PM
Location: Delaware B

Measuring the shape complexity of areal features is fundamental to the understanding of geospatial phenomena. Of the many metrics on shape complexity, compactness is particularly useful for applications from cartographic generalization, to environmental planning and management, and to gerrymandering assessment. Existing spatial pattern analysis methods can measure compactness using both spatial distribution and nonspatial attributes; however, spatial context and topology are often ignored as if those areal features were isolated and independent from each other. For example, when evaluating gerrymandering using simple area-perimeter ratio or mass movement of inertia, those electoral districts are treated separately without considering the state boundary and their topological relationships although the shape of any district influences all its neighbors within the state boundary.

In this presentation, I present a quantitative metric that can delineate the complexity of geographic shapes, specifically the compactness, with explicit consideration of context, external constraints, and topology. This metric integrates areal features’ geometric distribution, nonspatial attributes, as well as the context and topology. When applied to gerrymandering in congressional districts, for instance, the population distribution, the number of districts, and the state boundaries would be integrated into the metric to allow better and more accurate evaluation. This method is based on a concept similar to the moment of inertia, but constructs a virtual network within the examined areal features and utilizes their interconnectivity to produce a correction factor that takes context and constraints into consideration. Such a virtual network makes it possible to calculate a series of minimum paths within the state boundary from unit representative features to the centers of areal features. The metric would then apply a multiplier to those areal features that produce a network path length longer than the minimum one. Collectively, these multipliers could reduce the effects of external boundaries and topologies. Additionally, the method also has the option to produce a compactness curve, in contrast to a single quantitative metric, to delineate the complexity of the areal features. This method is implemented using R. Examples of the U.S. congressional districts are used to illustrate the effectiveness of the metric and its differences from existing methods.

Shipeng Sun

Assistant Professor
University of Illinois at Springfield

Shipeng Sun is an Assistant Professor in the Department of Environmental Studies at University of Illinois Springfield. His research mainly focuses on developing and applying various spatial analysis and modeling techniques, including geovisualization, network analysis, geocomputation, and complexity modeling, to study urban and human-environment systems.


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Guillaume Touya

Senior Researcher
IGN France, LASTIG, COGIT team

Guillaume Touya is a senior researcher at the LASTIG, COGIT team, IGN France (the French mapping agency). He holds a PhD in GI science from Paris-Est University. His research interests focus on automated cartography, map generalization and volunteered geographic information. He currently leads the MapMuxing (https://mapmuxing .ign.fr) research project.


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4602.3 - An Area Compactness Metric considering Spatial Context and Topology

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