An efficient measure of compactness for two-dimensional shapes and its application in regionalization problems

WenWen Li, Michael Goodchild, Richard Church

Research output: Contribution to journalArticlepeer-review

124 Scopus citations


A measure of shape compactness is a numerical quantity representing the degree to which a shape is compact. Ways to provide an accurate measure have been given great attention due to its application in a broad range of GIS problems, such as detecting clustering patterns from remote-sensing images, understanding urban sprawl, and redrawing electoral districts to avoid gerrymandering. In this article, we propose an effective and efficient approach to computing shape compactness based on the moment of inertia (MI), a well-known concept in physics. The mathematical framework and the computer implementation for both raster and vector models are discussed in detail. In addition to computing compactness for a single shape, we propose a computational method that is capable of calculating the variations in compactness as a shape grows or shrinks, which is a typical application found in regionalization problems. We conducted a number of experiments that demonstrate the superiority of the MI over the popular isoperimetric quotient approach in terms of (1) computational efficiency; (2) tolerance of positional uncertainty and irregular boundaries; (3) ability to handle shapes with holes and multiple parts; and (4) applicability and efficacy in districting/zonation/regionalization problems.

Original languageEnglish (US)
Pages (from-to)1227-1250
Number of pages24
JournalInternational Journal of Geographical Information Science
Issue number6
StatePublished - Jun 2013


  • automated zoning procedure
  • compactness
  • districting
  • geographic Information Science
  • moment of inertia
  • pattern recognition
  • raster data modelling
  • regionalization
  • shape analysis
  • shape index
  • vector data modelling

ASJC Scopus subject areas

  • Information Systems
  • Geography, Planning and Development
  • Library and Information Sciences


Dive into the research topics of 'An efficient measure of compactness for two-dimensional shapes and its application in regionalization problems'. Together they form a unique fingerprint.

Cite this