Description

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,

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.

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Title
  • An Efficient Measure of Compactness for Two-Dimensional Shapes and Its Application in Regionalization Problems
Contributors
Date Created
2013-08-15
Resource Type
  • Text
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    Identifier
    • Digital object identifier: 10.1080/13658816.2012.752093
    • Identifier Type
      International standard serial number
      Identifier Value
      1365-8816
    • Identifier Type
      International standard serial number
      Identifier Value
      1365-8824
    Note
    • "This is an Author's Accepted Manuscript of the article. The final version of the article is published in the INTERNATIONAL JOURNAL OF GEOGRAPHICAL INFORMATION SCIENCE copyright 2013 Taylor & Francis, available online at: http://www.tandfonline.com/10.1080/13658816.2012.752093."

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    This is a suggested citation. Consult the appropriate style guide for specific citation guidelines.

    Li, W., Goodchild, M. F., & Church, R. (2013). An efficient measure of compactness for two-dimensional shapes and its application in regionalization problems. International Journal of Geographical Information Science, 27(6), 1227-1250. doi:10.1080/13658816.2012.752093

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