Compactness: A Comprehensive Set of Metrics and Rationale for Use
Author(s): Jason Parent
Shape compactness is an important attribute in various fields including geography and landscape ecology. An abundance of metrics can be found in the literature for measuring shape compactness. However, the rationale for using a given metric is often lacking. In this presentation, we describe a comprehensive set of metrics to quantify shape compactness as well as a theoretical framework from which to justify the use of a particular metric.
The appropriate metric to use for analyzing shape compactness depends on what the shape represents and what aspect of the shape is being studied. No single metric, found to date, can adequately capture all aspects of a shape’s compactness. We present 10 metrics along with the rationale for selecting one metric over another. These metrics allow for robust comparisons among the compactness of different shapes regardless of size. We developed a Python script to facilitate the calculation of the proposed metrics.
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