Computes the normalized moment of inertia (NMI), a compactness measure for polygon geometries. The NMI ranges between 0 and 1, where 1 is the most compact shape (a circle) and 0 is an infinitely extending shape (Feng et al. 2022).
Details
The NMI is defined as follows, where \(A\) is the area of a geometry, and \(I\) is the second moment of inertia (i.e., the second areal moment): $$\frac{A^2}{2 \pi I}$$ See Li et al. (2013, 2014) for additional details.
References
Feng, X., Rey, S., and Wei, R. (2022). "The max-p-compact-regions problem." Transactions in GIS, 26, 717–734. https://doi.org/10.1111/tgis.12874.
Li, W., Goodchild, M.F., and Church, R.L. 2013. "An Efficient Measure of Compactness for Two-Dimensional Shapes and Its Application in Regionalization Problems." International Journal of Geographical Information Science 27 (6): 1227–50. doi:10.1080/13658816.2012.752093.
Li, W., Church, R.L. and Goodchild, M.F. 2014. "The p-Compact-regions Problem." Geogr Anal, 46: 250-273. https://doi.org/10.1111/gean.12038.