Foal Getis-ord on rasters

The rasterized Focal Getis-Ord formula looks as follows:

\[ FocalG^*(R, W, N, M, S) = \frac{ R{\stackrel{\mathtt{sum}}{\circ}}W - M*\sum_{w \in W}{w} }{ S \sqrt{ \frac{ N*\sum_{w \in W}{w^2} - (\sum_{w \in W}{w})^2 }{ N - 1 } } } \]

where:

  • \(R\) is the input raster.
  • \(W\) is a weight matrix of values between 0 and 1. The matrix is square and has odd dimensions, e.g. \(5 \times 5\), \(31 \times 31\) ...
  • \(N\) represents the focal count of pixels TODO (there can be NA values)
  • \(M\) represents the focal mean TODO.
  • \(S\) represents the focal standard deviation TODO.

It can be seen that the formula can be nicely refactored into:

  • TODO