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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 etc. ...
  • N represents the the number of pixels in the focal window (there can be NA values)
  • M represents the focal mean.
  • S represents the focal standard deviation.