Standard deviation shape index (Shape metric)

## Arguments

- landscape
A categorical raster object: SpatRaster; Raster* Layer, Stack, Brick; stars or a list of SpatRasters.

- directions
The number of directions in which patches should be connected: 4 (rook's case) or 8 (queen's case).

## Details

$$SHAPE_{SD} = sd(SHAPE[patch_{ij}])$$ where \(SHAPE[patch_{ij}]\) is the shape index of each patch.

SHAPE_SD is a 'Shape metric'. The landscape summarised as the standard deviation of all patches in the landscape. SHAPE describes the ratio between the actual perimeter of the patch and the square root of patch area.

Because the metric is based on distances or areas please make sure your data
is valid using `check_landscape`

.

## References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

Patton, D. R. 1975. A diversity index for quantifying habitat "edge". Wildl. Soc.Bull. 3:171-173.