$$PARA_{SD} = sd(PARA[patch_{ij}]$$
where \(PARA[patch_{ij}]\) is the perimeter area ratio of each patch.
PARA_SD is a 'Shape metric'. It summarises each class as the standard deviation of
each patch belonging to class i. The perimeter-area ratio describes the patch complexity
in a straightforward way. However, because it is not standarised to a certain shape
(e.g. a square), it is not scale independent, meaning that increasing the patch size
while not changing the patch form will change the ratio.
Because the metric is based on distances or areas please make sure your data
is valid using check_landscape.
Behaviour
Equals PARA_SD = 0 if the perimeter-area ratio is identical for
all patches. Increases, without limit, as the variation of the perimeter-area ratio
increases.