$$PARA_{MN} = mean(PARA[patch_{ij}]$$
where \(PARA[patch_{ij}]\) is the perimeter area ratio of each patch.
PARA_MN is a 'Shape metric'. It summarises each class as the mean 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.
Behaviour
Approaches PARA_MN > 0 if PARA for each patch approaches PARA > 0,
i.e. the form approaches a rather small square. Increases, without limit, as PARA increases,
i.e. patches become more complex.