# Equivalence between structural elements

Greetings.

I have the following questions:

Suppose you want to apply a morphological transformation (eg erosion) on an image with a structuring element solid 3 * 3 (ie, full of 1s) and a number of iterations 'n'.

What would be the dimension (rows * columns) of the structuring element that would produce the same result, but only with an iteration?, Ie, if we want to apply the same morphological transformation on the image and get the same result, but using only one iteration ... What should be the dimensions 'rows * columns' of the structuring element?

More concisely, find the value de 'M' for which a structuring element de 'M * M' applied only once (one iteration) produces the same result as applying a SE 3 * 3 a number of iterations equal to 'n' (Being 'n' a known value).

Is there a general formula for finding this equivalence?

Thanks in advance for any replies / help.