Editing Mathematical morphology (section)

=== Structuring element ===

The basic idea in binary morphology is to probe an image with a simple, pre-defined shape, drawing conclusions on how this shape fits or misses the shapes in the image. This simple "probe" is called the [[structuring element]], and is itself a binary image (i.e., a subset of the space or grid).

Here are some examples of widely used structuring elements (denoted by ''B''):

* Let <math>E = \mathbb{R}^2</math>; ''B'' is an open disk of radius ''r'', centered at the origin.
* Let <math>E = \mathbb{Z}^2</math>; ''B'' is a 3 × 3 square, that is, ''B'' = {(−1, −1), (−1, 0), (−1, 1), (0, −1), (0, 0), (0, 1), (1, −1), (1, 0), (1, 1)}.
* Let <math>E = \mathbb{Z}^2</math>; ''B'' is the "cross" given by ''B'' = {(−1, 0), (0, −1), (0, 0), (0, 1), (1, 0)}.