It is typically used in morphological operations, such as dilation, erosion, opening, and closing, as well as the hit-or-miss transform.
According to Georges Matheron, knowledge about an object (e.g., an image) depends on the manner in which we probe (observe) it.
[1] In particular, the choice of a certain structuring element for a particular morphological operation influences the information one can obtain.
In mathematical morphology, binary images are subsets of a Euclidean space Rd or the integer grid Zd, for some dimension d. Here are some examples of widely used structuring elements (denoted by B): In the discrete case, a structuring element can also be represented as a set of pixels on a grid, assuming the values 1 (if the pixel belongs to the structuring element) or 0 (otherwise).
When used by a hit-or-miss transform, usually the structuring element is a composite of two disjoint sets (two simple structuring elements), one associated to the foreground, and one associated to the background of the image to be probed.