Structuring element

In mathematical morphology, a structuring element is a shape, used to probe or interact with a given image, with the purpose of drawing conclusions on how this shape fits or misses the shapes in the image. 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. There are two main characteristics that are directly related to structuring elements:

• Shape. For example, the structuring element can be a "ball" or a line; convex or a ring, etc. By choosing a particular structuring element, one sets a way of differentiating some objects (or parts of objects) from others, according to their shape or spatial orientation.
• Size. For example, one structuring element can be a ${\displaystyle 3\times 3}$ square or a ${\displaystyle 21\times 21}$ square. Setting the size of the structuring element is similar to setting the observation scale, and setting the criterion to differentiate image objects or features according to size.