Thinning is the transformation of a digital image into a simplified, but topologically equivalent image. It is a type of topological skeleton, but computed using mathematical morphology operators.
Let , and consider the eight composite structuring elements, composed by:
and the three rotations of each by , , and . The corresponding composite structuring elements are denoted .
For any i between 1 and 8, and any binary image X, define
where denotes the set-theoretical difference and denotes the hit-or-miss transform.
The thinning of an image A is obtained by cyclically iterating until convergence:
Thickening is the dual of thinning that is used to grow selected regions of foreground pixels. In most cases in image processing thickening is performed by thinning the background
where denotes the set-theoretical difference and denotes the hit-or-miss transform, and is the structural element and is the image being operated on.