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 ,
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: