Thinning (morphology)

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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: