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.
, and consider the eight composite structuring elements, composed by: and the three rotations of each by
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 [1]
denotes the set-theoretical difference and
denotes the hit-or-miss transform, and