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.

Example[]

Let , and consider the eight composite structuring elements, composed by:

and ,
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:

.

Thickening[]

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]

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.

References[]

  1. ^ Gonzalez, Rafael C. (2002). Digital image processing. Woods, Richard E. (Richard Eugene), 1954- (2nd ed.). Upper Saddle River, N.J. ISBN 0-201-18075-8. OCLC 48944550.
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