Erosion (morphology): Difference between revisions

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[[Image:Closing.png|thumb|right|The closing of the dark-blue shape (union of two squares) by a disk, resulting in the union of the dark-blue shape and the light-blue areas.]]
In [[mathematical morphology]], the '''closing ''' of a set ([[binary image]]) ''A'' by a [[structuring element]] ''B'' is the [[erosion (morphology)|erosion]] of the [[dilation (morphology)|dilation]] of that set,


:<math>A\bullet B = (A\oplus B)\ominus B, \, </math>


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where <math>\oplus</math> and <math>\ominus</math> denote the dilation and erosion, respectively.  
 
In [[image processing]], closing is, together with [[opening (morphology)|opening]], the basic workhorse of morphological [[signal noise|noise]] removal. Opening removes small objects, while closing removes small holes.
 
==Properties==
* It is [[idempotent]], that is, <math>(A\bullet B)\bullet B=A\bullet B</math>.
* It is [[increasing]], that is, if <math>A\subseteq C</math>, then <math>A\bullet B \subseteq C\bullet B</math>.
* It is [[extensive]], i.e., <math>A\subseteq A\bullet B</math>.
* It is [[Translational invariance|translation invariant]].
 
==See also==
*[[Mathematical morphology]]
*[[Dilation (morphology)|Dilation]]
*[[Erosion (morphology)|Erosion]]
*[[Opening (morphology)|Opening]]
*[[Top-hat_transform|Top-hat transformation]]
 
==Bibliography==
* ''Image Analysis and Mathematical Morphology'' by Jean Serra, ISBN 0-12-637240-3 (1982)
* ''Image Analysis and Mathematical Morphology, Volume 2: Theoretical Advances'' by Jean Serra, ISBN 0-12-637241-1 (1988)
* ''An Introduction to Morphological Image Processing'' by Edward R. Dougherty, ISBN 0-8194-0845-X (1992)
 
==External links==
* [http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/OWENS/LECT3/node3.html Introduction to mathematical morphology]
 
{{Mathapplied-stub}}
 
[[Category:Mathematical morphology]]
[[Category:Digital geometry]]

Revision as of 17:27, 10 December 2013

The closing of the dark-blue shape (union of two squares) by a disk, resulting in the union of the dark-blue shape and the light-blue areas.

In mathematical morphology, the closing of a set (binary image) A by a structuring element B is the erosion of the dilation of that set,

where and denote the dilation and erosion, respectively.

In image processing, closing is, together with opening, the basic workhorse of morphological noise removal. Opening removes small objects, while closing removes small holes.

Properties

See also

Bibliography

  • Image Analysis and Mathematical Morphology by Jean Serra, ISBN 0-12-637240-3 (1982)
  • Image Analysis and Mathematical Morphology, Volume 2: Theoretical Advances by Jean Serra, ISBN 0-12-637241-1 (1988)
  • An Introduction to Morphological Image Processing by Edward R. Dougherty, ISBN 0-8194-0845-X (1992)

External links

Template:Mathapplied-stub