# closing

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##### Morphological Closing

Perform morphological closing of a window, a line segment pattern or a point pattern.

Keywords
spatial, math
##### Usage
closing(w, r, ...)
## S3 method for class 'owin':
closing(w, r, \dots, polygonal=NULL)
## S3 method for class 'ppp':
closing(w, r, \dots, polygonal=TRUE)
## S3 method for class 'psp':
closing(w, r, \dots, polygonal=TRUE)
##### Arguments
w
A window (object of class "owin" or a line segment pattern (object of class "psp") or a point pattern (object of class "ppp").
r
positive number: the radius of the closing.
...
extra arguments passed to as.mask controlling the pixel resolution, if a pixel approximation is used
polygonal
Logical flag indicating whether to compute a polygonal approximation to the erosion (polygonal=TRUE) or a pixel grid approximation (polygonal=FALSE).
##### Details

The morphological closing (Serra, 1982) of a set $W$ by a distance $r > 0$ is the set of all points that cannot be separated from $W$ by any circle of radius $r$. That is, a point $x$ belongs to the closing $W*$ if it is impossible to draw any circle of radius $r$ that has $x$ on the inside and $W$ on the outside. The closing $W*$ contains the original set $W$.

For a small radius $r$, the closing operation has the effect of smoothing out irregularities in the boundary of $W$. For larger radii, the closing operation smooths out concave features in the boundary. For very large radii, the closed set $W*$ becomes more and more convex.

The algorithm applies dilation followed by erosion.

##### Value

• If r > 0, an object of class "owin" representing the closed region. If r=0, the result is identical to w.

##### References

Serra, J. (1982) Image analysis and mathematical morphology. Academic Press.

opening for the opposite operation.

dilation, erosion for the basic operations. owin, as.owin for information about windows.

• closing
• closing.owin
• closing.ppp
• closing.psp
##### Examples
data(letterR)
v <- closing(letterR, 0.25, dimyx=256)
plot(v, main="closing")
plot(letterR, add=TRUE)
Documentation reproduced from package spatstat, version 1.16-3, License: GPL (>= 2)

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