# opening

##### Morphological Opening

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

##### Usage

`opening(w, r, …)` # S3 method for owin
opening(w, r, …, polygonal=NULL)

# S3 method for ppp
opening(w, r, …)

# S3 method for psp
opening(w, r, …)

##### 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 opening.

- …
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 opening (Serra, 1982)
of a set \(W\) by a distance \(r > 0\)
is the subset of points in \(W\) that can be
separated from the boundary of \(W\) by a circle of radius \(r\).
That is, a point \(x\) belongs to the opening
if it is possible to draw a circle of radius \(r\) (not necessarily
centred on \(x\)) that has \(x\) on the inside
and the boundary of \(W\) on the outside.
The opened set is a subset of `W`

.

For a small radius \(r\), the opening operation has the effect of smoothing out irregularities in the boundary of \(W\). For larger radii, the opening operation removes promontories in the boundary. For very large radii, the opened set is empty.

##### Value

If `r > 0`

, an object of class `"owin"`

representing the
opened region. If `r=0`

, the result is identical to `w`

.

##### References

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

##### See Also

`closing`

for the opposite operation.

##### Examples

```
# NOT RUN {
v <- opening(letterR, 0.3)
plot(letterR, type="n", main="opening")
plot(v, add=TRUE, col="grey")
plot(letterR, add=TRUE)
# }
```

*Documentation reproduced from package spatstat, version 1.55-1, License: GPL (>= 2)*