# opening

##### Morphological Opening

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

##### Usage

```
opening(w, r, ...)
## S3 method for class 'owin':
opening(w, r, \dots, polygonal=NULL)
## S3 method for class 'ppp':
opening(w, r, \dots)
## S3 method for class 'psp':
opening(w, r, \dots)
```

##### 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.

`dilation`

, `erosion`

for the basic
operations.
`owin`

,
`as.owin`

for information about windows.

##### Examples

```
data(letterR)
v <- opening(letterR, 0.3, dimyx=256)
plot(v, main="opening")
plot(letterR, add=TRUE)
```

*Documentation reproduced from package spatstat, version 1.25-5, License: GPL (>= 2)*