# dilation

##### Morphological Dilation

Perform morphological dilation of a window, a line segment pattern or a point pattern

##### Usage

```
dilation(w, r, ...)
## S3 method for class 'owin':
dilation(w, r, \dots, polygonal=NULL, tight=TRUE)
## S3 method for class 'ppp':
dilation(w, r, \dots, polygonal=TRUE, tight=TRUE)
## S3 method for class 'psp':
dilation(w, r, \dots, polygonal=TRUE, tight=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 dilation.
- ...
- extra arguments passed to
`as.mask`

controlling the pixel resolution, if the pixel approximation is used. - polygonal
- Logical flag indicating whether to compute a polygonal
approximation to the dilation (
`polygonal=TRUE`

) or a pixel grid approximation (`polygonal=FALSE`

). - tight
- Logical flag indicating whether the bounding frame of the window
should be taken as the smallest rectangle enclosing the dilated region
(
`tight=TRUE`

), or should be the dilation of the bounding frame of`w`

(`tight=F`

##### Details

The morphological dilation of a set $W$ by a distance $r > 0$ is the set consisting of all points lying at most $r$ units away from $W$. Effectively, dilation adds a margin of width $r$ onto the set $W$.

If `polygonal=TRUE`

then a polygonal approximation
to the dilation is computed.
If `polygonal=FALSE`

then a pixel approximation
to the dilation is computed from the distance map of `w`

.
The arguments `"..."`

are passed to `as.mask`

to control the pixel resolution.

When `w`

is a window, the default (when `polygonal=NULL`

)
is to compute a polygonal approximation if
`w`

is a rectangle or polygonal window, and to compute a
pixel approximation if `w`

is a window of type `"mask"`

.

##### Value

- If
`r > 0`

, an object of class`"owin"`

representing the dilated region. If`r=0`

, the result is identical to`w`

.

##### See Also

##### Examples

```
plot(dilation(letterR, 0.2))
plot(letterR, add=TRUE, lwd=2, border="red")
X <- psp(runif(10), runif(10), runif(10), runif(10), window=owin())
plot(dilation(X, 0.1))
plot(X, add=TRUE, col="red")
```

*Documentation reproduced from package spatstat, version 1.37-0, License: GPL (>= 2)*