# dilation

##### Morphological Dilation

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

##### Usage

```
dilation(w, r, …)
# S3 method for owin
dilation(w, r, …, polygonal=NULL, tight=TRUE)
# S3 method for ppp
dilation(w, r, …, polygonal=TRUE, tight=TRUE)
# S3 method for psp
dilation(w, r, …, 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; or passed to`disc`

if the polygonal 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=FALSE`

).

##### 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 `"\dots"`

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

`erosion`

for the opposite operation.

`dilationAny`

for morphological dilation using any shape.

##### Examples

```
# NOT RUN {
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 1.55-1, License: GPL (>= 2)*