# erosion

##### Morphological Erosion

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

##### Usage

```
erosion(w, r, ...)
## S3 method for class 'owin':
erosion(w, r, shrink.frame=TRUE, \dots,
strict=FALSE, polygonal=NULL)
## S3 method for class 'ppp':
erosion(w, r,\dots)
## S3 method for class 'psp':
erosion(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 erosion.
- shrink.frame
- logical: if
`TRUE`

, erode the bounding rectangle as well. - ...
- extra arguments to
`as.mask`

controlling the pixel resolution, if pixel approximation is used. - strict
- Logical flag determining the fate of boundary pixels, if pixel approximation is used. See details.
- 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 erosion of a set $W$ by a distance $r > 0$ is the subset consisting of all points $x \in W$ such that the distance from $x$ to the boundary of $W$ is greater than or equal to $r$. In other words it is the result of trimming a margin of width $r$ off the set $W$.

If `polygonal=TRUE`

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

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

.
The arguments `"..."`

are passed to `as.mask`

to control the pixel resolution.
The erosion consists of all pixels whose distance
from the boundary of `w`

is strictly greater than `r`

(if
`strict=TRUE`

) or is greater than or equal to `r`

(if
`strict=FALSE`

).
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"`

.

If `shrink.frame`

is false, the resulting window is given the
same outer, bounding rectangle as the original window `w`

.
If `shrink.frame`

is true, the original bounding rectangle
is also eroded by the same distance `r`

.

To simply compute the area of the eroded window,
use `eroded.areas`

.

##### Value

- If
`r > 0`

, an object of class`"owin"`

representing the eroded region (or`NULL`

if this region is empty). If`r=0`

, the result is identical to`w`

.

##### See Also

`dilation`

for the opposite operation.
`owin`

,
`as.owin`

,
`eroded.areas`

##### Examples

```
w <- owin(c(0,1),c(0,1))
v <- erosion(w, 0.1)
# returns rectangle [0.1, 0.9] x [0.1,0.9]
v <- erosion(w, 0.6)
# erosion is empty
```

*Documentation reproduced from package spatstat, version 1.16-3, License: GPL (>= 2)*