# eroded.areas

##### Areas of Morphological Erosions

Computes the areas of successive morphological erosions of a window.

##### Usage

`eroded.areas(w, r)`

##### Arguments

- w
- A window.
- r
- Numeric vector of radii at which erosions will be performed.

##### Details

This function computes the areas of the erosions of the window
`w`

by each of the radii `r[i]`

.

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 $W$.

The argument `r`

should be a vector of positive numbers.
The argument `w`

should be a window (an object of class
`"owin"`

, see `owin.object`

for details)
or can be given in any format acceptable to `as.owin()`

.

Unless `w`

is a rectangle, the computation is performed
using a pixel raster approximation.

To compute the eroded window itself, use `erosion`

.

##### Value

- Numeric vector, of the same length as
`r`

, giving the areas of the successive erosions.

##### See Also

##### Examples

```
w <- owin(c(0,1),c(0,1))
a <- eroded.areas(w, seq(0.01,0.49,by=0.01))
```

*Documentation reproduced from package spatstat, version 1.23-3, License: GPL (>= 2)*