# eroded.areas

0th

Percentile

##### Areas of Morphological Erosions

Computes the areas of successive morphological erosions of a window.

Keywords
spatial, math
##### 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.

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