# dilated.areas

0th

Percentile

##### Areas of Morphological Dilations

Computes the areas of successive morphological dilations.

Keywords
spatial, math
##### Usage
dilated.areas(X, r, W=NULL, ..., exact = FALSE)
##### Arguments
X
Object to be dilated. A point pattern (object of class "ppp"), a line segment pattern (object of class "psp"), or a window (object of class "owin").
r
Numeric vector of radii for the dilations.
W
Optional. Window (object of class "owin") inside which the areas will be computed, or NULL indicating the entire area should be computed.
...
Ignored.
exact
Logical flag indicating whether areas should be computed using analytic geometry (which is slower but more accurate). Currently available only when X is a point pattern.
##### Details

This function computes the areas of the dilations of X by each of the radii r[i]. Areas may also be computed inside a specified window W.

The morphological dilation of a set $X$ by a distance $r > 0$ is the subset consisting of all points $x$ such that the distance from $x$ to $X$ is less than or equal to $r$.

When X is a point pattern, the dilation by a distance $r$ is the union of discs of radius $r$ centred at the points of X.

The argument r should be a vector of nonnegative numbers.

If exact=TRUE and if X is a point pattern, then the areas are computed using analytic geometry, which is slower but much more accurate. Otherwise the computation is performed using distmap.

To compute the dilated object itself, use dilation.

owin, as.owin, dilation, eroded.areas
X <- runifpoint(10)
a <- dilated.areas(X, c(0.1,0.2), W=square(1), exact=TRUE)