Perform morphological opening of a window, a line segment pattern
or a point pattern.
Usage
opening(w, r, ...)
"opening"(w, r, ..., polygonal=NULL)
"opening"(w, r, ...)
"opening"(w, r, ...)
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 the opening.
...
extra arguments passed to as.mask
controlling the pixel resolution, if a pixel approximation is used
polygonal
Logical flag indicating whether to compute a polygonal
approximation to the erosion (polygonal=TRUE) or
a pixel grid approximation (polygonal=FALSE).
Value
If r > 0, an object of class "owin" representing the
opened region. If r=0, the result is identical to w.
Details
The morphological opening (Serra, 1982)
of a set $W$ by a distance $r > 0$
is the subset of points in $W$ that can be
separated from the boundary of $W$ by a circle of radius $r$.
That is, a point $x$ belongs to the opening
if it is possible to draw a circle of radius $r$ (not necessarily
centred on $x$) that has $x$ on the inside
and the boundary of $W$ on the outside.
The opened set is a subset of W.
For a small radius $r$, the opening operation
has the effect of smoothing out irregularities in the boundary of
$W$. For larger radii, the opening operation removes promontories
in the boundary. For very large radii, the opened set is empty.