Perform morphological opening of a window, a line segment pattern or a point pattern.
opening(w, r, ...) ## S3 method for class 'owin': opening(w, r, \dots, polygonal=NULL) ## S3 method for class 'ppp': opening(w, r, \dots) ## S3 method for class 'psp': opening(w, r, \dots)
- A window (object of class
"owin"or a line segment pattern (object of class
"psp") or a point pattern (object of class
- positive number: the radius of the opening.
- extra arguments passed to
as.maskcontrolling the pixel resolution, if a pixel approximation is used
- Logical flag indicating whether to compute a polygonal
approximation to the erosion (
polygonal=TRUE) or a pixel grid approximation (
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
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.
r > 0, an object of class
"owin"representing the opened region. If
r=0, the result is identical to
Serra, J. (1982) Image analysis and mathematical morphology. Academic Press.
closing for the opposite operation.
data(letterR) v <- opening(letterR, 0.3, dimyx=256) plot(v, main="opening") plot(letterR, add=TRUE)