opening
Morphological Opening
Perform morphological opening of a window, a line segment pattern or a point pattern.
Usage
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)
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
).
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.
Value
- If
r > 0
, an object of class"owin"
representing the opened region. Ifr=0
, the result is identical tow
.
References
Serra, J. (1982) Image analysis and mathematical morphology. Academic Press.
See Also
closing
for the opposite operation.
dilation
, erosion
for the basic
operations.
owin
,
as.owin
for information about windows.
Examples
v <- opening(letterR, 0.3)
plot(letterR, type="n", main="opening")
plot(v, add=TRUE, col="grey")
plot(letterR, add=TRUE)