# opening

0th

Percentile

##### Morphological Opening

Perform morphological opening of a window, a line segment pattern or a point pattern.

Keywords
spatial, math
##### 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.

The algorithm applies erosion followed by dilation.

##### Value

• If r > 0, an object of class "owin" representing the opened region. If r=0, the result is identical to w.

##### References

Serra, J. (1982) Image analysis and mathematical morphology. Academic Press.

closing for the opposite operation.

dilation, erosion for the basic operations. owin, as.owin for information about windows.

• opening
• opening.owin
• opening.psp
• opening.ppp
##### Examples
v <- opening(letterR, 0.3)
plot(letterR, type="n", main="opening")
plot(letterR, add=TRUE)