# opening.owin

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##### Morphological Opening of a Window

Perform morphological opening of a window

Keywords
spatial, math
##### Usage
opening.owin(w, r, ...)
##### Arguments
w
A window (object of class "owin".
r
positive number: the radius of the opening.
...
extra arguments passed to as.mask controlling the pixel resolution
##### 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.

This function computes the opening of the window w as a binary pixel mask. If w is not already a mask, it is first converted to a mask by as.mask. The arguments "..." determine the pixel resolution. There is a sensible default.

The algorithm simply applies erode.owin followed by dilate.owin.

##### Value

• Another object of class "owin" representing the opened window.

##### References

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

closing.owin for the opposite operation.

dilate.owin, erode.owin for the basic operations. owin, as.owin for information about windows.

• opening.owin
##### Examples
data(letterR)
v <- opening.owin(letterR, 0.3, dimyx=256)
plot(v, main="opening.owin")