spatstat (version 1.16-1)

# opening: Morphological Opening

## Description

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`).

## 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.

The algorithm applies `erosion` followed by `dilation`.

## 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.

## Examples

Run this code
``````data(letterR)
v <- opening(letterR, 0.3, dimyx=256)
plot(v, main="opening")