# erosionAny

##### Morphological Erosion of Windows

Compute the morphological erosion of one spatial window by another.

##### Usage

`erosionAny(A, B)`A %(-)% B

##### Arguments

- A,B
Windows (objects of class

`"owin"`

).

##### Details

The operator `A %(-)% B`

and function `erosionAny(A,B)`

are synonymous: they both compute the
morphological erosion of the window `A`

by the window `B`

.

The morphological erosion \(A \ominus B\) of region \(A\) by region \(B\) is the spatial region consisting of all vectors \(z\) such that, when \(B\) is shifted by the vector \(z\), the result is a subset of \(A\).

Equivalently $$ A \ominus B = ((A^c \oplus (-B))^c $$ where \(\oplus\) is the Minkowski sum, \(A^c\) denotes the set complement, and \((-B)\) is the reflection of \(B\) through the origin, consisting of all vectors \(-b\) where \(b\) is a point in \(B\).

If `B`

is a disc of radius `r`

, then
`erosionAny(A, B)`

is equivalent to `erosion(A, r)`

.
See `erosion`

.

The algorithm currently computes the result as a polygonal window using the polyclip library. It will be quite slow if applied to binary mask windows.

##### Value

Another window (object of class `"owin"`

).

##### See Also

##### Examples

```
# NOT RUN {
B <- square(c(-0.1, 0.1))
RminusB <- letterR %(-)% B
FR <- grow.rectangle(Frame(letterR), 0.3)
plot(FR, main="", type="n")
plot(letterR, add=TRUE, lwd=2, hatch=TRUE, box=FALSE)
plot(RminusB, add=TRUE, col="blue", box=FALSE)
plot(shift(B, vec=c(3.49, 2.98)),
add=TRUE, border="red", lwd=2)
# }
```

*Documentation reproduced from package spatstat, version 1.64-1, License: GPL (>= 2)*