R: Morphological Erosion of Windows

erosionAny {spatstat} | R Documentation

## Morphological Erosion of Windows

### Description

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 %(-)% 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^c %+% (-B))^c

where %+% 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"`).

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk

### See Also

`erosion`, `MinkowskiSum`

### Examples

      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)

[Package spatstat version 1.54-0 Index]