erosionAny {spatstat.geom}

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 \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").

Author(s)

Adrian Baddeley [e-mail], Rolf Turner [e-mail] and Ege Rubak [e-mail]

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)