Morphological Erosion of Windows
Compute the morphological erosion of one spatial window by another.
erosionAny(A, B) A %(-)% B
A,B |
Windows (objects of class |
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.
Another window (object of class "owin").
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk
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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.