spatstat.geom (version 3.3-3)

setcov: Set Covariance of a Window

Description

Computes the set covariance function of a window.

Usage

setcov(W, V=W, ...)

Value

A pixel image (an object of class "im") representing the set covariance function of W, or the cross-covariance of W and V.

Arguments

W

A window (object of class "owin".

V

Optional. Another window.

...

Optional arguments passed to as.mask to control the pixel resolution.

Author

Adrian Baddeley

and Rolf Turner

Details

The set covariance function of a region \(W\) in the plane is the function \(C(v)\) defined for each vector \(v\) as the area of the intersection between \(W\) and \(W+v\), where \(W+v\) is the set obtained by shifting (translating) \(W\) by \(v\).

We may interpret \(C(v)\) as the area of the set of all points \(x\) in \(W\) such that \(x+v\) also lies in \(W\).

This command computes a discretised approximation to the set covariance function of any plane region \(W\) represented as a window object (of class "owin", see owin.object). The return value is a pixel image (object of class "im") whose greyscale values are values of the set covariance function.

The set covariance is computed using the Fast Fourier Transform, unless W is a rectangle, when an exact formula is used.

If the argument V is present, then setcov(W,V) computes the set cross-covariance function \(C(x)\) defined for each vector \(x\) as the area of the intersection between \(W\) and \(V+x\).

See Also

imcov, owin, as.owin, erosion

Examples

  w <- owin(c(0,1),c(0,1))
  v <- setcov(w)
  plot(v)