setcov: Set Covariance of a Window

In spatstat.geom: Geometrical Functionality of the 'spatstat' Family

Set Covariance of a Window

Description

Computes the set covariance function of a window.

Usage

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

Arguments

W	A window (object of class "owin".
V	Optional. Another window.
...	Optional arguments passed to as.mask to control the pixel resolution.

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.

Value

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

Author(s)

\adrian

and \rolf

See Also

imcov, owin, as.owin, erosion

Examples

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

spatstat.geom documentation built on Sept. 18, 2024, 9:08 a.m.