spatstat (version 1.31-3)

setcov: 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.

Value

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

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)