Set Covariance of a Window
Computes the set covariance function of a window.
setcov(W, V=W, ...)
- A window (object of class
- Optional. Another window.
- Optional arguments passed to
as.maskto control the pixel resolution.
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
This command computes a discretised approximation to
the set covariance function of any
plane region $W$ represented as a window object (of class
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,
W is a rectangle, when an exact formula is used.
If the argument
V is present, then
computes the set cross-covariance function $C(x)$
defined for each vector $x$
as the area of the intersection between $W$ and $V+x$.
- A pixel image (an object of class
"im") representing the set covariance function of
W, or the cross-covariance of
w <- owin(c(0,1),c(0,1)) v <- setcov(w) plot(v)