https://github.com/cran/spatstat
Tip revision: 967fc2de73b44e75d7d8497a8d21770604051e17 authored by Adrian Baddeley on 21 December 2011, 08:53:46 UTC
version 1.25-1
version 1.25-1
Tip revision: 967fc2d
setcov.Rd
\name{setcov}
\alias{setcov}
\title{Set Covariance of a Window}
\description{
Computes the set covariance function of a window.
}
\usage{
setcov(W, V=W, \dots)
}
\arguments{
\item{W}{
A window (object of class \code{"owin"}.
}
\item{V}{
Optional. Another window.
}
\item{\dots}{
Optional arguments passed to \code{\link{as.mask}}
to control the pixel resolution.
}
}
\value{
A pixel image (an object of class \code{"im"}) representing the
set covariance function of \code{W},
or the cross-covariance of \code{W} and \code{V}.
}
\details{
The set covariance function of a region \eqn{W} in the plane
is the function \eqn{C(v)} defined for each vector \eqn{v}
as the area of the intersection between \eqn{W} and \eqn{W+v},
where \eqn{W+v} is the set obtained by shifting (translating)
\eqn{W} by \eqn{v}.
We may interpret \eqn{C(v)} as the area of the set of
all points \eqn{x} in \eqn{W} such that \eqn{x+v} also lies in
\eqn{W}.
This command computes a discretised approximation to
the set covariance function of any
plane region \eqn{W} represented as a window object (of class
\code{"owin"}, see \code{\link{owin.object}}). The return value is
a pixel image (object of class \code{"im"}) whose greyscale values
are values of the set covariance function.
The set covariance is computed using the Fast Fourier Transform,
unless \code{W} is a rectangle, when an exact formula is used.
If the argument \code{V} is present, then \code{setcov(W,V)}
computes the set \emph{cross-covariance} function \eqn{C(x)}
defined for each vector \eqn{x}
as the area of the intersection between \eqn{W} and \eqn{V+x}.
}
\seealso{
\code{\link{imcov}},
\code{\link{owin}},
\code{\link{as.owin}},
\code{\link{erosion}}
}
\examples{
w <- owin(c(0,1),c(0,1))
v <- setcov(w)
plot(v)
}
\author{Adrian Baddeley
\email{Adrian.Baddeley@csiro.au}
\url{http://www.maths.uwa.edu.au/~adrian/}
and Rolf Turner
\email{r.turner@auckland.ac.nz}
}
\keyword{spatial}
\keyword{math}