Revision 6ebd6ff5fb7707ef87961f50ee794d8eb7143d0a authored by Adrian Baddeley on 10 August 2005, 00:00:00 UTC, committed by Gabor Csardi on 10 August 2005, 00:00:00 UTC
1 parent 5493ce5
setcov.Rd
\name{setcov}
\alias{setcov}
\title{Set Covariance of a Window}
\description{
Computes the set covariance function of a window.
}
\usage{
setcov(W)
}
\arguments{
\item{W}{A window (object of class \code{"owin"}.}
}
\value{
A pixel image (an object of class \code{"im"}) representing the
set covariance function of \code{W}.
}
\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.
}
\seealso{
\code{\link{owin}},
\code{\link{as.owin}},
\code{\link{erode.owin}}
}
\examples{
w <- owin(c(0,1),c(0,1))
v <- setcov(w)
plot(v)
}
\author{Adrian Baddeley
\email{adrian@maths.uwa.edu.au}
\url{http://www.maths.uwa.edu.au/~adrian/}
and Rolf Turner
\email{rolf@math.unb.ca}
\url{http://www.math.unb.ca/~rolf}
}
\keyword{spatial}
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