sharpen.Rd
\name{sharpen}
\alias{sharpen}
\alias{sharpen.ppp}
\title{Data Sharpening of Point Pattern}
\description{
Performs Choi-Hall data sharpening of a spatial point pattern.
}
\usage{
sharpen(X, ...)
\method{sharpen}{ppp}(X, sigma=NULL, ..., varcov=NULL,
edgecorrect=FALSE)
}
\arguments{
\item{X}{A marked point pattern (object of class \code{"ppp"}).}
\item{sigma}{
Standard deviation of isotropic Gaussian smoothing kernel.
}
\item{varcov}{
Variance-covariance matrix of anisotropic Gaussian kernel.
Incompatible with \code{sigma}.
}
\item{edgecorrect}{
Logical value indicating whether to apply
edge effect bias correction.
}
\item{\dots}{Arguments passed to \code{\link{density.ppp}}
to control the pixel resolution of the result.}
}
\details{
Choi and Hall (2001) proposed a procedure for
\emph{data sharpening} of spatial point patterns.
This procedure is appropriate for earthquake epicentres
and other point patterns which are believed to exhibit
strong concentrations of points along a curve. Data sharpening
causes such points to concentrate more tightly along the curve.
If the original data points are
\eqn{X_1, \ldots, X_n}{X[1],..., X[n]}
then the sharpened points are
\deqn{
\hat X_i = \frac{\sum_j X_j k(X_j-X_i)}{\sum_j k(X_j - X_i)}
}{
X^[i] = (sum[j] X[j] * k(X[j] - X[i]))/(sum[j] k(X[j] - X[i]))
}
where \eqn{k} is a smoothing kernel in two dimensions.
Thus, the new point \eqn{\hat X_i}{X^[i]} is a
vector average of the nearby points \eqn{X[j]}.
The function \code{sharpen} is generic. It currently has only one
method, for two-dimensional point patterns (objects of class
\code{"ppp"}).
If \code{sigma} is given, the smoothing kernel is the
isotropic two-dimensional Gaussian density with standard deviation
\code{sigma} in each axis. If \code{varcov} is given, the smoothing
kernel is the Gaussian density with variance-covariance matrix
\code{varcov}.
The data sharpening procedure tends to cause the point pattern
to contract away from the boundary of the window. That is,
points \code{X_i}{X[i]} that lie `quite close to the edge of the window
of the point pattern tend to be displaced inward.
If \code{edgecorrect=TRUE} then the algorithm is modified to
correct this vector bias.
}
\value{
A point pattern (object of class \code{"ppp"}) in the same window
as the original pattern \code{X}, and with the same marks as \code{X}.
}
\seealso{
\code{\link{density.ppp}},
\code{\link{smooth.ppp}}.
}
\examples{
data(shapley)
X <- unmark(shapley)
\dontshow{
if(!(interactive())) X <- rthin(X, 0.05)
}
Y <- sharpen(X, sigma=0.5)
}
\references{
Choi, E. and Hall, P. (2001)
Nonparametric analysis of earthquake point-process data.
In M. de Gunst, C. Klaassen and A. van der Vaart (eds.)
\emph{State of the art in probability and statistics:
Festschrift for Willem R. van Zwet},
Institute of Mathematical Statistics, Beachwood, Ohio.
Pages 324--344.
}
\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{nonparametric}