Revision d606122dc24b56ecf537d55eda38f4bf5ac4de1f authored by Adrian Baddeley on 25 October 2010, 10:40:51 UTC, committed by cran-robot on 25 October 2010, 10:40:51 UTC
1 parent 66bc933
opening.Rd
\name{opening}
\alias{opening}
\alias{opening.owin}
\alias{opening.psp}
\alias{opening.ppp}
\title{Morphological Opening}
\description{
Perform morphological opening of a window, a line segment pattern
or a point pattern.
}
\usage{
opening(w, r, \dots)
\method{opening}{owin}(w, r, \dots, polygonal=NULL)
\method{opening}{ppp}(w, r, \dots)
\method{opening}{psp}(w, r, \dots)
}
\arguments{
\item{w}{
A window (object of class \code{"owin"}
or a line segment pattern (object of class \code{"psp"})
or a point pattern (object of class \code{"ppp"}).
}
\item{r}{positive number: the radius of the opening.}
\item{\dots}{extra arguments passed to \code{\link{as.mask}}
controlling the pixel resolution, if a pixel approximation is used}
\item{polygonal}{
Logical flag indicating whether to compute a polygonal
approximation to the erosion (\code{polygonal=TRUE}) or
a pixel grid approximation (\code{polygonal=FALSE}).
}
}
\value{
If \code{r > 0}, an object of class \code{"owin"} representing the
opened region. If \code{r=0}, the result is identical to \code{w}.
}
\details{
The morphological opening (Serra, 1982)
of a set \eqn{W} by a distance \eqn{r > 0}
is the subset of points in \eqn{W} that can be
separated from the boundary of \eqn{W} by a circle of radius \eqn{r}.
That is, a point \eqn{x} belongs to the opening
if it is possible to draw a circle of radius \eqn{r} (not necessarily
centred on \eqn{x}) that has \eqn{x} on the inside
and the boundary of \eqn{W} on the outside.
The opened set is a subset of \code{W}.
For a small radius \eqn{r}, the opening operation
has the effect of smoothing out irregularities in the boundary of
\eqn{W}. For larger radii, the opening operation removes promontories
in the boundary. For very large radii, the opened set is empty.
The algorithm applies \code{\link{erosion}} followed by
\code{\link{dilation}}.
}
\seealso{
\code{\link{closing}} for the opposite operation.
\code{\link{dilation}}, \code{\link{erosion}} for the basic
operations.
\code{\link{owin}},
\code{\link{as.owin}} for information about windows.
}
\examples{
data(letterR)
v <- opening(letterR, 0.3, dimyx=256)
plot(v, main="opening")
plot(letterR, add=TRUE)
}
\references{
Serra, J. (1982)
Image analysis and mathematical morphology.
Academic Press.
}
\author{Adrian Baddeley
\email{adrian@maths.uwa.edu.au}
\url{http://www.maths.uwa.edu.au/~adrian/}
and Rolf Turner
\email{r.turner@auckland.ac.nz}
}
\keyword{spatial}
\keyword{math}
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