Revision 04bbc417cf2927b827660bc07743429783569aec authored by HwB on 10 February 2013, 00:00:00 UTC, committed by Gabor Csardi on 10 February 2013, 00:00:00 UTC
1 parent 0e3ae6b
hausdorff.Rd
\name{hausdorff_dist}
\alias{hausdorff_dist}
\title{Hausdorff Distance}
\description{
Hausdorff distance (aka Hausdorff dimension)
}
\usage{
hausdorff_dist(P, Q)
}
\arguments{
\item{P, Q}{numerical matrices, representing points in an m-dim. space.}
}
\details{
Calculates the Hausdorff Distance between two sets of points, P and Q.
Sets P and Q must be matrices with the same number of columns (dimensions).
The `directional' Hausdorff distance (dhd) is defined as:
dhd(P,Q) = max p in P [ min q in Q [ ||p-q|| ] ]
Intuitively dhd finds the point p from the set P that is farthest from any
point in Q and measures the distance from p to its nearest neighbor in Q.
The Hausdorff Distance is defined as max(dhd(P,Q),dhd(Q,P)).
}
\value{
A single scalar, the Hausdorff distance (dimension).
}
\references{
Barnsley, M. (1993). Fractals Everywhere. Morgan Kaufmann, San Francisco.
}
\seealso{
\code{\link{distmat}}
}
\examples{
P <- matrix(c(1,1,2,2, 5,4,5,4), 4, 2)
Q <- matrix(c(4,4,5,5, 2,1,2,1), 4, 2)
hausdorff_dist(P, Q) # 4.242641 = sqrt(sum((c(4,2)-c(1,5))^2))
}
\keyword{ math }
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