metric.hausdorff

Compute the Hausdorff distances between two curves.

Hausdorff distance is the greatest of all the distances from a point in one curve to the closest point in the other curve (been closest the euclidean distance).

Usage

metric.hausdorff(fdata1, fdata2 = fdata1)

Details

Let \(G(X)=\left\{ (t,X(t))\in R^2 \right\}\) and \(G(Y)=\left\{(t,Y(t))\in R^2\right\}\) be two graphs of the considered curves \(X\) and \(Y\) respectively, the Hausdorff distance \(d_H(X, Y)\) is defined as,

$$ d_H(X,Y)=max\left\{ sup_{x\in G(X)} inf_{y\in G(Y)} d_2(x,y), sup_{y\in G(Y)} inf_{x\in G(X)}d_2(x,y)\right\},$$ where \(d_2(x,y)\) is the euclidean distance, see metric.lp.

Aliases

• metric.hausdorff

Examples

# NOT RUN {
data(poblenou)
nox<-poblenou$nox[1:6]
# Hausdorff vs maximum distance
out1<-metric.hausdorff(nox)       
out2<-metric.lp(nox,lp=0) 
out1
out2
par(mfrow=c(1,3))
plot(nox)
plot(hclust(as.dist(out1)))
plot(hclust(as.dist(out2)))
# }
# NOT RUN {
# }