fda.usc (version 2.0.2)

metric.hausdorff: Compute the Hausdorff distances between two curves.

Description

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)

Arguments

fdata1

Curves 1 of fdata class. The dimension of fdata1 object is (n1 x m), where n1 is the number of points observed in t coordinates with lenght m.

fdata2

Curves 2 of fdata class. The dimension of fdata2 object is (n2 x m), where n2 is the number of points observed in t coordinates with lenght m.

Author

Manuel Febrero-Bande, Manuel Oviedo de la Fuente

Details

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

$$d_H(X,Y)=max\{su{p}_{x\in G(X)}in{f}_{y\in G(Y)}{d}_2(x,y),su{p}_{y\in G(Y)}in{f}_{x\in G(X)}{d}_2(x,y)\},$$ where $d_2(x,y)$ is the euclidean distance, see metric.lp.

Examples

if (FALSE) {   
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)))
}