R: Hausdorff Distance

hausdorff_dist {pracma} | R Documentation

## Hausdorff Distance

### Description

Hausdorff distance (aka Hausdorff dimension)

### Usage

    hausdorff_dist(P, Q)

### Arguments

`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.

### See Also

`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))

[Package pracma version 2.0.4 Index]