numerical matrices, representing points in an m-dim. space.

Value

A single scalar, the Hausdorff distance (dimension).

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)).

References

Barnsley, M. (1993). Fractals Everywhere. Morgan Kaufmann, San Francisco.