Hausdorff Distance
Hausdorff distance (aka Hausdorff dimension)
hausdorff_dist(P, Q)
P, Q |
numerical matrices, representing points in an m-dim. space. |
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)).
A single scalar, the Hausdorff distance (dimension).
Barnsley, M. (1993). Fractals Everywhere. Morgan Kaufmann, San Francisco.
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))
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.