scipy.spatial.distance.directed_hausdorff(u, v, seed=0)[source]#

Compute the directed Hausdorff distance between two 2-D arrays.

Distances between pairs are calculated using a Euclidean metric.

u(M,N) array_like

Input array with M points in N dimensions.

v(O,N) array_like

Input array with O points in N dimensions.

seedint or None, optional

Local numpy.random.RandomState seed. Default is 0, a random shuffling of u and v that guarantees reproducibility.


The directed Hausdorff distance between arrays u and v,


index of point contributing to Hausdorff pair in u


index of point contributing to Hausdorff pair in v


An exception is thrown if u and v do not have the same number of columns.

See also


Another similarity test for two data sets


Uses the early break technique and the random sampling approach described by [1]. Although worst-case performance is O(m * o) (as with the brute force algorithm), this is unlikely in practice as the input data would have to require the algorithm to explore every single point interaction, and after the algorithm shuffles the input points at that. The best case performance is O(m), which is satisfied by selecting an inner loop distance that is less than cmax and leads to an early break as often as possible. The authors have formally shown that the average runtime is closer to O(m).

Added in version 0.19.0.



A. A. Taha and A. Hanbury, “An efficient algorithm for calculating the exact Hausdorff distance.” IEEE Transactions On Pattern Analysis And Machine Intelligence, vol. 37 pp. 2153-63, 2015.


Find the directed Hausdorff distance between two 2-D arrays of coordinates:

>>> from scipy.spatial.distance import directed_hausdorff
>>> import numpy as np
>>> u = np.array([(1.0, 0.0),
...               (0.0, 1.0),
...               (-1.0, 0.0),
...               (0.0, -1.0)])
>>> v = np.array([(2.0, 0.0),
...               (0.0, 2.0),
...               (-2.0, 0.0),
...               (0.0, -4.0)])
>>> directed_hausdorff(u, v)[0]
>>> directed_hausdorff(v, u)[0]

Find the general (symmetric) Hausdorff distance between two 2-D arrays of coordinates:

>>> max(directed_hausdorff(u, v)[0], directed_hausdorff(v, u)[0])

Find the indices of the points that generate the Hausdorff distance (the Hausdorff pair):

>>> directed_hausdorff(v, u)[1:]
(3, 3)