Calculate two-side Hausdorff distance between two sets using a brute force approach.

hausdorff.py

# -*- coding: utf-8 -*-
"""
Calculate two-side Hausdorff distance between two sets using a brute
force approach.

References
[1] http://en.wikipedia.org/wiki/Hausdorff_distance

@author: Nicolas Guarin-Zapata
"""
import numpy as np

def brute_force_hausdorff(set1, set2, dist):
    """ Compute the Hausforff distance of two sets
    
    Parameters
    ----------
    set1 : (m) iterable of points
        Set of points.
    set2 : (n) iterable of points
        Set of points.
    dist : function
        Distance function.
    
    Returns
    -------
    dH : float
        Two side Hausdorff distance for the given distance function.
    
    
    """
    m = len(set1)
    n = len(set2)
    M = np.zeros((m,n))
    for row, x1 in enumerate(set1):
        for col, x2 in enumerate(set2):
            M[row, col] = dist(x1, x2)
    
    dH = np.max([np.max(np.min(M,axis=1)), np.max(np.min(M,axis=0))])
    
    return dH
    
# %%   
    
set1 = [1, 2, 3, 5]
set2 = [1, 2]

def dist(x, y):
    return abs(x - y)
    
dH = brute_force_hausdorff(set1, set2, dist)

print dH