import warnings
import numpy as np
from scipy.spatial import cKDTree
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def hausdorff_distance(image0, image1, method="standard"):
"""Calculate the Hausdorff distance between nonzero elements of given images.
Parameters
----------
image0, image1 : ndarray
Arrays where ``True`` represents a point that is included in a
set of points. Both arrays must have the same shape.
method : {'standard', 'modified'}, optional, default = 'standard'
The method to use for calculating the Hausdorff distance.
``standard`` is the standard Hausdorff distance, while ``modified``
is the modified Hausdorff distance.
Returns
-------
distance : float
The Hausdorff distance between coordinates of nonzero pixels in
``image0`` and ``image1``, using the Euclidean distance.
Notes
-----
The Hausdorff distance [1]_ is the maximum distance between any point on
``image0`` and its nearest point on ``image1``, and vice-versa.
The Modified Hausdorff Distance (MHD) has been shown to perform better
than the directed Hausdorff Distance (HD) in the following work by
Dubuisson et al. [2]_. The function calculates forward and backward
mean distances and returns the largest of the two.
References
----------
.. [1] http://en.wikipedia.org/wiki/Hausdorff_distance
.. [2] M. P. Dubuisson and A. K. Jain. A Modified Hausdorff distance for object
matching. In ICPR94, pages A:566-568, Jerusalem, Israel, 1994.
:DOI:`10.1109/ICPR.1994.576361`
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1.8155
Examples
--------
>>> points_a = (3, 0)
>>> points_b = (6, 0)
>>> shape = (7, 1)
>>> image_a = np.zeros(shape, dtype=bool)
>>> image_b = np.zeros(shape, dtype=bool)
>>> image_a[points_a] = True
>>> image_b[points_b] = True
>>> hausdorff_distance(image_a, image_b)
3.0
"""
if method not in ('standard', 'modified'):
raise ValueError(f'unrecognized method {method}')
a_points = np.transpose(np.nonzero(image0))
b_points = np.transpose(np.nonzero(image1))
# Handle empty sets properly:
# - if both sets are empty, return zero
# - if only one set is empty, return infinity
if len(a_points) == 0:
return 0 if len(b_points) == 0 else np.inf
elif len(b_points) == 0:
return np.inf
fwd, bwd = (
cKDTree(a_points).query(b_points, k=1)[0],
cKDTree(b_points).query(a_points, k=1)[0],
)
if method == 'standard': # standard Hausdorff distance
return max(max(fwd), max(bwd))
elif method == 'modified': # modified Hausdorff distance
return max(np.mean(fwd), np.mean(bwd))
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def hausdorff_pair(image0, image1):
"""Returns pair of points that are Hausdorff distance apart between nonzero
elements of given images.
The Hausdorff distance [1]_ is the maximum distance between any point on
``image0`` and its nearest point on ``image1``, and vice-versa.
Parameters
----------
image0, image1 : ndarray
Arrays where ``True`` represents a point that is included in a
set of points. Both arrays must have the same shape.
Returns
-------
point_a, point_b : array
A pair of points that have Hausdorff distance between them.
References
----------
.. [1] http://en.wikipedia.org/wiki/Hausdorff_distance
Examples
--------
>>> points_a = (3, 0)
>>> points_b = (6, 0)
>>> shape = (7, 1)
>>> image_a = np.zeros(shape, dtype=bool)
>>> image_b = np.zeros(shape, dtype=bool)
>>> image_a[points_a] = True
>>> image_b[points_b] = True
>>> hausdorff_pair(image_a, image_b)
(array([3, 0]), array([6, 0]))
"""
a_points = np.transpose(np.nonzero(image0))
b_points = np.transpose(np.nonzero(image1))
# If either of the sets are empty, there is no corresponding pair of points
if len(a_points) == 0 or len(b_points) == 0:
warnings.warn("One or both of the images is empty.", stacklevel=2)
return (), ()
nearest_dists_from_b, nearest_a_point_indices_from_b = cKDTree(a_points).query(
b_points
)
nearest_dists_from_a, nearest_b_point_indices_from_a = cKDTree(b_points).query(
a_points
)
max_index_from_a = nearest_dists_from_b.argmax()
max_index_from_b = nearest_dists_from_a.argmax()
max_dist_from_a = nearest_dists_from_b[max_index_from_a]
max_dist_from_b = nearest_dists_from_a[max_index_from_b]
if max_dist_from_b > max_dist_from_a:
return (
a_points[max_index_from_b],
b_points[nearest_b_point_indices_from_a[max_index_from_b]],
)
else:
return (
a_points[nearest_a_point_indices_from_b[max_index_from_a]],
b_points[max_index_from_a],
)
