117 lines
3.6 KiB
Python
117 lines
3.6 KiB
Python
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import warnings
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import numpy as np
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from scipy.spatial import cKDTree
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def hausdorff_distance(image0, image1):
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"""Calculate the Hausdorff distance between nonzero elements of given images.
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The Hausdorff distance [1]_ is the maximum distance between any point on
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``image0`` and its nearest point on ``image1``, and vice-versa.
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Parameters
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----------
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image0, image1 : ndarray
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Arrays where ``True`` represents a point that is included in a
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set of points. Both arrays must have the same shape.
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Returns
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-------
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distance : float
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The Hausdorff distance between coordinates of nonzero pixels in
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``image0`` and ``image1``, using the Euclidian distance.
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References
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----------
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.. [1] http://en.wikipedia.org/wiki/Hausdorff_distance
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Examples
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--------
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>>> points_a = (3, 0)
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>>> points_b = (6, 0)
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>>> shape = (7, 1)
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>>> image_a = np.zeros(shape, dtype=bool)
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>>> image_b = np.zeros(shape, dtype=bool)
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>>> image_a[points_a] = True
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>>> image_b[points_b] = True
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>>> hausdorff_distance(image_a, image_b)
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3.0
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"""
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a_points = np.transpose(np.nonzero(image0))
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b_points = np.transpose(np.nonzero(image1))
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# Handle empty sets properly:
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# - if both sets are empty, return zero
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# - if only one set is empty, return infinity
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if len(a_points) == 0:
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return 0 if len(b_points) == 0 else np.inf
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elif len(b_points) == 0:
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return np.inf
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return max(max(cKDTree(a_points).query(b_points, k=1)[0]),
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max(cKDTree(b_points).query(a_points, k=1)[0]))
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def hausdorff_pair(image0, image1):
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"""Returns pair of points that are Hausdorff distance apart between nonzero
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elements of given images.
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The Hausdorff distance [1]_ is the maximum distance between any point on
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``image0`` and its nearest point on ``image1``, and vice-versa.
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Parameters
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----------
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image0, image1 : ndarray
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Arrays where ``True`` represents a point that is included in a
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set of points. Both arrays must have the same shape.
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Returns
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-------
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point_a, point_b : array
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A pair of points that have Hausdorff distance between them.
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References
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----------
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.. [1] http://en.wikipedia.org/wiki/Hausdorff_distance
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Examples
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--------
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>>> points_a = (3, 0)
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>>> points_b = (6, 0)
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>>> shape = (7, 1)
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>>> image_a = np.zeros(shape, dtype=bool)
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>>> image_b = np.zeros(shape, dtype=bool)
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>>> image_a[points_a] = True
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>>> image_b[points_b] = True
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>>> hausdorff_pair(image_a, image_b)
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(array([3, 0]), array([6, 0]))
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"""
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a_points = np.transpose(np.nonzero(image0))
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b_points = np.transpose(np.nonzero(image1))
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# If either of the sets are empty, there is no corresponding pair of points
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if len(a_points) == 0 or len(b_points) == 0:
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warnings.warn("One or both of the images is empty.", stacklevel=2)
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return (), ()
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nearest_dists_from_b, nearest_a_point_indices_from_b = cKDTree(a_points) \
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.query(b_points)
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nearest_dists_from_a, nearest_b_point_indices_from_a = cKDTree(b_points) \
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.query(a_points)
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max_index_from_a = nearest_dists_from_b.argmax()
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max_index_from_b = nearest_dists_from_a.argmax()
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max_dist_from_a = nearest_dists_from_b[max_index_from_a]
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max_dist_from_b = nearest_dists_from_a[max_index_from_b]
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if max_dist_from_b > max_dist_from_a:
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return a_points[max_index_from_b], \
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b_points[nearest_b_point_indices_from_a[max_index_from_b]]
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else:
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return a_points[nearest_a_point_indices_from_b[max_index_from_a]], \
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b_points[max_index_from_a]
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