def test_hausdorff_empty():
empty = np.zeros((0, 2), dtype=bool)
non_empty = np.zeros((3, 2), dtype=bool)
assert hausdorff_distance(empty, non_empty) == 0.
assert_array_equal(hausdorff_pair(empty, non_empty), [(), ()])
assert hausdorff_distance(non_empty, empty) == 0.
assert_array_equal(hausdorff_pair(non_empty, empty), [(), ()])
assert hausdorff_distance(empty, non_empty) == 0.
assert_array_equal(hausdorff_pair(empty, non_empty), [(), ()])
def test_hausdorff_empty():
empty = np.zeros((0, 2), dtype=bool)
non_empty = np.zeros((3, 2), dtype=bool)
assert hausdorff_distance(empty, non_empty) == 0.0 # standard Hausdorff
assert (hausdorff_distance(empty, non_empty,
method="modified") == 0.0) # modified Hausdorff
with expected_warnings(["One or both of the images is empty"]):
assert_array_equal(hausdorff_pair(empty, non_empty), [(), ()])
assert hausdorff_distance(non_empty, empty) == 0.0 # standard Hausdorff
assert (hausdorff_distance(non_empty, empty,
method="modified") == 0.0) # modified Hausdorff
with expected_warnings(["One or both of the images is empty"]):
assert_array_equal(hausdorff_pair(non_empty, empty), [(), ()])
assert hausdorff_distance(empty, non_empty) == 0.0 # standard Hausdorff
assert (hausdorff_distance(empty, non_empty,
method="modified") == 0.0) # modified Hausdorff
with expected_warnings(["One or both of the images is empty"]):
assert_array_equal(hausdorff_pair(empty, non_empty), [(), ()])
def test_hausdorff_region_different_points(points_a, points_b):
shape = (7, 7)
coords_a = np.zeros(shape, dtype=bool)
coords_b = np.zeros(shape, dtype=bool)
coords_a[points_a] = True
coords_b[points_b] = True
dist = np.sqrt(sum((ca - cb)**2 for ca, cb in zip(points_a, points_b)))
assert_almost_equal(hausdorff_distance(coords_a, coords_b), dist)
assert_array_equal(hausdorff_pair(coords_a, coords_b),
(points_a, points_b))
def test_hausdorff_simple():
points_a = (3, 0)
points_b = (6, 0)
shape = (7, 1)
coords_a = np.zeros(shape, dtype=bool)
coords_b = np.zeros(shape, dtype=bool)
coords_a[points_a] = True
coords_b[points_b] = True
dist = np.sqrt(sum((ca - cb)**2 for ca, cb in zip(points_a, points_b)))
assert_almost_equal(hausdorff_distance(coords_a, coords_b), dist)
assert_array_equal(hausdorff_pair(coords_a, coords_b),
(points_a, points_b))
def test_gallery():
shape = (60, 60)
# Create a diamond-like shape where the four corners form the 1st set
# of points
x_diamond = 30
y_diamond = 30
r = 10
plt_x = [0, 1, 0, -1]
plt_y = [1, 0, -1, 0]
set_ax = [(x_diamond + r * x) for x in plt_x]
set_ay = [(y_diamond + r * y) for y in plt_y]
# Create a kite-like shape where the four corners form the 2nd set of
# points
x_kite = 30
y_kite = 30
x_r = 15
y_r = 20
set_bx = [(x_kite + x_r * x) for x in plt_x]
set_by = [(y_kite + y_r * y) for y in plt_y]
# Set up the data to compute the Hausdorff distance
coords_a = np.zeros(shape, dtype=bool)
coords_b = np.zeros(shape, dtype=bool)
for x, y in zip(set_ax, set_ay):
coords_a[(x, y)] = True
for x, y in zip(set_bx, set_by):
coords_b[(x, y)] = True
# Test the Hausdorff function on the coordinates
# Should return 10, the distance between the furthest tip of the kite and
# its closest point on the diamond, which is the furthest someone can make
# you travel to encounter your nearest neighboring point on the other set.
assert_almost_equal(hausdorff_distance(coords_a, coords_b), 10.0)
# There are two pairs of points ((30, 20), (30, 10) or (30, 40), (30, 50)),
# that are Hausdorff distance apart. This tests for either of them.
hd_points = hausdorff_pair(coords_a, coords_b)
assert (np.equal(hd_points, ((30, 20), (30, 10))).all()
or np.equal(hd_points, ((30, 40), (30, 50))).all())
# Test the Modified Hausdorff function on the coordinates
# Should return 7.5.
assert_almost_equal(
hausdorff_distance(coords_a, coords_b, method="modified"), 7.5)
def test_hausdorff_metrics_match():
# Test that Hausdorff distance is the Euclidean distance between Hausdorff
# pair
points_a = (3, 0)
points_b = (6, 0)
shape = (7, 1)
coords_a = np.zeros(shape, dtype=bool)
coords_b = np.zeros(shape, dtype=bool)
coords_a[points_a] = True
coords_b[points_b] = True
assert_array_equal(hausdorff_pair(coords_a, coords_b),
(points_a, points_b))
euclidean_distance = distance.euclidean(points_a, points_b)
assert_almost_equal(euclidean_distance,
hausdorff_distance(coords_a, coords_b))
def test_hausdorff_region_different_points(points_a, points_b):
shape = (7, 7)
coords_a = np.zeros(shape, dtype=bool)
coords_b = np.zeros(shape, dtype=bool)
coords_a[points_a] = True
coords_b[points_b] = True
dist = np.sqrt(sum((ca - cb)**2 for ca, cb in zip(points_a, points_b)))
d = distance.cdist([points_a], [points_b])
dist_modified = max(np.mean(np.min(d, axis=0)), np.mean(np.min(d, axis=1)))
assert_almost_equal(hausdorff_distance(coords_a, coords_b), dist)
assert_array_equal(hausdorff_pair(coords_a, coords_b),
(points_a, points_b))
assert_almost_equal(
hausdorff_distance(coords_a, coords_b, method="modified"),
dist_modified)
def time_hausdorff_pair(self):
metrics.hausdorff_pair(self.coords_a, self.coords_b)
set_bx = [(x_kite + x_r * x) for x in plt_x]
set_by = [(y_kite + y_r * y) for y in plt_y]
plt.plot(set_bx, set_by, 'og')
# Set up the data to compute the Hausdorff distance
coords_a = np.zeros(shape, dtype=bool)
coords_b = np.zeros(shape, dtype=bool)
for x, y in zip(set_ax, set_ay):
coords_a[(x, y)] = True
for x, y in zip(set_bx, set_by):
coords_b[(x, y)] = True
# Call the Hausdorff function on the coordinates
metrics.hausdorff_distance(coords_a, coords_b)
hausdorff_point_a, hausdorff_point_b = metrics.hausdorff_pair(
coords_a, coords_b)
# Plot the lines that shows the length of the Hausdorff distance
x_line = [30, 30]
y_line = [20, 10]
plt.plot(x_line, y_line, 'y')
x_line = [30, 30]
y_line = [40, 50]
plt.plot(x_line, y_line, 'y')
# Plot circles to show that at this distance, the Hausdorff distance can
# travel to its nearest neighbor (in this case, from the kite to diamond)
ax.add_artist(plt.Circle((30, 10), 10, color='y', fill=None))
ax.add_artist(plt.Circle((30, 50), 10, color='y', fill=None))
ax.add_artist(plt.Circle((15, 30), 10, color='y', fill=None))