def test_cross_correlate_masked_over_axes():
"""Masked normalized cross-correlation over axes should be
equivalent to a loop over non-transform axes."""
# See random number generator for reproducible results
np.random.seed(23)
arr1 = np.random.random((8, 8, 5))
arr2 = np.random.random((8, 8, 5))
m1 = np.random.choice([True, False], arr1.shape)
m2 = np.random.choice([True, False], arr2.shape)
# Loop over last axis
with_loop = np.empty_like(arr1, dtype=np.complex)
for index in range(arr1.shape[-1]):
with_loop[:, :, index] = cross_correlate_masked(arr1[:, :, index],
arr2[:, :, index],
m1[:, :, index],
m2[:, :, index],
axes=(0, 1),
mode='same')
over_axes = cross_correlate_masked(
arr1, arr2, m1, m2, axes=(0, 1), mode='same')
testing.assert_array_almost_equal(with_loop, over_axes)
def test_cross_correlate_masked_over_axes():
"""Masked normalized cross-correlation over axes should be
equivalent to a loop over non-transform axes."""
# See random number generator for reproducible results
np.random.seed(23)
arr1 = np.random.random((8, 8, 5))
arr2 = np.random.random((8, 8, 5))
m1 = np.random.choice([True, False], arr1.shape)
m2 = np.random.choice([True, False], arr2.shape)
# Loop over last axis
with_loop = np.empty_like(arr1, dtype=np.complex)
for index in range(arr1.shape[-1]):
with_loop[:, :, index] = cross_correlate_masked(arr1[:, :, index],
arr2[:, :, index],
m1[:, :, index],
m2[:, :, index],
axes=(0, 1),
mode='same')
over_axes = cross_correlate_masked(arr1,
arr2,
m1,
m2,
axes=(0, 1),
mode='same')
testing.assert_array_almost_equal(with_loop, over_axes)
def test_cross_correlate_masked_output_shape():
"""Masked normalized cross-correlation should return a shape
of N + M + 1 for each transform axis."""
shape1 = (15, 4, 5)
shape2 = (6, 12, 7)
expected_full_shape = tuple(np.array(shape1) + np.array(shape2) - 1)
expected_same_shape = shape1
arr1 = np.zeros(shape1)
arr2 = np.zeros(shape2)
# Trivial masks
m1 = np.ones_like(arr1)
m2 = np.ones_like(arr2)
full_xcorr = cross_correlate_masked(arr1,
arr2,
m1,
m2,
axes=(0, 1, 2),
mode='full')
assert_equal(full_xcorr.shape, expected_full_shape)
same_xcorr = cross_correlate_masked(arr1,
arr2,
m1,
m2,
axes=(0, 1, 2),
mode='same')
assert_equal(same_xcorr.shape, expected_same_shape)
def test_cross_correlate_masked_test_against_mismatched_dimensions():
"""Masked normalized cross-correlation should raise an error if array
dimensions along non-transformation axes are mismatched."""
shape1 = (23, 1, 1)
shape2 = (6, 2, 2)
arr1 = np.zeros(shape1)
arr2 = np.zeros(shape2)
# Trivial masks
m1 = np.ones_like(arr1)
m2 = np.ones_like(arr2)
with testing.raises(ValueError):
cross_correlate_masked(arr1, arr2, m1, m2, axes=(1, 2))
def test_cross_correlate_masked_test_against_mismatched_dimensions():
"""Masked normalized cross-correlation should raise an error if array
dimensions along non-transformation axes are mismatched."""
shape1 = (23, 1, 1)
shape2 = (6, 2, 2)
arr1 = np.zeros(shape1)
arr2 = np.zeros(shape2)
# Trivial masks
m1 = np.ones_like(arr1)
m2 = np.ones_like(arr2)
with testing.raises(ValueError):
cross_correlate_masked(arr1, arr2, m1, m2, axes=(1, 2))
def test_cross_correlate_masked_autocorrelation_trivial_masks():
"""Masked normalized cross-correlation between identical arrays
should reduce to an autocorrelation even with random masks."""
# See random number generator for reproducible results
np.random.seed(23)
arr1 = camera()
arr2 = camera()
# Random masks with 75% of pixels being valid
m1 = np.random.choice([True, False], arr1.shape, p=[3 / 4, 1 / 4])
m2 = np.random.choice([True, False], arr2.shape, p=[3 / 4, 1 / 4])
xcorr = cross_correlate_masked(arr1,
arr1,
m1,
m1,
axes=(0, 1),
mode='same',
overlap_ratio=0).real
max_index = np.unravel_index(np.argmax(xcorr), xcorr.shape)
# Autocorrelation should have maximum in center of array
testing.assert_almost_equal(xcorr.max(), 1)
testing.assert_array_equal(max_index, np.array(arr1.shape) / 2)
def test_cross_correlate_masked_side_effects():
"""Masked normalized cross-correlation should not modify the inputs."""
shape1 = (2, 2, 2)
shape2 = (2, 2, 2)
arr1 = np.zeros(shape1)
arr2 = np.zeros(shape2)
# Trivial masks
m1 = np.ones_like(arr1)
m2 = np.ones_like(arr2)
for arr in (arr1, arr2, m1, m2):
arr.setflags(write=False)
cross_correlate_masked(arr1, arr2, m1, m2)
def test_cross_correlate_masked_output_range():
"""Masked normalized cross-correlation should return between 1 and -1."""
# See random number generator for reproducible results
np.random.seed(23)
# Array dimensions must match along non-transformation axes, in
# this case
# axis 0
shape1 = (15, 4, 5)
shape2 = (15, 12, 7)
# Initial array ranges between -5 and 5
arr1 = 10 * np.random.random(shape1) - 5
arr2 = 10 * np.random.random(shape2) - 5
# random masks
m1 = np.random.choice([True, False], arr1.shape)
m2 = np.random.choice([True, False], arr2.shape)
xcorr = cross_correlate_masked(arr1, arr2, m1, m2, axes=(1, 2))
# No assert array less or equal, so we add an eps
# Also could not find an `assert_array_greater`, Use (-xcorr) instead
eps = np.finfo(np.float).eps
testing.assert_array_less(xcorr, 1 + eps)
testing.assert_array_less(-xcorr, 1 + eps)
def test_cross_correlate_masked_side_effects():
"""Masked normalized cross-correlation should not modify the inputs."""
shape1 = (2, 2, 2)
shape2 = (2, 2, 2)
arr1 = np.zeros(shape1)
arr2 = np.zeros(shape2)
# Trivial masks
m1 = np.ones_like(arr1)
m2 = np.ones_like(arr2)
for arr in (arr1, arr2, m1, m2):
arr.setflags(write=False)
cross_correlate_masked(arr1, arr2, m1, m2)
def test_cross_correlate_masked_output_range():
"""Masked normalized cross-correlation should return between 1 and -1."""
# See random number generator for reproducible results
np.random.seed(23)
# Array dimensions must match along non-transformation axes, in
# this case
# axis 0
shape1 = (15, 4, 5)
shape2 = (15, 12, 7)
# Initial array ranges between -5 and 5
arr1 = 10 * np.random.random(shape1) - 5
arr2 = 10 * np.random.random(shape2) - 5
# random masks
m1 = np.random.choice([True, False], arr1.shape)
m2 = np.random.choice([True, False], arr2.shape)
xcorr = cross_correlate_masked(arr1, arr2, m1, m2, axes=(1, 2))
# No assert array less or equal, so we add an eps
# Also could not find an `assert_array_greater`, Use (-xcorr) instead
eps = np.finfo(np.float).eps
testing.assert_array_less(xcorr, 1 + eps)
testing.assert_array_less(-xcorr, 1 + eps)
def test_cross_correlate_masked_output_shape():
"""Masked normalized cross-correlation should return a shape
of N + M + 1 for each transform axis."""
shape1 = (15, 4, 5)
shape2 = (6, 12, 7)
expected_full_shape = tuple(np.array(shape1) + np.array(shape2) - 1)
expected_same_shape = shape1
arr1 = np.zeros(shape1)
arr2 = np.zeros(shape2)
# Trivial masks
m1 = np.ones_like(arr1)
m2 = np.ones_like(arr2)
full_xcorr = cross_correlate_masked(
arr1, arr2, m1, m2, axes=(0, 1, 2), mode='full')
assert_equal(full_xcorr.shape, expected_full_shape)
same_xcorr = cross_correlate_masked(
arr1, arr2, m1, m2, axes=(0, 1, 2), mode='same')
assert_equal(same_xcorr.shape, expected_same_shape)
def test_cross_correlate_masked_autocorrelation_trivial_masks():
"""Masked normalized cross-correlation between identical arrays
should reduce to an autocorrelation even with random masks."""
# See random number generator for reproducible results
np.random.seed(23)
arr1 = camera()
arr2 = camera()
# Random masks with 75% of pixels being valid
m1 = np.random.choice([True, False], arr1.shape, p=[3 / 4, 1 / 4])
m2 = np.random.choice([True, False], arr2.shape, p=[3 / 4, 1 / 4])
xcorr = cross_correlate_masked(arr1, arr1, m1, m1, axes=(0, 1),
mode='same', overlap_ratio=0).real
max_index = np.unravel_index(np.argmax(xcorr), xcorr.shape)
# Autocorrelation should have maximum in center of array
testing.assert_almost_equal(xcorr.max(), 1)
testing.assert_array_equal(max_index, np.array(arr1.shape) / 2)
