def test_identity_affine_constant_velocity_fields(self, deform_to):
num_timesteps = 10
template_shape = (3, 4, 5)
template_resolution = 1
target_shape = (2, 4, 6)
target_resolution = 1
velocity_fields = np.ones(
(*template_shape, num_timesteps, len(template_shape)))
velocity_field_resolution = 1
affine = np.eye(4)
if deform_to == "template":
expected_output = (_lddmm_utilities._compute_coords(
template_shape, template_resolution) + 1)
elif deform_to == "target":
expected_output = (_lddmm_utilities._compute_coords(
target_shape, target_resolution) - 1)
position_field = generate_position_field(
affine=affine,
velocity_fields=velocity_fields,
velocity_field_resolution=velocity_field_resolution,
template_shape=template_shape,
template_resolution=template_resolution,
target_shape=target_shape,
target_resolution=target_resolution,
deform_to=deform_to,
)
assert np.allclose(position_field, expected_output)
def test_identity_position_field_different_output_resolution(self):
subject = np.array([
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
])
subject_resolution = 1
output_resolution = 2
output_shape = None
position_field_resolution = subject_resolution
position_field = _lddmm_utilities._compute_coords(
subject.shape, position_field_resolution)
deformed_subject = _transform_image(
subject=subject,
subject_resolution=subject_resolution,
output_resolution=output_resolution,
output_shape=output_shape,
position_field=position_field,
position_field_resolution=position_field_resolution,
)
expected_output = np.array([
[0, 0, 0, 0],
[0, 1, 1, 0],
[0, 1, 1, 0],
[0, 0, 0, 0],
])
assert np.allclose(deformed_subject, expected_output)
def test_identity_position_fields(self, deform_to):
subject = np.array([
[0, 0, 0, 0],
[0, 1, 1, 0],
[0, 1, 1, 0],
[0, 0, 0, 0],
])
subject_resolution = 1
output_resolution = None
output_shape = None
template_shape = (3, 4)
template_resolution = 1
target_shape = (2, 5)
target_resolution = 1
extrapolation_fill_value = np.quantile(subject, 10**-subject.ndim)
affine_phi = _lddmm_utilities._compute_coords(template_shape,
template_resolution)
phi_inv_affine_inv = _lddmm_utilities._compute_coords(
target_shape, target_resolution)
expected_output = _transform_image(
subject,
subject_resolution,
output_resolution,
output_shape,
position_field=affine_phi
if deform_to == "template" else phi_inv_affine_inv,
position_field_resolution=template_resolution
if deform_to == "template" else target_resolution,
extrapolation_fill_value=extrapolation_fill_value,
)
deformed_subject = lddmm_transform_image(
subject=subject,
subject_resolution=subject_resolution,
output_resolution=output_resolution,
deform_to=deform_to,
extrapolation_fill_value=extrapolation_fill_value,
affine_phi=affine_phi,
phi_inv_affine_inv=phi_inv_affine_inv,
template_resolution=template_resolution,
target_resolution=target_resolution,
)
assert np.array_equal(deformed_subject, expected_output)
def test_2D_shape_zero_origin(self):
kwargs = dict(shape=(3, 4), resolution=1, origin="zero")
correct_output = np.array([
[[0, 0], [0, 1], [0, 2], [0, 3]],
[[1, 0], [1, 1], [1, 2], [1, 3]],
[[2, 0], [2, 1], [2, 2], [2, 3]],
])
assert np.array_equal(_compute_coords(**kwargs), correct_output)
def test_identity_position_field(self):
subject = np.arange(3 * 4).reshape(3, 4)
subject_resolution = 1
position_field_resolution = subject_resolution
position_field = _lddmm_utilities._compute_coords(
subject.shape, position_field_resolution)
points = _lddmm_utilities._compute_coords(subject.shape,
position_field_resolution)
transformed_points = _transform_points(
points=points,
position_field=position_field,
position_field_resolution=position_field_resolution,
)
expected_output = points
assert np.array_equal(transformed_points, expected_output)
def test_rotational_affine_identity_velocity_fields(self, deform_to):
num_timesteps = 10
template_shape = (3, 4, 5)
template_resolution = 1
target_shape = (2, 4, 6)
target_resolution = 1
velocity_fields = np.zeros(
(*template_shape, num_timesteps, len(template_shape)))
velocity_field_resolution = 1
# Indicates a 90 degree rotation to the right.
affine = np.array([
[0, 1, 0, 0],
[-1, 0, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1],
])
if deform_to == "template":
expected_output = _lddmm_utilities._multiply_coords_by_affine(
affine,
_lddmm_utilities._compute_coords(template_shape,
template_resolution),
)
elif deform_to == "target":
expected_output = _lddmm_utilities._multiply_coords_by_affine(
inv(affine),
_lddmm_utilities._compute_coords(target_shape,
target_resolution),
)
position_field = generate_position_field(
affine=affine,
velocity_fields=velocity_fields,
velocity_field_resolution=velocity_field_resolution,
template_shape=template_shape,
template_resolution=template_resolution,
target_shape=target_shape,
target_resolution=target_resolution,
deform_to=deform_to,
)
assert np.allclose(position_field, expected_output)
def test_identity_affine_3D(self):
affine = (
np.eye(4)
+ np.append(np.arange(3 * 4).reshape(3, 4), np.zeros((1, 4)), 0) ** 2
)
array = _compute_coords((3, 4, 5), 1)
result = _multiply_coords_by_affine(affine, array)
arrays = []
for dim in range(3):
arrays.append(np.sum(affine[dim, :-1] * array, axis=-1) + affine[dim, -1])
expected = np.stack(arrays=arrays, axis=-1)
assert np.array_equal(result, expected)
def test_identity_position_fields(self, deform_to):
template_shape = (3, 4)
template_resolution = 1
target_shape = (2, 5)
target_resolution = 1
affine_phi = _lddmm_utilities._compute_coords(template_shape,
template_resolution)
phi_inv_affine_inv = _lddmm_utilities._compute_coords(
target_shape, target_resolution)
if deform_to == "template":
points = _lddmm_utilities._compute_coords(target_shape,
target_resolution)
position_field = phi_inv_affine_inv
position_field_resolution = target_resolution
else:
points = _lddmm_utilities._compute_coords(template_shape,
template_resolution)
position_field = affine_phi
position_field_resolution = template_resolution
expected_output = _transform_points(
points=points,
position_field=position_field,
position_field_resolution=position_field_resolution,
)
transformed_points = lddmm_transform_points(
points=points,
deform_to=deform_to,
affine_phi=affine_phi,
phi_inv_affine_inv=phi_inv_affine_inv,
template_resolution=template_resolution,
target_resolution=target_resolution,
)
assert np.array_equal(transformed_points, expected_output)
def test_constant_position_field_trivial_extrapolation(self):
# Note: applying a leftward shift to the position_field is done by subtracting 1 from the appropriate dimension.
# The corresponding effect on the deformed_subject is a shift to the right.
subject = np.array([
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 0, 0],
[0, 0, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
])
subject_resolution = 1
output_resolution = 1
output_shape = None
position_field_resolution = subject_resolution
position_field = _lddmm_utilities._compute_coords(
subject.shape, position_field_resolution) + [
0,
-1,
] # Shift to the left by 1.
deformed_subject = _transform_image(
subject=subject,
subject_resolution=subject_resolution,
output_resolution=output_resolution,
output_shape=output_shape,
position_field=position_field,
position_field_resolution=position_field_resolution,
)
expected_output = np.array([
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 1, 0],
[0, 0, 0, 1, 1, 1, 1, 0],
[0, 0, 0, 1, 1, 1, 1, 0],
[0, 0, 0, 1, 1, 1, 1, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
])
assert np.allclose(deformed_subject, expected_output)
def test_rotational_position_field(self):
# Note: applying an affine indicating a clockwise-rotation to a position_field produces a position _ield rotated counter-clockwise.
# The corresponding effect on the deformed_subject is a counter-clockwise rotation.
subject = np.array([
[0, 1, 0, 0],
[0, 1, 0, 0],
[0, 1, 0, 0],
[0, 1, 1, 1],
])
subject_resolution = 1
output_resolution = 1
output_shape = None
position_field_resolution = subject_resolution
# Indicates a 90 degree rotation to the right.
affine = np.array([
[0, 1, 0],
[-1, 0, 0],
[0, 0, 1],
])
position_field = _lddmm_utilities._multiply_coords_by_affine(
affine,
_lddmm_utilities._compute_coords(subject.shape,
position_field_resolution),
)
deformed_subject = _transform_image(
subject=subject,
subject_resolution=subject_resolution,
output_resolution=output_resolution,
output_shape=output_shape,
position_field=position_field,
position_field_resolution=position_field_resolution,
)
expected_output = np.array([
[0, 0, 0, 1],
[0, 0, 0, 1],
[1, 1, 1, 1],
[0, 0, 0, 0],
])
assert np.allclose(deformed_subject, expected_output)
def test_rotational_position_field(self):
# Note: applying an affine indicating a clockwise-rotation to a position_field produces a position _ield rotated counter-clockwise.
# The corresponding effect on a deformed image is a counter-clockwise rotation.
subject = np.array([
[0, 1, 0],
[0, 1, 0],
[0, 1, 1],
])
subject_resolution = 1
position_field_resolution = subject_resolution
# Indicates a 90 degree rotation to the right.
affine = np.array([
[0, 1, 0],
[-1, 0, 0],
[0, 0, 1],
])
position_field = _lddmm_utilities._multiply_coords_by_affine(
affine,
_lddmm_utilities._compute_coords(subject.shape,
position_field_resolution),
)
# The middle column.
points = np.array([
[-1, 0],
[0, 0],
[1, 0],
])
transformed_points = _transform_points(
points=points,
position_field=position_field,
position_field_resolution=position_field_resolution,
)
# The middle row.
expected_output = np.array([
[0, 1],
[0, 0],
[0, -1],
])
assert np.array_equal(transformed_points, expected_output)
def test_identity_position_field_equal_output_resolution(self):
subject = np.arange(3 * 4).reshape(3, 4)
subject_resolution = 1
output_resolution = 1
output_shape = None
position_field_resolution = subject_resolution
position_field = _lddmm_utilities._compute_coords(
subject.shape, position_field_resolution)
deformed_subject = _transform_image(
subject=subject,
subject_resolution=subject_resolution,
output_resolution=output_resolution,
output_shape=output_shape,
position_field=position_field,
position_field_resolution=position_field_resolution,
)
expected_output = subject
assert np.allclose(deformed_subject, expected_output)
def test_constant_position_field(self):
# Note: applying a leftward shift to the position_field is done by subtracting 1 from the appropriate dimension.
# The corresponding effect on a deformed image is a shift to the right.
subject = np.array([
[0, 1, 3],
[4, 5, 6],
[7, 8, 9],
])
subject_resolution = 1
position_field_resolution = subject_resolution
position_field = _lddmm_utilities._compute_coords(
subject.shape, position_field_resolution) + [
0,
-1,
] # Shift to the left by 1.
# The right column.
points = np.array([
[-1, 1],
[0, 1],
[1, 1],
])
transformed_points = _transform_points(
points=points,
position_field=position_field,
position_field_resolution=position_field_resolution,
)
# The middle column.
expected_output = np.array([
[-1, 0],
[0, 0],
[1, 0],
])
assert np.array_equal(transformed_points, expected_output)
def test_constant_position_field_linear_extrapolation(self):
# Idiosyncratic extrapolation behavior is demonstrated with a nonzero gradient at the extrapolated edge.
subject = np.array([
[0, 0, 0, 0],
[0, 1, 1, 0],
[0, 1, 1, 0],
[0, 0, 0, 0],
])
subject_resolution = 1
output_resolution = 1
output_shape = None
position_field_resolution = subject_resolution
position_field = _lddmm_utilities._compute_coords(
subject.shape, position_field_resolution) + [
0,
-1,
] # Shift to the left by 1.
deformed_subject = _transform_image(
subject=subject,
subject_resolution=subject_resolution,
output_resolution=output_resolution,
output_shape=output_shape,
position_field=position_field,
position_field_resolution=position_field_resolution,
)
expected_output = np.array([
[0, 0, 0, 0],
[-1, 0, 1, 1],
[-1, 0, 1, 1],
[0, 0, 0, 0],
])
assert np.allclose(deformed_subject, expected_output)
def test_1D_shape_center_origin(self):
kwargs = dict(shape=5, resolution=1, origin="center")
correct_output = np.array([[-2], [-1], [0], [1], [2]])
assert np.array_equal(_compute_coords(**kwargs), correct_output)