def test_diffeomorphic_map_simplification_3d():
r""" Test simplification of 3D diffeomorphic maps
Create an invertible deformation field, and define a DiffeomorphicMap
using different voxel-to-space transforms for domain, codomain, and
reference discretizations, also use a non-identity pre-aligning matrix.
Warp a sphere using the diffeomorphic map to obtain the expected warped
sphere. Now simplify the DiffeomorphicMap and warp the same sphere
using this simplified map. Verify that the two warped spheres are equal
up to numerical precision.
"""
# create a simple affine transformation
domain_shape = (64, 64, 64)
codomain_shape = (80, 80, 80)
nr = domain_shape[0]
nc = domain_shape[1]
ns = domain_shape[2]
s = 1.1
t = 0.25
trans = np.array([[1, 0, 0, -t * ns], [0, 1, 0, -t * nr],
[0, 0, 1, -t * nc], [0, 0, 0, 1]])
trans_inv = np.linalg.inv(trans)
scale = np.array([[1 * s, 0, 0, 0], [0, 1 * s, 0, 0], [0, 0, 1 * s, 0],
[0, 0, 0, 1]])
gt_affine = trans_inv.dot(scale.dot(trans))
# Create the invertible displacement fields and the sphere
radius = 16
sphere = vfu.create_sphere(codomain_shape[0], codomain_shape[1],
codomain_shape[2], radius)
d, dinv = vfu.create_harmonic_fields_3d(domain_shape[0], domain_shape[1],
domain_shape[2], 0.3, 6)
# Define different voxel-to-space transforms for domain, codomain and
# reference grid, also, use a non-identity pre-align transform
D = gt_affine
C = imwarp.mult_aff(gt_affine, gt_affine)
R = np.eye(4)
P = gt_affine
# Create the original diffeomorphic map
diff_map = imwarp.DiffeomorphicMap(3, domain_shape, R, domain_shape, D,
codomain_shape, C, P)
diff_map.forward = np.array(d, dtype=floating)
diff_map.backward = np.array(dinv, dtype=floating)
# Warp the sphere to obtain the expected image
expected = diff_map.transform(sphere, 'linear')
# Simplify
simplified = diff_map.get_simplified_transform()
# warp the sphere
warped = simplified.transform(sphere, 'linear')
# verify that the simplified map is equivalent to the
# original one
assert_array_almost_equal(warped, expected)
# And of course, it must be simpler...
assert_equal(simplified.domain_grid2world, None)
assert_equal(simplified.codomain_grid2world, None)
assert_equal(simplified.disp_grid2world, None)
assert_equal(simplified.domain_world2grid, None)
assert_equal(simplified.codomain_world2grid, None)
assert_equal(simplified.disp_world2grid, None)
def test_diffeomorphic_map_simplification_3d():
r"""
Create an invertible deformation field, and define a DiffeomorphicMap
using different voxel-to-space transforms for domain, codomain, and
reference discretizations, also use a non-identity pre-aligning matrix.
Warp a sphere using the diffeomorphic map to obtain the expected warped
sphere. Now simplify the DiffeomorphicMap and warp the same sphere using
this simplified map. Verify that the two warped spheres are equal up to
numerical precision.
"""
#create a simple affine transformation
domain_shape = (64, 64, 64)
codomain_shape = (80, 80, 80)
nr = domain_shape[0]
nc = domain_shape[1]
ns = domain_shape[2]
s = 1.1
t = 0.25
trans = np.array([[1, 0, 0, -t*ns],
[0, 1, 0, -t*nr],
[0, 0, 1, -t*nc],
[0, 0, 0, 1]])
trans_inv = np.linalg.inv(trans)
scale = np.array([[1*s, 0, 0, 0],
[0, 1*s, 0, 0],
[0, 0, 1*s, 0],
[0, 0, 0, 1]])
gt_affine = trans_inv.dot(scale.dot(trans))
# Create the invertible displacement fields and the sphere
radius = 16
sphere = vfu.create_sphere(codomain_shape[0], codomain_shape[1],
codomain_shape[2], radius)
d, dinv = vfu.create_harmonic_fields_3d(domain_shape[0], domain_shape[1],
domain_shape[2], 0.3, 6)
#Define different voxel-to-space transforms for domain, codomain and
#reference grid, also, use a non-identity pre-align transform
D = gt_affine
C = imwarp.mult_aff(gt_affine, gt_affine)
R = np.eye(4)
P = gt_affine
#Create the original diffeomorphic map
diff_map = imwarp.DiffeomorphicMap(3, domain_shape, R,
domain_shape, D,
codomain_shape, C,
P)
diff_map.forward = np.array(d, dtype = floating)
diff_map.backward = np.array(dinv, dtype = floating)
#Warp the sphere to obtain the expected image
expected = diff_map.transform(sphere, 'linear')
#Simplify
simplified = diff_map.get_simplified_transform()
#warp the sphere
warped = simplified.transform(sphere, 'linear')
#verify that the simplified map is equivalent to the
#original one
assert_array_almost_equal(warped, expected)
#And of course, it must be simpler...
assert_equal(simplified.domain_affine, None)
assert_equal(simplified.codomain_affine, None)
assert_equal(simplified.disp_affine, None)
assert_equal(simplified.domain_affine_inv, None)
assert_equal(simplified.codomain_affine_inv, None)
assert_equal(simplified.disp_affine_inv, None)
from dipy.align import vector_fields as vfu # from dipy.align.transforms import regtransforms # from dipy.align.parzenhist import sample_domain_regular sh = (64, 64, 64) ns = sh[0] nr = sh[1] nc = sh[2] # Create an image of a sphere radius = 24 sphere = vfu.create_sphere(ns, nr, nc, radius) sphere = np.array(sphere, dtype=floating) # Create a displacement field for warping d, dinv = vfu.create_harmonic_fields_3d(ns, nr, nc, 0.2, 8) d = np.asarray(d).astype(floating) # Create grid coordinates x_0 = np.asarray(range(sh[0])) x_1 = np.asarray(range(sh[1])) x_2 = np.asarray(range(sh[2])) X = np.empty((4, ) + sh, dtype=np.float64) O = np.ones(sh) X[0, ...] = x_0[:, None, None] * O X[1, ...] = x_1[None, :, None] * O X[2, ...] = x_2[None, None, :] * O X[3, ...] = 1 # Select an arbitrary rotation axis axis = np.array([.5, 2.0, 1.5])
def test_warp(shape):
"""Tests the cython implementation of the 3d warpings against scipy."""
ndim = len(shape)
radius = shape[0] / 3
if ndim == 3:
# Create an image of a sphere
volume = vfu.create_sphere(*shape, radius)
volume = np.array(volume, dtype=floating)
# Create a displacement field for warping
d, dinv = vfu.create_harmonic_fields_3d(*shape, 0.2, 8)
else:
# Create an image of a circle
volume = vfu.create_circle(*shape, radius)
volume = np.array(volume, dtype=floating)
# Create a displacement field for warping
d, dinv = vfu.create_harmonic_fields_2d(*shape, 0.2, 8)
d = np.asarray(d).astype(floating)
if ndim == 3:
# Select an arbitrary rotation axis
axis = np.array([0.5, 2.0, 1.5])
# Select an arbitrary translation matrix
t = 0.1
trans = np.array([
[1, 0, 0, -t * shape[0]],
[0, 1, 0, -t * shape[1]],
[0, 0, 1, -t * shape[2]],
[0, 0, 0, 1],
])
trans_inv = np.linalg.inv(trans)
theta = np.pi / 5
s = 1.1
rot = np.zeros(shape=(4, 4))
rot[:3, :3] = geometry.rodrigues_axis_rotation(axis, theta)
rot[3, 3] = 1.0
scale = np.array([[1 * s, 0, 0, 0], [0, 1 * s, 0, 0], [0, 0, 1 * s, 0],
[0, 0, 0, 1]])
elif ndim == 2:
# Select an arbitrary translation matrix
t = 0.1
trans = np.array([[1, 0, -t * shape[0]], [0, 1, -t * shape[1]],
[0, 0, 1]])
trans_inv = np.linalg.inv(trans)
theta = -1 * np.pi / 6.0
s = 0.42
ct = np.cos(theta)
st = np.sin(theta)
rot = np.array([[ct, -st, 0], [st, ct, 0], [0, 0, 1]])
scale = np.array([[1 * s, 0, 0], [0, 1 * s, 0], [0, 0, 1]])
aff = trans_inv.dot(scale.dot(rot.dot(trans)))
# Select arbitrary (but different) grid-to-space transforms
sampling_grid2world = scale
field_grid2world = aff
field_world2grid = np.linalg.inv(field_grid2world)
image_grid2world = aff.dot(scale)
image_world2grid = np.linalg.inv(image_grid2world)
A = field_world2grid.dot(sampling_grid2world)
B = image_world2grid.dot(sampling_grid2world)
C = image_world2grid
# Reorient the displacement field according to its grid-to-space
# transform
dcopy = np.copy(d)
if ndim == 3:
vfu.reorient_vector_field_3d(dcopy, field_grid2world)
expected = vfu.warp_3d(volume, dcopy, A, B, C,
np.array(shape, dtype=np.int32))
elif ndim == 2:
vfu.reorient_vector_field_2d(dcopy, field_grid2world)
expected = vfu.warp_2d(volume, dcopy, A, B, C,
np.array(shape, dtype=np.int32))
dcopyg = cupy.asarray(dcopy)
volumeg = cupy.asarray(volume)
Ag = cupy.asarray(A)
Bg = cupy.asarray(B)
Cg = cupy.asarray(C)
warped = warp(volumeg, dcopyg, Ag, Bg, Cg, order=1, mode="constant")
cupy.testing.assert_array_almost_equal(warped, expected, decimal=4)
