# Reorient the displacement field according to its grid-to-space
# transform
dcopy = np.copy(d)
vfu.reorient_vector_field_3d(dcopy, field_grid2world)
extended_dcopy = np.zeros((ns + 2, nr + 2, nc + 2, 3), dtype=floating)
extended_dcopy[1:ns + 1, 1:nr + 1, 1:nc + 1, :] = dcopy
# Compute the warping coordinates (see warp_2d documentation)
Y = np.apply_along_axis(A.dot, 0, X)[0:3, ...]
Z = np.zeros_like(X)
Z[0, ...] = map_coordinates(extended_dcopy[..., 0], Y + 1, order=1)
Z[1, ...] = map_coordinates(extended_dcopy[..., 1], Y + 1, order=1)
Z[2, ...] = map_coordinates(extended_dcopy[..., 2], Y + 1, order=1)
Z[3, ...] = 0
Z = np.apply_along_axis(C.dot, 0, Z)[0:3, ...]
T = np.apply_along_axis(B.dot, 0, X)[0:3, ...]
W = T + Z
# Test bilinear interpolation
expected = map_coordinates(sphere, W, order=1)
warped = vfu.warp_3d(sphere, dcopy, A, B, C, np.array(sh, dtype=np.int32))
# assert_array_almost_equal(warped, expected, decimal=5)
np.save('sl_syn_warp_3d.npy', warped)
# Test nearest neighbor interpolation
# expected = map_coordinates(sphere, W, order=0)
# warped = vfu.warp_3d_nn(sphere, dcopy, A, B, C,
# np.array(sh, dtype=np.int32))
# assert_array_almost_equal(warped, expected, decimal=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)