def test_interpolate_vector_3d():
np.random.seed(7711219)
sz = 64
target_shape = (sz, sz, sz)
field = np.empty(target_shape + (3, ), dtype=floating)
field[...] =\
np.random.randint(0, 10, np.size(field)).reshape(target_shape + (3,))
extended_field = np.zeros((sz + 2, sz + 2, sz + 2, 3), dtype=floating)
extended_field[1:sz + 1, 1:sz + 1, 1:sz + 1] = field
# Select some coordinates to interpolate at
nsamples = 800
locations =\
np.random.ranf(3 * nsamples).reshape((nsamples, 3)) * (sz + 2) - 1.0
extended_locations = locations + 1
# Call the implementation under test
interp, inside = interpolate_vector_3d(field, locations)
# Call the reference implementation
expected = np.zeros_like(interp)
for i in range(3):
expected[..., i] = map_coordinates(extended_field[..., i],
extended_locations.transpose(),
order=1)
npt.assert_array_almost_equal(expected, interp)
# Test interpolation stability along the boundary
epsilon = 5e-8
for k in range(3):
for offset in [0, sz - 1]:
delta = ((np.random.ranf(nsamples) * 2) - 1) * epsilon
locations[:, k] = delta + offset
locations[:, (k + 1) % 3] = np.random.ranf(nsamples) * (sz - 1)
locations[:, (k + 2) % 3] = np.random.ranf(nsamples) * (sz - 1)
interp, inside = interpolate_vector_3d(field, locations)
locations[:, k] = offset
for i in range(3):
expected[..., i] = map_coordinates(field[..., i],
locations.transpose(),
order=1)
npt.assert_array_almost_equal(expected, interp)
if offset == 0:
expected_flag = np.array(delta >= 0, dtype=np.int32)
else:
expected_flag = np.array(delta <= 0, dtype=np.int32)
npt.assert_array_almost_equal(expected_flag, inside)
def _extract_vals(data, streamlines, affine, threedvec=False):
"""
Helper function for use with `values_from_volume`.
Parameters
----------
data : 3D or 4D array
Scalar (for 3D) and vector (for 4D) values to be extracted. For 4D
data, interpolation will be done on the 3 spatial dimensions in each
volume.
streamlines : ndarray or list
If array, of shape (n_streamlines, n_nodes, 3)
If list, len(n_streamlines) with (n_nodes, 3) array in
each element of the list.
affine : array_like (4, 4)
The mapping from voxel coordinates to streamline points.
The voxel_to_rasmm matrix, typically from a NIFTI file.
threedvec : bool
Whether the last dimension has length 3. This is a special case in
which we can use :func:`dipy.core.interpolate.interpolate_vector_3d`
for the interploation of 4D volumes without looping over the elements
of the last dimension.
Returns
---------
array or list (depending on the input) : values interpolate to each
coordinate along the length of each streamline
"""
data = data.astype(np.float)
if (isinstance(streamlines, list)
or isinstance(streamlines, types.GeneratorType)
or isinstance(streamlines, Streamlines)):
streamlines = transform_streamlines(streamlines, np.linalg.inv(affine))
vals = []
for sl in streamlines:
if threedvec:
vals.append(
list(interpolate_vector_3d(data, sl.astype(np.float))[0]))
else:
vals.append(
list(interpolate_scalar_3d(data, sl.astype(np.float))[0]))
elif isinstance(streamlines, np.ndarray):
sl_shape = streamlines.shape
sl_cat = streamlines.reshape(sl_shape[0] * sl_shape[1],
3).astype(np.float)
inv_affine = np.linalg.inv(affine)
sl_cat = (np.dot(sl_cat, inv_affine[:3, :3]) + inv_affine[:3, 3])
# So that we can index in one operation:
if threedvec:
vals = np.array(interpolate_vector_3d(data, sl_cat)[0])
else:
vals = np.array(interpolate_scalar_3d(data, sl_cat)[0])
vals = np.reshape(vals, (sl_shape[0], sl_shape[1], -1))
if vals.shape[-1] == 1:
vals = np.reshape(vals, vals.shape[:-1])
else:
raise RuntimeError("Extracting values from a volume ",
"requires streamlines input as an array, ",
"a list of arrays, or a streamline generator.")
return vals