def test_resizing_op_mixed_uni_nonuni():
"""Check if resizing along uniform axes in mixed discretizations works."""
nonuni_part = odl.nonuniform_partition([0, 1, 4])
uni_part = odl.uniform_partition(-1, 1, 4)
part = uni_part.append(nonuni_part, uni_part, nonuni_part)
fspace = odl.FunctionSpace(odl.IntervalProd(part.min_pt, part.max_pt))
tspace = odl.rn(part.shape)
space = odl.DiscreteLp(fspace, part, tspace)
# Keep non-uniform axes fixed
res_op = odl.ResizingOperator(space, ran_shp=(6, 3, 6, 3))
assert res_op.axes == (0, 2)
assert res_op.offset == (1, 0, 1, 0)
# Evaluation test with a simpler case
part = uni_part.append(nonuni_part)
fspace = odl.FunctionSpace(odl.IntervalProd(part.min_pt, part.max_pt))
tspace = odl.rn(part.shape)
space = odl.DiscreteLp(fspace, part, tspace)
res_op = odl.ResizingOperator(space, ran_shp=(6, 3))
result = res_op(space.one())
true_result = [[0, 0, 0], [1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1],
[0, 0, 0]]
assert np.array_equal(result, true_result)
# Test adjoint
elem = noise_element(space)
res_elem = noise_element(res_op.range)
inner1 = res_op(elem).inner(res_elem)
inner2 = elem.inner(res_op.adjoint(res_elem))
assert almost_equal(inner1, inner2)
def test_norm_nonuniform():
"""Check if norms are correct in non-uniform discretizations."""
part = odl.nonuniform_partition([0, 2, 3, 5], min_pt=0, max_pt=5)
weights = part.cell_sizes_vecs[0]
tspace = odl.rn(part.size, weighting=weights)
discr = odl.DiscretizedSpace(part, tspace)
sqrt = discr.element(lambda x: np.sqrt(x))
# Exact norm is the square root of the integral from 0 to 5 of x,
# which is sqrt(5**2 / 2)
exact_norm = np.sqrt(5**2 / 2.0)
norm = sqrt.norm()
assert norm == pytest.approx(exact_norm)
def test_inner_nonuniform():
"""Check if inner products are correct in non-uniform discretizations."""
part = odl.nonuniform_partition([0, 2, 3, 5], min_pt=0, max_pt=5)
weights = part.cell_sizes_vecs[0]
tspace = odl.rn(part.size, weighting=weights)
discr = odl.DiscretizedSpace(part, tspace)
one = discr.one()
linear = discr.element(lambda x: x)
# Exact inner product is the integral from 0 to 5 of x, which is 5**2 / 2
exact_inner = 5**2 / 2.0
inner = one.inner(linear)
assert inner == pytest.approx(exact_inner)
def ExpOp_builder(bin_param, filter_space, interp):
# Create binning scheme
if interp == 'Full':
spf_space = filter_space
Exp_op = odl.IdentityOperator(filter_space)
elif interp == 'uniform':
# Create binning scheme
dpix = np.size(filter_space)
dsize = filter_space.max_pt
filt_bin_space = odl.uniform_discr(-dsize, dsize, dpix // (bin_param))
spf_space = odl.uniform_discr(0, dsize, dpix // (2 * bin_param))
resamp = odl.Resampling(filt_bin_space, filter_space)
sym = SymOp(spf_space, filt_bin_space)
Exp_op = resamp * sym
else:
if interp == 'constant':
interp = 'nearest'
elif interp == 'linear':
pass
else:
raise ValueError('unknown `expansion operator type` ({})'
''.format(interp))
B = ExpBin(bin_param, np.size(filter_space)) * \
filter_space.weighting.const
B[-1] -= 1 / 2 * filter_space.weighting.const
# Create sparse filter space
spf_part = odl.nonuniform_partition(B, min_pt=0, max_pt=B[-1])
spf_weight = np.ravel(
np.multiply.reduce(np.meshgrid(*spf_part.cell_sizes_vecs)))
spf_fspace = odl.FunctionSpace(spf_part.set)
spf_space = odl.DiscreteLp(spf_fspace,
spf_part,
odl.rn(spf_part.size, weighting=spf_weight),
interp=interp)
filt_pos_part = odl.uniform_partition(0, B[-1],
int(np.size(filter_space) / 2))
filt_pos_space = odl.uniform_discr_frompartition(filt_pos_part,
dtype='float64')
lin_interp = odl.Resampling(spf_space, filt_pos_space)
# Create symmetry operator
sym = SymOp(filt_pos_space, filter_space)
# Create sparse filter operator
Exp_op = sym * lin_interp
return spf_space, Exp_op
def elekta_icon_geometry(sad=780.0,
sdd=1000.0,
piercing_point=(390.0, 0.0),
angles=None,
num_angles=None,
detector_shape=(780, 720)):
sad = float(sad)
assert sad > 0
sdd = float(sdd)
assert sdd > sad
piercing_point = np.array(piercing_point, dtype=float)
assert piercing_point.shape == (2, )
if angles is not None and num_angles is not None:
raise ValueError('cannot provide both `angles` and `num_angles`')
elif angles is not None:
angles = odl.nonuniform_partition(angles)
assert angles.ndim == 1
elif num_angles is not None:
angles = odl.uniform_partition(1.2, 5.0, num_angles)
else:
angles = odl.uniform_partition(1.2, 5.0, 332)
detector_shape = np.array(detector_shape, dtype=int)
# Constant system parameters
pixel_size = 0.368
det_extent_mm = np.array([287.04, 264.96])
# Compute the detector partition
piercing_point_mm = pixel_size * piercing_point
det_min_pt = -piercing_point_mm
det_max_pt = det_min_pt + det_extent_mm
detector_partition = odl.uniform_partition(min_pt=det_min_pt,
max_pt=det_max_pt,
shape=detector_shape)
# Create the geometry
geometry = odl.tomo.ConeFlatGeometry(angles,
detector_partition,
src_radius=sad,
det_radius=sdd - sad)
return geometry
def __init__(self, dataset, angle_indices, impl=None):
"""
Parameters
----------
dataset : `Dataset`
Basis CT dataset.
Requirements:
- sample elements are ``(observation, ground_truth)``
- :meth:`get_ray_trafo` gives corresponding ray transform.
angle_indices : array-like or slice
Indices of the angles to use from the observations.
impl : {``'skimage'``, ``'astra_cpu'``, ``'astra_cuda'``},\
optional
Implementation passed to :class:`odl.tomo.RayTransform` to
construct :attr:`ray_trafo`.
"""
self.dataset = dataset
self.angle_indices = (angle_indices if isinstance(angle_indices, slice)
else np.asarray(angle_indices))
self.train_len = self.dataset.get_len('train')
self.validation_len = self.dataset.get_len('validation')
self.test_len = self.dataset.get_len('test')
self.random_access = self.dataset.supports_random_access()
self.num_elements_per_sample = (
self.dataset.get_num_elements_per_sample())
orig_geometry = self.dataset.get_ray_trafo(impl=impl).geometry
apart = nonuniform_partition(
orig_geometry.angles[self.angle_indices])
self.geometry = Parallel2dGeometry(
apart=apart, dpart=orig_geometry.det_partition)
orig_shape = self.dataset.get_shape()
self.shape = ((apart.shape[0], orig_shape[0][1]), orig_shape[1])
self.space = (None, self.dataset.space[1]) # preliminary, needed for
# call to get_ray_trafo
self.ray_trafo = self.get_ray_trafo(impl=impl)
super().__init__(space=(self.ray_trafo.range, self.dataset.space[1]))
def projector(request, dtype):
n_angles = 200
geom, impl, angle = request.param.split()
if angle == 'uniform':
apart = odl.uniform_partition(0, 2 * np.pi, n_angles)
elif angle == 'random':
# Linearly spaced with random noise
min_pt = 2 * (2.0 * np.pi) / n_angles
max_pt = (2.0 * np.pi) - 2 * (2.0 * np.pi) / n_angles
points = np.linspace(min_pt, max_pt, n_angles)
points += np.random.rand(n_angles) * (max_pt - min_pt) / (5 * n_angles)
apart = odl.nonuniform_partition(points)
elif angle == 'nonuniform':
# Angles spaced quadratically
min_pt = 2 * (2.0 * np.pi) / n_angles
max_pt = (2.0 * np.pi) - 2 * (2.0 * np.pi) / n_angles
points = np.linspace(min_pt ** 0.5, max_pt ** 0.5, n_angles) ** 2
apart = odl.nonuniform_partition(points)
else:
raise ValueError('angle not valid')
if geom == 'par2d':
# Discrete reconstruction space
discr_reco_space = odl.uniform_discr([-20, -20], [20, 20],
[100, 100], dtype=dtype)
# Geometry
dpart = odl.uniform_partition(-30, 30, 200)
geom = tomo.Parallel2dGeometry(apart, dpart)
# Ray transform
return tomo.RayTransform(discr_reco_space, geom,
impl=impl)
elif geom == 'par3d':
# Discrete reconstruction space
discr_reco_space = odl.uniform_discr([-20, -20, -20], [20, 20, 20],
[100, 100, 100], dtype=dtype)
# Geometry
dpart = odl.uniform_partition([-30, -30], [30, 30], [200, 200])
geom = tomo.Parallel3dAxisGeometry(apart, dpart, axis=[1, 0, 0])
# Ray transform
return tomo.RayTransform(discr_reco_space, geom,
impl=impl)
elif geom == 'cone2d':
# Discrete reconstruction space
discr_reco_space = odl.uniform_discr([-20, -20], [20, 20],
[100, 100], dtype=dtype)
# Geometry
dpart = odl.uniform_partition(-30, 30, 200)
geom = tomo.FanFlatGeometry(apart, dpart,
src_radius=200, det_radius=100)
# Ray transform
return tomo.RayTransform(discr_reco_space, geom,
impl=impl)
elif geom == 'cone3d':
# Discrete reconstruction space
discr_reco_space = odl.uniform_discr([-20, -20, -20], [20, 20, 20],
[100, 100, 100], dtype=dtype)
# Geometry
dpart = odl.uniform_partition([-30, -30], [30, 30], [200, 200])
geom = tomo.CircularConeFlatGeometry(
apart, dpart, src_radius=200, det_radius=100, axis=[1, 0, 0])
# Ray transform
return tomo.RayTransform(discr_reco_space, geom,
impl=impl)
elif geom == 'helical':
# Discrete reconstruction space
discr_reco_space = odl.uniform_discr([-20, -20, 0], [20, 20, 40],
[100, 100, 100], dtype=dtype)
# Geometry
# TODO: angles
n_angle = 700
apart = odl.uniform_partition(0, 8 * 2 * np.pi, n_angle)
dpart = odl.uniform_partition([-30, -3], [30, 3], [200, 20])
geom = tomo.HelicalConeFlatGeometry(apart, dpart, pitch=5.0,
src_radius=200, det_radius=100)
# Ray transform
return tomo.RayTransform(discr_reco_space, geom,
impl=impl)
else:
raise ValueError('param not valid')
def test_shifted_volume(geometry_type):
"""Check that geometry shifts are handled correctly.
We forward project a square/cube of all ones and check that the
correct portion of the detector gets nonzero values. In the default
setup, at angle 0, the source (if existing) is at (0, -s[, 0]), and
the detector at (0, +d[, 0]) with the positive x axis as (first)
detector axis. Thus, when shifting enough in the negative x direction,
the object should be visible at the left half of the detector only.
A shift in y should not influence the result (much).
At +90 degrees, a shift in the negative y direction should have the same
effect.
"""
apart = odl.nonuniform_partition([0, np.pi / 2, np.pi, 3 * np.pi / 2])
if geometry_type == 'par2d' and odl.tomo.ASTRA_AVAILABLE:
ndim = 2
dpart = odl.uniform_partition(-30, 30, 30)
geometry = odl.tomo.Parallel2dGeometry(apart, dpart)
elif geometry_type == 'par3d' and odl.tomo.ASTRA_CUDA_AVAILABLE:
ndim = 3
dpart = odl.uniform_partition([-30, -30], [30, 30], (30, 30))
geometry = odl.tomo.Parallel3dAxisGeometry(apart, dpart)
if geometry_type == 'cone2d' and odl.tomo.ASTRA_AVAILABLE:
ndim = 2
dpart = odl.uniform_partition(-30, 30, 30)
geometry = odl.tomo.FanFlatGeometry(apart, dpart,
src_radius=200, det_radius=100)
elif geometry_type == 'cone3d' and odl.tomo.ASTRA_CUDA_AVAILABLE:
ndim = 3
dpart = odl.uniform_partition([-30, -30], [30, 30], (30, 30))
geometry = odl.tomo.ConeFlatGeometry(apart, dpart,
src_radius=200, det_radius=100)
else:
pytest.skip('no projector available for geometry type')
min_pt = np.array([-5.0] * ndim)
max_pt = np.array([5.0] * ndim)
shift_len = 6 # enough to move the projection to one side of the detector
# Shift along axis 0
shift = np.zeros(ndim)
shift[0] = -shift_len
# Generate 4 projections with 90 degrees increment
space = odl.uniform_discr(min_pt + shift, max_pt + shift, [10] * ndim)
ray_trafo = odl.tomo.RayTransform(space, geometry)
proj = ray_trafo(space.one())
# Check that the object is projected to the correct place. With the
# chosen setup, at least one ray should go through a substantial
# part of the volume, yielding a value around 10 (=side length).
# 0 degrees: All on the left
assert np.max(proj[0, :15]) > 5
assert np.max(proj[0, 15:]) == 0
# 90 degrees: Left and right
assert np.max(proj[1, :15]) > 5
assert np.max(proj[1, 15:]) > 5
# 180 degrees: All on the right
assert np.max(proj[2, :15]) == 0
assert np.max(proj[2, 15:]) > 5
# 270 degrees: Left and right
assert np.max(proj[3, :15]) > 5
assert np.max(proj[3, 15:]) > 5
# Do the same for axis 1
shift = np.zeros(ndim)
shift[1] = -shift_len
space = odl.uniform_discr(min_pt + shift, max_pt + shift, [10] * ndim)
ray_trafo = odl.tomo.RayTransform(space, geometry)
proj = ray_trafo(space.one())
# 0 degrees: Left and right
assert np.max(proj[0, :15]) > 5
assert np.max(proj[0, 15:]) > 5
# 90 degrees: All on the left
assert np.max(proj[1, :15]) > 5
assert np.max(proj[1, 15:]) == 0
# 180 degrees: Left and right
assert np.max(proj[2, :15]) > 5
assert np.max(proj[2, 15:]) > 5
# 270 degrees: All on the right
assert np.max(proj[3, :15]) == 0
assert np.max(proj[3, 15:]) > 5
def projector(request):
n = 100
m = 100
n_angles = 100
dtype = 'float32'
geom, impl, angle = request.param.split()
if angle == 'uniform':
apart = odl.uniform_partition(0, 2 * np.pi, n_angles)
elif angle == 'half_uniform':
apart = odl.uniform_partition(0, np.pi, n_angles)
elif angle == 'random':
# Linearly spaced with random noise
min_pt = 2 * (2.0 * np.pi) / n_angles
max_pt = (2.0 * np.pi) - 2 * (2.0 * np.pi) / n_angles
points = np.linspace(min_pt, max_pt, n_angles)
points += np.random.rand(n_angles) * (max_pt - min_pt) / (5 * n_angles)
apart = odl.nonuniform_partition(points)
elif angle == 'nonuniform':
# Angles spaced quadratically
min_pt = 2 * (2.0 * np.pi) / n_angles
max_pt = (2.0 * np.pi) - 2 * (2.0 * np.pi) / n_angles
points = np.linspace(min_pt ** 0.5, max_pt ** 0.5, n_angles) ** 2
apart = odl.nonuniform_partition(points)
else:
raise ValueError('angle not valid')
if geom == 'par2d':
# Reconstruction space
reco_space = odl.uniform_discr([-20] * 2, [20] * 2, [n] * 2,
dtype=dtype)
# Geometry
dpart = odl.uniform_partition(-30, 30, m)
geom = odl.tomo.Parallel2dGeometry(apart, dpart)
# Ray transform
return odl.tomo.RayTransform(reco_space, geom, impl=impl)
elif geom == 'par3d':
# Reconstruction space
reco_space = odl.uniform_discr([-20] * 3, [20] * 3, [n] * 3,
dtype=dtype)
# Geometry
dpart = odl.uniform_partition([-30] * 2, [30] * 2, [m] * 2)
geom = odl.tomo.Parallel3dAxisGeometry(apart, dpart)
# Ray transform
return odl.tomo.RayTransform(reco_space, geom, impl=impl)
elif geom == 'cone2d':
# Reconstruction space
reco_space = odl.uniform_discr([-20] * 2, [20] * 2, [n] * 2,
dtype=dtype)
# Geometry
dpart = odl.uniform_partition(-30, 30, m)
geom = odl.tomo.FanFlatGeometry(apart, dpart, src_radius=200,
det_radius=100)
# Ray transform
return odl.tomo.RayTransform(reco_space, geom, impl=impl)
elif geom == 'cone3d':
# Reconstruction space
reco_space = odl.uniform_discr([-20] * 3, [20] * 3, [n] * 3,
dtype=dtype)
# Geometry
dpart = odl.uniform_partition([-60] * 2, [60] * 2, [m] * 2)
geom = odl.tomo.ConeFlatGeometry(apart, dpart,
src_radius=200, det_radius=100)
# Ray transform
return odl.tomo.RayTransform(reco_space, geom, impl=impl)
elif geom == 'helical':
# Reconstruction space
reco_space = odl.uniform_discr([-20, -20, 0], [20, 20, 40],
[n] * 3, dtype=dtype)
# Geometry, overwriting angle partition
apart = odl.uniform_partition(0, 8 * 2 * np.pi, n_angles)
dpart = odl.uniform_partition([-30, -3], [30, 3], [m] * 2)
geom = odl.tomo.ConeFlatGeometry(apart, dpart, pitch=5.0,
src_radius=200, det_radius=100)
# Ray transform
return odl.tomo.RayTransform(reco_space, geom, impl=impl)
else:
raise ValueError('geom not valid')
det_part = odl.uniform_partition(-10, 10, 1024)
# Ray transform implementation (`None` means "take fastest available")
impl = None
# %% Define X1, Y1 and R11
# The size of the spatial region is such that it would fit onto the detector
# in parallel beam geometry (14 x 14 [cm^2]).
X1 = odl.uniform_discr([-7, -7], [7, 7], shape=(128, 128))
print('X1_px_size / Y1_px_size:', X1.cell_sides[0] / det_part.cell_sides[0])
# Full scan, 1 degree increment
# TODO: this can probably be made significantly coarser
Y1_angles = np.linspace(0, 2 * np.pi, 360, endpoint=False)
Y1_angle_part = odl.nonuniform_partition(Y1_angles, min_pt=0, max_pt=2 * np.pi)
# Put the detector close to the object to keep the magnification low.
# Here it is roughly 1.2 ((50 + 10) / 50).
Y1_geom = odl.tomo.FanFlatGeometry(Y1_angle_part,
det_part,
src_radius=50,
det_radius=10)
print('Y1 magnification:',
(Y1_geom.src_radius + Y1_geom.det_radius) / Y1_geom.src_radius)
R11 = odl.tomo.RayTransform(X1, Y1_geom, impl=impl)
# Show footprint of a 10 x 10 [cm^2] square, this should not go outside
# the detector region.
R11(odl.phantom.cuboid(X1, [-5, -5],
[5, 5])).show('Detector footprint of a 10x10 square')
def elekta_xvi_geometry(sad=1000.0,
sdd=1500.0,
piercing_point=(512.0, 512.0),
angles=None,
num_angles=None,
detector_shape=(1024, 1024)):
"""Tomographic geometry of the Elekta XVI system.
All measurments are given in millimeters unless otherwise stated.
Parameters
----------
sad : float, optional
Source to Axis distance.
sdd : float, optional
Source to Detector distance.
piercing_point : sequence of foat, optional
Position in the detector (in pixel coordinates) that a beam from the
source, passing through the axis of rotation perpendicularly, hits.
angles : array-like, optional
List of angles given in radians that the projection images were taken
at. Exclusive with num_angles.
Default: np.linspace(0, 2 * np.pi, 650, endpoint=False)
num_angles : int, optional
Number of angles. Exclusive with angles.
Default: 332
detector_shape : sequence of int, optional
Shape of the detector (in pixels). Useful if a sub-sampled system
should be studied.
Returns
-------
elekta_xvi_geometry : `ConeBeamGeometry`
Examples
--------
Create default geometry:
>>> from odl.contrib import tomo
>>> geometry = tomo.elekta_xvi_geometry()
Use a smaller detector (improves efficiency):
>>> small_geometry = tomo.elekta_xvi_geometry(detector_shape=[100, 100])
See Also
--------
elekta_xvi_space : Default reconstruction space for the Elekta XVI CBCT.
elekta_xvi_fbp: Default reconstruction method for the Elekta XVI CBCT.
"""
sad = float(sad)
assert sad > 0
sdd = float(sdd)
assert sdd > sad
piercing_point = np.array(piercing_point, dtype=float)
assert piercing_point.shape == (2, )
if angles is not None and num_angles is not None:
raise ValueError('cannot provide both `angles` and `num_angles`')
elif angles is not None:
angles = odl.nonuniform_partition(angles)
assert angles.ndim == 1
elif num_angles is not None:
angles = odl.uniform_partition(0, 2 * np.pi, num_angles)
else:
angles = odl.uniform_partition(0, 2 * np.pi, 650)
detector_shape = np.array(detector_shape, dtype=int)
# Constant system parameters
pixel_size = 0.4
det_extent_mm = np.array([409.6, 409.6])
# Compute the detector partition
piercing_point_mm = pixel_size * piercing_point
det_min_pt = -piercing_point_mm
det_max_pt = det_min_pt + det_extent_mm
detector_partition = odl.uniform_partition(min_pt=det_min_pt,
max_pt=det_max_pt,
shape=detector_shape)
# Create the geometry
geometry = odl.tomo.ConeBeamGeometry(angles,
detector_partition,
src_radius=sad,
det_radius=sdd - sad)
return geometry
def elekta_icon_geometry(sad=780.0,
sdd=1000.0,
piercing_point=(390.0, 0.0),
angles=None,
num_angles=None,
detector_shape=(780, 720)):
"""Tomographic geometry of the Elekta Icon CBCT system.
See the [whitepaper]_ for specific descriptions of each parameter.
All measurments are given in millimeters unless otherwise stated.
Parameters
----------
sad : float, optional
Source to Axis distance.
sdd : float, optional
Source to Detector distance.
piercing_point : sequence of foat, optional
Position in the detector (in pixel coordinates) that a beam from the
source, passing through the axis of rotation perpendicularly, hits.
angles : array-like, optional
List of angles given in radians that the projection images were taken
at. Exclusive with num_angles.
Default: np.linspace(1.2, 5.0, 332)
num_angles : int, optional
Number of angles. Exclusive with angles.
Default: 332
detector_shape : sequence of int, optional
Shape of the detector (in pixels). Useful if a sub-sampled system
should be studied.
Returns
-------
elekta_icon_geometry : `ConeBeamGeometry`
Examples
--------
Create default geometry:
>>> from odl.contrib import tomo
>>> geometry = tomo.elekta_icon_geometry()
Use a smaller detector (improves efficiency):
>>> small_geometry = tomo.elekta_icon_geometry(detector_shape=[100, 100])
See Also
--------
elekta_icon_space : Default reconstruction space for the Elekta Icon CBCT.
elekta_icon_fbp: Default reconstruction method for the Elekta Icon CBCT.
References
----------
.. [whitepaper] *Design and performance characteristics of a Cone Beam
CT system for Leksell Gamma Knife Icon*
"""
sad = float(sad)
assert sad > 0
sdd = float(sdd)
assert sdd > sad
piercing_point = np.array(piercing_point, dtype=float)
assert piercing_point.shape == (2, )
if angles is not None and num_angles is not None:
raise ValueError('cannot provide both `angles` and `num_angles`')
elif angles is not None:
angles = odl.nonuniform_partition(angles)
assert angles.ndim == 1
elif num_angles is not None:
angles = odl.uniform_partition(1.2, 5.0, num_angles)
else:
angles = odl.uniform_partition(1.2, 5.0, 332)
detector_shape = np.array(detector_shape, dtype=int)
# Constant system parameters
pixel_size = 0.368
det_extent_mm = np.array([287.04, 264.96])
# Compute the detector partition
piercing_point_mm = pixel_size * piercing_point
det_min_pt = -piercing_point_mm
det_max_pt = det_min_pt + det_extent_mm
detector_partition = odl.uniform_partition(min_pt=det_min_pt,
max_pt=det_max_pt,
shape=detector_shape)
# Create the geometry
geometry = odl.tomo.ConeBeamGeometry(angles,
detector_partition,
src_radius=sad,
det_radius=sdd - sad)
return geometry
def projector(request):
n_angles = 500
dtype = 'float32'
geom, impl, angle = request.param.split()
if angle == 'uniform':
apart = odl.uniform_partition(0, 2 * np.pi, n_angles)
elif angle == 'random':
# Linearly spaced with random noise
min_pt = 2 * (2.0 * np.pi) / n_angles
max_pt = (2.0 * np.pi) - 2 * (2.0 * np.pi) / n_angles
points = np.linspace(min_pt, max_pt, n_angles)
points += np.random.rand(n_angles) * (max_pt - min_pt) / (5 * n_angles)
apart = odl.nonuniform_partition(points)
elif angle == 'nonuniform':
# Angles spaced quadratically
min_pt = 2 * (2.0 * np.pi) / n_angles
max_pt = (2.0 * np.pi) - 2 * (2.0 * np.pi) / n_angles
points = np.linspace(min_pt ** 0.5, max_pt ** 0.5, n_angles) ** 2
apart = odl.nonuniform_partition(points)
else:
raise ValueError('angle not valid')
if geom == 'par2d':
# Discrete reconstruction space
discr_reco_space = odl.uniform_discr([-20, -20], [20, 20],
[100, 100], dtype=dtype)
# Geometry
dpart = odl.uniform_partition(-30, 30, 500)
geom = tomo.Parallel2dGeometry(apart, dpart)
# Ray transform
return tomo.RayTransform(discr_reco_space, geom, impl=impl)
elif geom == 'par3d':
# Discrete reconstruction space
discr_reco_space = odl.uniform_discr([-20, -20, -20], [20, 20, 20],
[100, 100, 100], dtype=dtype)
# Geometry
dpart = odl.uniform_partition([-30, -30], [30, 30], [200, 200])
geom = tomo.Parallel3dAxisGeometry(apart, dpart, axis=[1, 1, 0])
# Ray transform
return tomo.RayTransform(discr_reco_space, geom, impl=impl)
elif geom == 'cone2d':
# Discrete reconstruction space
discr_reco_space = odl.uniform_discr([-20, -20], [20, 20],
[100, 100], dtype=dtype)
# Geometry
dpart = odl.uniform_partition(-40, 40, 200)
geom = tomo.FanFlatGeometry(apart, dpart,
src_radius=100, det_radius=100)
# Ray transform
return tomo.RayTransform(discr_reco_space, geom, impl=impl)
elif geom == 'cone3d':
# Discrete reconstruction space
discr_reco_space = odl.uniform_discr([-20, -20, -20], [20, 20, 20],
[100, 100, 100], dtype=dtype)
# Geometry
dpart = odl.uniform_partition([-50, -50], [50, 50], [200, 200])
geom = tomo.CircularConeFlatGeometry(
apart, dpart, src_radius=100, det_radius=100, axis=[1, 0, 0])
# Ray transform
return tomo.RayTransform(discr_reco_space, geom, impl=impl)
elif geom == 'helical':
# Discrete reconstruction space
discr_reco_space = odl.uniform_discr([-20, -20, 0], [20, 20, 40],
[100, 100, 100], dtype=dtype)
# Geometry
# TODO: angles
n_angle = 2000
apart = odl.uniform_partition(0, 8 * 2 * np.pi, n_angle)
dpart = odl.uniform_partition([-50, -4], [50, 4], [200, 20])
geom = tomo.HelicalConeFlatGeometry(apart, dpart, pitch=5.0,
src_radius=100, det_radius=100)
# Windowed ray transform
return tomo.RayTransform(discr_reco_space, geom, impl=impl)
else:
raise ValueError('param not valid')
def load_projections(folder, indices=None):
"""Load geometry and data stored in Mayo format from folder.
Parameters
----------
folder : str
Path to the folder where the Mayo DICOM files are stored.
indices : optional
Indices of the projections to load.
Accepts advanced indexing such as slice or list of indices.
Returns
-------
geometry : ConeFlatGeometry
Geometry corresponding to the Mayo projector.
proj_data : `numpy.ndarray`
Projection data, given as the line integral of the linear attenuation
coefficient (g/cm^3). Its unit is thus g/cm^2.
"""
datasets, data_array = _read_projections(folder, indices)
# Get the angles
angles = [d.DetectorFocalCenterAngularPosition for d in datasets]
angles = -np.unwrap(angles) - np.pi # different defintion of angles
# Set minimum and maximum corners
shape = np.array([
datasets[0].NumberofDetectorColumns, datasets[0].NumberofDetectorRows
])
pixel_size = np.array([
datasets[0].DetectorElementTransverseSpacing,
datasets[0].DetectorElementAxialSpacing
])
# Correct from center of pixel to corner of pixel
minp = -(np.array(datasets[0].DetectorCentralElement) - 0.5) * pixel_size
maxp = minp + shape * pixel_size
# Select geometry parameters
src_radius = datasets[0].DetectorFocalCenterRadialDistance
det_radius = (datasets[0].ConstantRadialDistance -
datasets[0].DetectorFocalCenterRadialDistance)
# For unknown reasons, mayo does not include the tag
# "TableFeedPerRotation", which is what we want.
# Instead we manually compute the pitch
pitch = ((datasets[-1].DetectorFocalCenterAxialPosition -
datasets[0].DetectorFocalCenterAxialPosition) /
((np.max(angles) - np.min(angles)) / (2 * np.pi)))
# Get flying focal spot data
offset_axial = np.array([d.SourceAxialPositionShift for d in datasets])
offset_angular = np.array([d.SourceAngularPositionShift for d in datasets])
offset_radial = np.array([d.SourceRadialDistanceShift for d in datasets])
# TODO(adler-j): Implement proper handling of flying focal spot.
# Currently we do not fully account for it, merely making some "first
# order corrections" to the detector position and radial offset.
# Update angles with flying focal spot (in plane direction).
# This increases the resolution of the reconstructions.
angles = angles - offset_angular
# We correct for the mean offset due to the rotated angles, we need to
# shift the detector.
offset_detector_by_angles = det_radius * np.mean(offset_angular)
minp[0] -= offset_detector_by_angles
maxp[0] -= offset_detector_by_angles
# We currently apply only the mean of the offsets
src_radius = src_radius + np.mean(offset_radial)
# Partially compensate for a movement of the source by moving the object
# instead. We need to rescale by the magnification to get the correct
# change in the detector. This approximation is only exactly valid on the
# axis of rotation.
mean_offset_along_axis_for_ffz = np.mean(offset_axial) * (
src_radius / (src_radius + det_radius))
# Create partition for detector
detector_partition = odl.uniform_partition(minp, maxp, shape)
# Convert offset to odl defintions
offset_along_axis = (mean_offset_along_axis_for_ffz +
datasets[0].DetectorFocalCenterAxialPosition -
angles[0] / (2 * np.pi) * pitch)
# Assemble geometry
angle_partition = odl.nonuniform_partition(angles)
geometry = odl.tomo.ConeFlatGeometry(angle_partition,
detector_partition,
src_radius=src_radius,
det_radius=det_radius,
pitch=pitch,
offset_along_axis=offset_along_axis)
# Create a *temporary* ray transform (we need its range)
spc = odl.uniform_discr([-1] * 3, [1] * 3, [32] * 3)
ray_trafo = odl.tomo.RayTransform(spc, geometry, interp='linear')
# convert coordinates
theta, up, vp = ray_trafo.range.grid.meshgrid
d = src_radius + det_radius
u = d * np.arctan(up / d)
v = d / np.sqrt(d**2 + up**2) * vp
# Calculate projection data in rectangular coordinates since we have no
# backend that supports cylindrical
proj_data_cylinder = ray_trafo.range.element(data_array)
interpolated_values = proj_data_cylinder.interpolation((theta, u, v))
proj_data = ray_trafo.range.element(interpolated_values)
return geometry, proj_data.asarray()
def projector(request):
n = 100
m = 100
n_angles = 100
dtype = 'float32'
geom, impl, angle = request.param.split()
if angle == 'uniform':
apart = odl.uniform_partition(0, 2 * np.pi, n_angles)
elif angle == 'half_uniform':
apart = odl.uniform_partition(0, np.pi, n_angles)
elif angle == 'random':
# Linearly spaced with random noise
min_pt = 2 * (2.0 * np.pi) / n_angles
max_pt = (2.0 * np.pi) - 2 * (2.0 * np.pi) / n_angles
points = np.linspace(min_pt, max_pt, n_angles)
points += np.random.rand(n_angles) * (max_pt - min_pt) / (5 * n_angles)
apart = odl.nonuniform_partition(points)
elif angle == 'nonuniform':
# Angles spaced quadratically
min_pt = 2 * (2.0 * np.pi) / n_angles
max_pt = (2.0 * np.pi) - 2 * (2.0 * np.pi) / n_angles
points = np.linspace(min_pt ** 0.5, max_pt ** 0.5, n_angles) ** 2
apart = odl.nonuniform_partition(points)
else:
raise ValueError('angle not valid')
if geom == 'par2d':
# Discrete reconstruction space
reco_space = odl.uniform_discr([-20] * 2, [20] * 2, [n] * 2,
dtype=dtype)
# Geometry
dpart = odl.uniform_partition(-30, 30, m)
geom = tomo.Parallel2dGeometry(apart, dpart)
return tomo.RayTransform(reco_space, geom, impl=impl)
elif geom == 'par3d':
# Discrete reconstruction space
reco_space = odl.uniform_discr([-20] * 3, [20] * 3, [n] * 3,
dtype=dtype)
# Geometry
dpart = odl.uniform_partition([-30] * 2, [30] * 2, [n] * 2)
geom = tomo.Parallel3dAxisGeometry(apart, dpart)
# Ray transform
return tomo.RayTransform(reco_space, geom, impl=impl)
elif geom == 'cone2d':
# Discrete reconstruction space
reco_space = odl.uniform_discr([-20] * 2, [20] * 2, [n] * 2,
dtype=dtype)
# Geometry
dpart = odl.uniform_partition(-30, 30, m)
geom = tomo.FanFlatGeometry(apart, dpart, src_radius=200,
det_radius=100)
# Ray transform
return tomo.RayTransform(reco_space, geom, impl=impl)
elif geom == 'cone3d':
# Discrete reconstruction space
reco_space = odl.uniform_discr([-20] * 3, [20] * 3, [n] * 3,
dtype=dtype)
# Geometry
dpart = odl.uniform_partition([-60] * 2, [60] * 2, [m] * 2)
geom = tomo.CircularConeFlatGeometry(apart, dpart, src_radius=200,
det_radius=100)
# Ray transform
return tomo.RayTransform(reco_space, geom, impl=impl)
elif geom == 'helical':
# Discrete reconstruction space
reco_space = odl.uniform_discr([-20, -20, 0], [20, 20, 40],
[n] * 3, dtype=dtype)
# overwrite angle
apart = odl.uniform_partition(0, 8 * 2 * np.pi, n_angles)
dpart = odl.uniform_partition([-30, -3], [30, 3], [m] * 2)
geom = tomo.HelicalConeFlatGeometry(apart, dpart, pitch=5.0,
src_radius=200, det_radius=100)
# Ray transform
return tomo.RayTransform(reco_space, geom, impl=impl)
else:
raise ValueError('geom not valid')
path = '/export/scratch2/kohr/data/Charge_Density/MIP'
fname = 'MIP_LH31'
with odl.tomo.FileReaderMRC(os.path.join(path, fname)) as reader:
header = reader.read_header()
data_arr = reader.read_data()
angles = np.deg2rad([
-48.0000, -44.0000, -42.0000, -40.0000, -38.0000, -36.0000, -34.0000,
-32.0000, -26.0000, -24.0000, -17.0000, -14.0000, -12.0000, -10.0000,
-8.00000, 1.00000, 3.00000, 6.00000, 9.00000, 12.0000, 15.0000, 18.0000,
21.0000, 24.0000, 27.0000, 30.0000, 33.0000, 36.0000, 40.0000, 43.0000,
46.0000
])
angle_part = odl.nonuniform_partition(angles,
min_pt=angles[0],
max_pt=angles[-1])
num_angles = reader.data_shape[0]
assert num_angles == angles.size
det_shape = reader.data_shape[1:]
det_width = np.array(det_shape, dtype=float)
det_part = odl.uniform_partition(-det_width / 2, det_width / 2, det_shape)
geom = odl.tomo.Parallel3dAxisGeometry(angle_part, det_part)
# Do some crude data rescaling and cropping
win_size = 50
# Subtract the background means
def load_projections(folder, proj_start=1, proj_end=-1):
"""Load geometry and data stored in Mayo format from folder.
Parameters
----------
folder : str
Path to the folder where the Mayo DICOM files are stored.
proj_start : int
Index of the first projection to use. Used for subsampling.
proj_end : int
Index of the final projection to use.
Returns
-------
geometry : ConeFlatGeometry
Geometry corresponding to the Mayo projector.
proj_data : `numpy.ndarray`
Projection data, given as the line integral of the linear attenuation
coefficient (g/cm^3). Its unit is thus g/cm^2.
"""
datasets, projections = _read_projections(folder, proj_start, proj_end)
data_array = np.empty((len(projections), ) + projections[0].shape,
dtype='float32')
# Move data to a big array, change order
for i, proj in enumerate(projections):
data_array[i] = proj[:, ::-1]
# Get the angles
angles = [d.DetectorFocalCenterAngularPosition for d in datasets]
angles = -np.unwrap(angles) - np.pi # different defintion of angles
# Make a parallel beam geometry with flat detector
angle_partition = odl.nonuniform_partition(angles)
# Set minimum and maximum point
shape = np.array([
datasets[0].NumberofDetectorColumns, datasets[0].NumberofDetectorRows
])
pixel_size = np.array([
datasets[0].DetectorElementTransverseSpacing,
datasets[0].DetectorElementAxialSpacing
])
minp = -(np.array(datasets[0].DetectorCentralElement) - 0.5) * pixel_size
maxp = minp + shape * pixel_size
# Create partition for detector
detector_partition = odl.uniform_partition(minp, maxp, shape)
# Select geometry parameters
src_radius = datasets[0].DetectorFocalCenterRadialDistance
det_radius = (datasets[0].ConstantRadialDistance -
datasets[0].DetectorFocalCenterRadialDistance)
# Convert pitch and offset to odl defintions
pitch = (pixel_size[1] * shape[1] * datasets[0].SpiralPitchFactor *
src_radius / (src_radius + det_radius))
offset_along_axis = (datasets[0].DetectorFocalCenterAxialPosition -
angles[0] / (2 * np.pi) * pitch)
# Get flying focal spot data
offset_axial = np.array([d.SourceAxialPositionShift for d in datasets])
offset_angular = np.array([d.SourceAngularPositionShift for d in datasets])
offset_radial = np.array([d.SourceRadialDistanceShift for d in datasets])
angles_offset = angles - offset_angular
src_rad_offset = src_radius + offset_radial
offset_x = (np.cos(angles_offset) * (-src_rad_offset) - np.cos(angles) *
(-src_radius))
offset_y = (np.sin(angles_offset) * (-src_rad_offset) - np.sin(angles) *
(-src_radius))
offset_z = offset_axial
# TODO: WE CURRENTLY IGNORE THE OFFSETS DUE TO FLYING FOCAL SPOT
source_offsets = np.array([offset_x, offset_y, offset_z]).T
# Assemble geometry
geometry = odl.tomo.ConeFlatGeometry(angle_partition,
detector_partition,
src_radius=src_radius,
det_radius=det_radius,
pitch=pitch,
offset_along_axis=offset_along_axis)
# Create a *temporary* ray transform (we need its range)
spc = odl.uniform_discr([-1] * 3, [1] * 3, [32] * 3)
ray_trafo = odl.tomo.RayTransform(spc, geometry, interp='linear')
# convert coordinates
theta, up, vp = ray_trafo.range.grid.meshgrid
d = src_radius + det_radius
u = d * np.arctan(up / d)
v = d / np.sqrt(d**2 + up**2) * vp
# Calculate projection data in rectangular coordinates since we have no
# backend that supports cylindrical
proj_data_cylinder = ray_trafo.range.element(data_array)
interpolated_values = proj_data_cylinder.interpolation((theta, u, v))
proj_data = ray_trafo.range.element(interpolated_values)
return geometry, proj_data.asarray()