def test_astra_cuda_projector_parallel3d():
"""Test 3D forward and backward projection functions on the GPU."""
# Create reco space and a phantom
reco_space = odl.uniform_discr([-4, -5, -6], [4, 5, 6], (4, 5, 6),
dtype='float32')
phantom = odl.phantom.cuboid(reco_space, min_pt=[0, 0, 0],
max_pt=[4, 5, 6])
# Create parallel geometry
angle_part = odl.uniform_partition(0, np.pi, 8)
det_part = odl.uniform_partition([-7, -8], [7, 8], (7, 8))
geom = odl.tomo.Parallel3dAxisGeometry(angle_part, det_part)
# Make projection space
proj_space = odl.uniform_discr_frompartition(geom.partition,
dtype='float32')
# Forward evaluation
proj_data = astra_cuda_forward_projector(phantom, geom, proj_space)
assert proj_data.shape == proj_space.shape
assert proj_data.norm() > 0
# Backward evaluation
backproj = astra_cuda_back_projector(proj_data, geom, reco_space)
assert backproj.shape == reco_space.shape
assert backproj.norm() > 0
def test_astra_cuda_projector_helical_conebeam():
"""Test 3D forward and backward projection functions on the GPU."""
# Create reco space and a phantom
reco_space = odl.uniform_discr([-4, -5, -6], [4, 5, 6], (4, 5, 6),
dtype='float32')
phantom = odl.phantom.cuboid(reco_space, min_pt=[0, 0, 0],
max_pt=[4, 5, 6])
# Create circular cone beam geometry with flat detector
angle_part = odl.uniform_partition(0, 2 * np.pi, 8)
det_part = odl.uniform_partition([-7, -8], [7, 8], (7, 8))
src_rad = 1000
det_rad = 100
pitch = 0.5
geom = odl.tomo.HelicalConeFlatGeometry(angle_part, det_part, src_rad,
det_rad, pitch)
# Make projection space
proj_space = odl.uniform_discr_frompartition(geom.partition,
dtype='float32')
# Forward evaluation
proj_data = astra_cuda_forward_projector(phantom, geom, proj_space)
assert proj_data.shape == proj_space.shape
assert proj_data.norm() > 0
# Backward evaluation
backproj = astra_cuda_back_projector(proj_data, geom, reco_space)
assert backproj.shape == reco_space.shape
assert backproj.norm() > 0
def test_astra_cpu_projector_parallel2d():
"""ASTRA CPU forward and back projection for 2d parallel geometry."""
# Create reco space and a phantom
reco_space = odl.uniform_discr([-4, -5], [4, 5], (4, 5), dtype='float32')
phantom = odl.phantom.cuboid(reco_space, begin=[0, 0], end=[4, 5])
# Create parallel geometry
angle_part = odl.uniform_partition(0, 2 * np.pi, 8)
det_part = odl.uniform_partition(-6, 6, 6)
geom = odl.tomo.Parallel2dGeometry(angle_part, det_part)
# Make projection space
proj_space = odl.uniform_discr_frompartition(geom.partition,
dtype='float32')
# Forward evaluation
proj_data = astra_cpu_forward_projector(phantom, geom, proj_space)
assert proj_data.shape == proj_space.shape
assert proj_data.norm() > 0
# Backward evaluation
backproj = astra_cpu_back_projector(proj_data, geom, reco_space)
assert backproj.shape == reco_space.shape
assert backproj.norm() > 0
def load_data():
"""Get the data from disk.
Returns
-------
mat1_sino, mat2_sino : numpy.ndarray
projection of material 1 and 2
geometry : odl.tomo.Geometry
Geometry of the data
"""
current_path = os.path.dirname(os.path.realpath(__file__))
data_path = os.path.join(current_path, 'data',
'aux_corr_in_real_ct_image.mat')
try:
data_mat = sio.loadmat(data_path)
except IOError:
raise IOError('data/aux_corr_in_real_ct_image.mat missing, contact '
'developers for a copy of the data or use another data '
'source.')
data = data_mat['decomposedBasisProjectionsmmObj']
data = data.swapaxes(0, 2)
angle_partition = odl.uniform_partition(0, np.pi, 180)
detector_partition = odl.uniform_partition(-150 * np.sqrt(2),
150 * np.sqrt(2), 853)
geometry = odl.tomo.Parallel2dGeometry(angle_partition, detector_partition)
return data, geometry
def test_astra_cpu_projector_fanflat():
"""ASTRA CPU forward and back projection for fanflat geometry."""
# Create reco space and a phantom
reco_space = odl.uniform_discr([-4, -5], [4, 5], (4, 5), dtype='float32')
phantom = odl.phantom.cuboid(reco_space, begin=[0, 0], end=[4, 5])
# Create fan beam geometry with flat detector
angle_part = odl.uniform_partition(0, 2 * np.pi, 8)
det_part = odl.uniform_partition(-6, 6, 6)
src_rad = 100
det_rad = 10
geom = odl.tomo.FanFlatGeometry(angle_part, det_part, src_rad, det_rad)
# Make projection space
proj_space = odl.uniform_discr_frompartition(geom.partition,
dtype='float32')
# Forward evaluation
proj_data = astra_cpu_forward_projector(phantom, geom, proj_space)
assert proj_data.shape == proj_space.shape
assert proj_data.norm() > 0
# Backward evaluation
backproj = astra_cpu_back_projector(proj_data, geom, reco_space)
assert backproj.shape == reco_space.shape
assert backproj.norm() > 0
def test_empty_partition():
"""Check if empty partitions behave as expected and all methods work."""
part = odl.RectPartition(odl.IntervalProd([], []),
odl.uniform_grid([], [], ()))
assert part.cell_boundary_vecs == ()
assert part.nodes_on_bdry is True
assert part.nodes_on_bdry_byaxis == ()
assert part.has_isotropic_cells
assert part.boundary_cell_fractions == ()
assert part.cell_sizes_vecs == ()
assert np.array_equal(part.cell_sides, [])
assert part.cell_volume == 0
same = odl.RectPartition(odl.IntervalProd([], []),
odl.uniform_grid([], [], ()))
assert part == same
assert hash(part) == hash(same)
other = odl.uniform_partition(0, 1, 4)
assert part != other
assert part[[]] == part
assert part.insert(0, other) == other
assert other.insert(0, part) == other
assert other.insert(1, part) == other
assert part.squeeze() == part
assert part.index([]) == ()
part.byaxis
assert part == odl.uniform_partition([], [], ())
repr(part)
def test_circular_cone_flat():
"""Conebeam geometry with circular acquisition and a flat 2D detector."""
# Parameters
full_angle = np.pi
apart = odl.uniform_partition(0, full_angle, 10)
dpart = odl.uniform_partition([0, 0], [1, 1], [10, 10])
src_rad = 10
det_rad = 5
with pytest.raises(TypeError):
odl.tomo.CircularConeFlatGeometry([0, 1], dpart, src_rad, det_rad)
with pytest.raises(TypeError):
odl.tomo.CircularConeFlatGeometry(apart, [0, 1], src_rad, det_rad)
with pytest.raises(ValueError):
odl.tomo.CircularConeFlatGeometry(apart, dpart, -1, det_rad)
with pytest.raises(ValueError):
odl.tomo.CircularConeFlatGeometry(apart, dpart, src_rad, -1)
# Initialize
geom = odl.tomo.CircularConeFlatGeometry(apart, dpart, src_rad, det_rad)
assert all_almost_equal(geom.angles, apart.points().ravel())
with pytest.raises(ValueError):
geom.det_refpoint(2 * full_angle)
assert geom.ndim == 3
assert np.linalg.norm(geom.det_refpoint(0)) == det_rad
assert np.linalg.norm(geom.src_position(np.pi)) == src_rad
assert isinstance(geom.detector, odl.tomo.Flat2dDetector)
# check str and repr work without crashing and return something
assert str(geom)
assert repr(geom)
def test_fbp_reconstruction_filters(filter_type, frequency_scaling):
"""Validate that the various filters work as expected."""
apart = odl.uniform_partition(0, np.pi, 500)
discr_reco_space = odl.uniform_discr([-20, -20], [20, 20],
[100, 100], dtype='float32')
# Geometry
dpart = odl.uniform_partition(-30, 30, 500)
geom = tomo.Parallel2dGeometry(apart, dpart)
# Ray transform
projector = tomo.RayTransform(discr_reco_space, geom, impl='astra_cuda')
# Create Shepp-Logan phantom
vol = odl.phantom.shepp_logan(projector.domain, modified=False)
# Project data
projections = projector(vol)
# Create FBP operator with filters and apply to projections
fbp_operator = odl.tomo.fbp_op(projector,
filter_type=filter_type,
frequency_scaling=frequency_scaling)
fbp_result = fbp_operator(projections)
maxerr = vol.norm() / 5.0
error = vol.dist(fbp_result)
assert error < maxerr
def test_circular_cone_flat():
"""Conebeam geometry with circular acquisition and a flat 2D detector."""
# Parameters
full_angle = np.pi
apart = odl.uniform_partition(0, full_angle, 10)
dpart = odl.uniform_partition([0, 0], [1, 1], [10, 10])
src_rad = 10
det_rad = 5
with pytest.raises(TypeError):
odl.tomo.CircularConeFlatGeometry([0, 1], dpart, src_rad, det_rad)
with pytest.raises(TypeError):
odl.tomo.CircularConeFlatGeometry(apart, [0, 1], src_rad, det_rad)
with pytest.raises(ValueError):
odl.tomo.CircularConeFlatGeometry(apart, dpart, -1, det_rad)
with pytest.raises(ValueError):
odl.tomo.CircularConeFlatGeometry(apart, dpart, src_rad, -1)
# Initialize
geom = odl.tomo.CircularConeFlatGeometry(apart, dpart, src_rad, det_rad)
assert all_almost_equal(geom.angles, apart.points().ravel())
with pytest.raises(ValueError):
geom.det_refpoint(2 * full_angle)
assert geom.ndim == 3
assert np.linalg.norm(geom.det_refpoint(0)) == det_rad
assert np.linalg.norm(geom.src_position(np.pi)) == src_rad
assert isinstance(geom.detector, odl.tomo.Flat2dDetector)
# check str and repr work without crashing and return something
assert str(geom)
assert repr(geom)
def test_parallel_2d_orientation(det_pos_init_2d):
"""Check if the orientation is positive for any ``det_pos_init``."""
full_angle = np.pi
apart = odl.uniform_partition(0, full_angle, 10)
dpart = odl.uniform_partition(0, 1, 10)
det_pos_init = det_pos_init_2d
geom = odl.tomo.Parallel2dGeometry(apart, dpart, det_pos_init=det_pos_init)
assert all_almost_equal(geom.det_pos_init, det_pos_init)
assert all_almost_equal(geom.det_refpoint(0), det_pos_init)
assert all_almost_equal(geom.det_point_position(0, 0), det_pos_init)
# The detector-to-source normal should always be perpendicular to the
# detector axis and form a positively oriented system
for angle in [0, np.pi / 2, 3 * np.pi / 4, np.pi]:
dot = np.dot(geom.det_to_src(angle, 0), geom.det_axis(angle))
assert dot == pytest.approx(0)
normal_det_to_src = (geom.det_to_src(angle, 0) /
np.linalg.norm(geom.det_to_src(angle, 0)))
orient = np.linalg.det(
np.vstack([normal_det_to_src,
geom.det_axis(angle)]))
assert orient == pytest.approx(1)
def test_fbp_reconstruction_filters(filter_type, frequency_scaling):
"""Validate that the various filters work as expected."""
apart = odl.uniform_partition(0, np.pi, 500)
discr_reco_space = odl.uniform_discr([-20, -20], [20, 20], [100, 100],
dtype='float32')
# Geometry
dpart = odl.uniform_partition(-30, 30, 500)
geom = tomo.Parallel2dGeometry(apart, dpart)
# Ray transform
projector = tomo.RayTransform(discr_reco_space, geom, impl='astra_cuda')
# Create Shepp-Logan phantom
vol = odl.phantom.shepp_logan(projector.domain, modified=False)
# Project data
projections = projector(vol)
# Create FBP operator with filters and apply to projections
fbp_operator = odl.tomo.fbp_op(projector,
filter_type=filter_type,
frequency_scaling=frequency_scaling)
fbp_result = fbp_operator(projections)
maxerr = vol.norm() / 5.0
error = vol.dist(fbp_result)
assert error < maxerr
def test_discretizedspace_init():
"""Test initialization and basic properties of DiscretizedSpace."""
# Real space
part = odl.uniform_partition([0, 0], [1, 1], (2, 4))
tspace = odl.rn(part.shape)
discr = DiscretizedSpace(part, tspace)
assert discr.tspace == tspace
assert discr.partition == part
assert discr.exponent == tspace.exponent
assert discr.axis_labels == ('$x$', '$y$')
assert discr.is_real
# Complex space
tspace_c = odl.cn(part.shape)
discr = DiscretizedSpace(part, tspace_c)
assert discr.is_complex
# Make sure repr shows something
assert repr(discr) != ''
# Error scenarios
part_1d = odl.uniform_partition(0, 1, 2)
with pytest.raises(ValueError):
DiscretizedSpace(part_1d, tspace) # wrong dimensionality
part_diffshp = odl.uniform_partition([0, 0], [1, 1], (3, 4))
with pytest.raises(ValueError):
DiscretizedSpace(part_diffshp, tspace) # shape mismatch
def test_geom_to_vec():
"""Create ASTRA projection geometry vectors using ODL geometries."""
apart = odl.uniform_partition(0, 2 * np.pi, 5)
dpart = odl.uniform_partition(-40, 40, 10)
# Fanbeam flat
src_rad = 10
det_rad = 5
geom_ff = odl.tomo.FanFlatGeometry(apart, dpart, src_rad, det_rad)
vec = odl.tomo.astra_conebeam_2d_geom_to_vec(geom_ff)
assert vec.shape == (apart.size, 6)
# Circular cone flat
dpart = odl.uniform_partition([-40, -3], [40, 3], (10, 5))
geom_ccf = odl.tomo.CircularConeFlatGeometry(apart, dpart, src_rad,
det_rad)
vec = odl.tomo.astra_conebeam_3d_geom_to_vec(geom_ccf)
assert vec.shape == (apart.size, 12)
# Helical cone flat
pitch = 1
geom_hcf = odl.tomo.HelicalConeFlatGeometry(apart, dpart, src_rad,
det_rad, pitch)
vec = odl.tomo.astra_conebeam_3d_geom_to_vec(geom_hcf)
assert vec.shape == (apart.size, 12)
def test_astra_cuda_projector_helical_conebeam():
"""Test 3D forward and backward projection functions on the GPU."""
# Create reco space and a phantom
reco_space = odl.uniform_discr([-4, -5, -6], [4, 5, 6], (4, 5, 6),
dtype='float32')
phantom = odl.phantom.cuboid(reco_space, begin=[0, 0, 0], end=[4, 5, 6])
# Create circular cone beam geometry with flat detector
angle_part = odl.uniform_partition(0, 2 * np.pi, 8)
det_part = odl.uniform_partition([-7, -8], [7, 8], (7, 8))
src_rad = 1000
det_rad = 100
pitch = 0.5
geom = odl.tomo.HelicalConeFlatGeometry(angle_part, det_part, src_rad,
det_rad, pitch)
# Make projection space
proj_space = odl.uniform_discr_frompartition(geom.partition,
dtype='float32')
# Forward evaluation
proj_data = astra_cuda_forward_projector(phantom, geom, proj_space)
assert proj_data.shape == proj_space.shape
assert proj_data.norm() > 0
# Backward evaluation
backproj = astra_cuda_back_projector(proj_data, geom, reco_space)
assert backproj.shape == reco_space.shape
assert backproj.norm() > 0
def test_parallel_3d_frommatrix():
"""Test the ``frommatrix`` constructor in 3d parallel geometry."""
full_angle = np.pi
apart = odl.uniform_partition(0, full_angle, 10)
dpart = odl.uniform_partition([0, 0], [1, 1], (10, 10))
# Need a somewhat simpler rotation in 3d to not go crazy imagining the
# rotation.
# This one rotates by +pi/2 in phi and -pi/2 in theta, resulting in the
# axis remapping x->y, y->-z, z->-x.
rot_matrix = np.array([[0, 0, -1], [1, 0, 0], [0, -1, 0]], dtype=float)
geom = odl.tomo.Parallel3dAxisGeometry.frommatrix(apart, dpart, rot_matrix)
# Axis was [0, 0, 1], gets mapped to [-1, 0, 0]
assert all_almost_equal(geom.axis, [-1, 0, 0])
# Detector position starts at [0, 1, 0] and gets mapped to [0, 0, -1]
assert all_almost_equal(geom.det_pos_init, [0, 0, -1])
# Detector axes start at [1, 0, 0] and [0, 0, 1], and get mapped to
# [0, 1, 0] and [-1, 0, 0]
assert all_almost_equal(geom.det_axes_init, ([0, 1, 0], [-1, 0, 0]))
# With translation (1, 1, 1)
matrix = np.hstack([rot_matrix, [[1], [1], [1]]])
geom = odl.tomo.Parallel3dAxisGeometry.frommatrix(apart, dpart, matrix)
assert all_almost_equal(geom.translation, (1, 1, 1))
assert all_almost_equal(geom.det_pos_init, geom.translation + [0, 0, -1])
def test_parallel_2d_slanted_detector():
"""Check if non-standard detector axis is handled correctly."""
full_angle = np.pi
apart = odl.uniform_partition(0, full_angle, 10)
dpart = odl.uniform_partition(0, 1, 10)
# Detector forms a 45 degree angle with the x axis at initial position,
# with positive direction upwards
init_axis = [1, 1]
geom = odl.tomo.Parallel2dGeometry(apart,
dpart,
det_pos_init=[0, 1],
det_axis_init=init_axis)
assert all_almost_equal(geom.det_pos_init, [0, 1])
norm_axis = np.array(init_axis, dtype=float)
norm_axis /= np.linalg.norm(norm_axis)
assert all_almost_equal(geom.det_axis_init, norm_axis)
sqrt_1_2 = np.sqrt(1.0 / 2.0)
# At angle 0: detector position at param 1 should be
# [0, 1] + [sqrt(1/2), sqrt(1/2)]
assert all_almost_equal(geom.det_point_position(0, 1),
[sqrt_1_2, 1 + sqrt_1_2])
# At angle pi/2: detector position at param 1 should be
# [-1, 0] + [-sqrt(1/2), +sqrt(1/2)]
assert all_almost_equal(geom.det_point_position(np.pi / 2, 1),
[-1 - sqrt_1_2, sqrt_1_2])
def test_parallel_3d_orientation(axis):
"""Check if the orientation is positive for any ``axis``."""
full_angle = np.pi
apart = odl.uniform_partition(0, full_angle, 10)
dpart = odl.uniform_partition([0, 0], [1, 1], (10, 10))
geom = odl.tomo.Parallel3dAxisGeometry(apart, dpart, axis=axis)
norm_axis = np.array(axis, dtype=float) / np.linalg.norm(axis)
assert all_almost_equal(geom.axis, norm_axis)
# The symmetry axis should be the second detector axis by default
assert all_almost_equal(geom.axis, geom.det_axes_init[1])
# The detector-to-source normal should always be perpendicular to both
# detector axes, and the triplet (normal, det_ax0, det_ax1) should form
# a positively oriented system
for angle in [0, np.pi / 2, 3 * np.pi / 4, np.pi]:
dot0 = np.dot(geom.det_to_src(angle, [0, 0]), geom.det_axes(angle)[0])
dot1 = np.dot(geom.det_to_src(angle, [0, 0]), geom.det_axes(angle)[1])
assert dot0 == pytest.approx(0)
assert dot1 == pytest.approx(0)
normal_det_to_src = (geom.det_to_src(angle, [0, 0]) /
np.linalg.norm(geom.det_to_src(angle, [0, 0])))
axis_0, axis_1 = geom.det_axes(angle)
orient = np.linalg.det(np.vstack([normal_det_to_src, axis_0, axis_1]))
assert orient == pytest.approx(1)
# check str and repr work without crashing and return a non-empty string
assert str(geom)
assert repr(geom)
def test_scikit_radon_projector_parallel2d():
"""Parallel 2D forward and backward projectors on the GPU."""
# Create reco space and a phantom
reco_space = odl.uniform_discr([-5, -5], [5, 5], (5, 5), dtype='float32')
phantom = odl.util.phantom.cuboid(reco_space, begin=0.5, end=1)
# Create parallel geometry
angle_part = odl.uniform_partition(0, 2 * np.pi, 8)
det_part = odl.uniform_partition(-6, 6, 6)
geom = odl.tomo.Parallel2dGeometry(angle_part, det_part)
# Make projection space
proj_space = odl.uniform_discr_frompartition(geom.partition,
dtype='float32')
# Forward evaluation
proj_data = scikit_radon_forward(phantom, geom, proj_space)
assert proj_data.shape == proj_space.shape
assert proj_data.norm() > 0
# Backward evaluation
backproj = scikit_radon_back_projector(proj_data, geom, reco_space)
assert backproj.shape == reco_space.shape
assert backproj.norm() > 0
def geometry(request):
geom = request.param
m = 100
n_angles = 100
if geom == 'par2d':
apart = odl.uniform_partition(0, np.pi, n_angles)
dpart = odl.uniform_partition(-30, 30, m)
return odl.tomo.Parallel2dGeometry(apart, dpart)
elif geom == 'par3d':
apart = odl.uniform_partition(0, np.pi, n_angles)
dpart = odl.uniform_partition([-30, -30], [30, 30], (m, m))
return odl.tomo.Parallel3dAxisGeometry(apart, dpart)
elif geom == 'cone2d':
apart = odl.uniform_partition(0, 2 * np.pi, n_angles)
dpart = odl.uniform_partition(-30, 30, m)
return odl.tomo.FanFlatGeometry(apart, dpart, src_radius=200,
det_radius=100)
elif geom == 'cone3d':
apart = odl.uniform_partition(0, 2 * np.pi, n_angles)
dpart = odl.uniform_partition([-60, -60], [60, 60], (m, m))
return odl.tomo.ConeFlatGeometry(apart, dpart,
src_radius=200, det_radius=100)
elif geom == 'helical':
apart = odl.uniform_partition(0, 8 * 2 * np.pi, n_angles)
dpart = odl.uniform_partition([-30, -3], [30, 3], (m, m))
return odl.tomo.ConeFlatGeometry(apart, dpart, pitch=5.0,
src_radius=200, det_radius=100)
else:
raise ValueError('geom not valid')
def test_scikit_radon_projector_parallel2d():
"""Parallel 2D forward and backward projectors on the GPU."""
# Create reco space and a phantom
reco_space = odl.uniform_discr([-5, -5], [5, 5], (5, 5), dtype='float32')
phantom = odl.phantom.cuboid(reco_space, begin=[0, 0], end=[5, 5])
# Create parallel geometry
angle_part = odl.uniform_partition(0, 2 * np.pi, 8)
det_part = odl.uniform_partition(-6, 6, 6)
geom = odl.tomo.Parallel2dGeometry(angle_part, det_part)
# Make projection space
proj_space = odl.uniform_discr_frompartition(geom.partition,
dtype='float32')
# Forward evaluation
proj_data = scikit_radon_forward(phantom, geom, proj_space)
assert proj_data.shape == proj_space.shape
assert proj_data.norm() > 0
# Backward evaluation
backproj = scikit_radon_back_projector(proj_data, geom, reco_space)
assert backproj.shape == reco_space.shape
assert backproj.norm() > 0
def test_astra_cuda_projector_parallel3d():
"""Test 3D forward and backward projection functions on the GPU."""
# Create reco space and a phantom
reco_space = odl.uniform_discr([-4, -5, -6], [4, 5, 6], (4, 5, 6),
dtype='float32')
phantom = odl.phantom.cuboid(reco_space, begin=[0, 0, 0], end=[4, 5, 6])
# Create parallel geometry
angle_part = odl.uniform_partition(0, 2 * np.pi, 8)
det_part = odl.uniform_partition([-7, -8], [7, 8], (7, 8))
geom = odl.tomo.Parallel3dAxisGeometry(angle_part, det_part)
# Make projection space
proj_space = odl.uniform_discr_frompartition(geom.partition,
dtype='float32')
# Forward evaluation
proj_data = astra_cuda_forward_projector(phantom, geom, proj_space)
assert proj_data.shape == proj_space.shape
assert proj_data.norm() > 0
# Backward evaluation
backproj = astra_cuda_back_projector(proj_data, geom, reco_space)
assert backproj.shape == reco_space.shape
assert backproj.norm() > 0
def test_geom_to_vec():
"""Create ASTRA projection geometry vectors using ODL geometries."""
apart = odl.uniform_partition(0, 2 * np.pi, 5)
dpart = odl.uniform_partition(-40, 40, 10)
# Fanbeam flat
src_rad = 10
det_rad = 5
geom_ff = odl.tomo.FanBeamGeometry(apart, dpart, src_rad, det_rad)
vec = odl.tomo.astra_conebeam_2d_geom_to_vec(geom_ff)
assert vec.shape == (apart.size, 6)
# Circular cone flat
dpart = odl.uniform_partition([-40, -3], [40, 3], (10, 5))
geom_ccf = odl.tomo.ConeBeamGeometry(apart, dpart, src_rad, det_rad)
vec = odl.tomo.astra_conebeam_3d_geom_to_vec(geom_ccf)
assert vec.shape == (apart.size, 12)
# Helical cone flat
pitch = 1
geom_hcf = odl.tomo.ConeBeamGeometry(apart, dpart, src_rad, det_rad,
pitch=pitch)
vec = odl.tomo.astra_conebeam_3d_geom_to_vec(geom_hcf)
assert vec.shape == (apart.size, 12)
def test_astra_cpu_projector_fanflat():
"""ASTRA CPU forward and back projection for fanflat geometry."""
# Create reco space and a phantom
reco_space = odl.uniform_discr([-4, -5], [4, 5], (4, 5), dtype='float32')
phantom = odl.phantom.cuboid(reco_space, min_pt=[0, 0], max_pt=[4, 5])
# Create fan beam geometry with flat detector
angle_part = odl.uniform_partition(0, 2 * np.pi, 8)
det_part = odl.uniform_partition(-6, 6, 6)
src_rad = 100
det_rad = 10
geom = odl.tomo.FanFlatGeometry(angle_part, det_part, src_rad, det_rad)
# Make projection space
proj_space = odl.uniform_discr_frompartition(geom.partition,
dtype='float32')
# Forward evaluation
proj_data = astra_cpu_forward_projector(phantom, geom, proj_space)
assert proj_data.shape == proj_space.shape
assert proj_data.norm() > 0
# Backward evaluation
backproj = astra_cpu_back_projector(proj_data, geom, reco_space)
assert backproj.shape == reco_space.shape
assert backproj.norm() > 0
def test_astra_cpu_projector_parallel2d():
"""ASTRA CPU forward and back projection for 2d parallel geometry."""
# Create reco space and a phantom
reco_space = odl.uniform_discr([-4, -5], [4, 5], (4, 5), dtype='float32')
phantom = odl.phantom.cuboid(reco_space, min_pt=[0, 0], max_pt=[4, 5])
# Create parallel geometry
angle_part = odl.uniform_partition(0, 2 * np.pi, 8)
det_part = odl.uniform_partition(-6, 6, 6)
geom = odl.tomo.Parallel2dGeometry(angle_part, det_part)
# Make projection space
proj_space = odl.uniform_discr_frompartition(geom.partition,
dtype='float32')
# Forward evaluation
proj_data = astra_cpu_forward_projector(phantom, geom, proj_space)
assert proj_data.shape == proj_space.shape
assert proj_data.norm() > 0
# Backward evaluation
backproj = astra_cpu_back_projector(proj_data, geom, reco_space)
assert backproj.shape == reco_space.shape
assert backproj.norm() > 0
def prj_factory(Nx, Ny, Np, Nd, ret_A=False):
'''
returns cuda fwd and bwd projectors for given 2d geometry.
Inputs
Nx,Ny -> voxels in x and y dims
Np -> number of angles
Nd -> number of det elements
Outputs
fwd -> forward projector, calculates Ax
Input Nx*Ny matrix
Output Np*Nd matrix
bwd -> backward projector, calculates A^Tx
Input Nx*Ny matrix
Output Np*Nd matrix
'''
reco_space = odl.uniform_discr([0, 0], [1, 1], [Nx, Ny], dtype='float32')
angle_partition = odl.uniform_partition(0, 2 * pi, Np)
detector_partition = odl.uniform_partition(-0.1, 1.1, Nd)
geometry = odl.tomo.Parallel2dGeometry(angle_partition, detector_partition)
ray_trafo = odl.tomo.RayTransform(reco_space, geometry, impl='astra_cuda')
fwd = lambda X: ray_trafo(X).asarray()
bwd = lambda X: ray_trafo.adjoint(X).asarray()
return fwd, bwd
def test_parallel_3d_single_axis_geometry():
"""General parallel 3D geometries."""
# Parameters
full_angle = np.pi
apart = odl.uniform_partition(0, full_angle, 10)
dpart = odl.uniform_partition([0, 0], [1, 1], [10, 10])
# Bad init
with pytest.raises(TypeError):
odl.tomo.Parallel3dAxisGeometry([0, 1], dpart)
with pytest.raises(TypeError):
odl.tomo.Parallel3dAxisGeometry(apart, [0, 1])
# Initialize
geom = odl.tomo.Parallel3dAxisGeometry(apart, dpart, axis=[0, 0, 1])
with pytest.raises(ValueError):
geom.rotation_matrix(2 * full_angle)
# rotation of cartesian basis vectors about each other
coords = np.eye(3)
geom = odl.tomo.Parallel3dAxisGeometry(apart, dpart, axis=[1, 0, 0])
rot_mat = geom.rotation_matrix(np.pi / 2)
assert all_almost_equal(rot_mat.dot(coords),
[[1, 0, 0], [0, 0, -1], [0, 1, 0]])
geom = odl.tomo.Parallel3dAxisGeometry(apart, dpart, axis=[0, 1, 0])
rot_mat = geom.rotation_matrix(np.pi / 2)
assert all_almost_equal(rot_mat.dot(coords),
[[0, 0, 1], [0, 1, 0], [-1, 0, 0]])
geom = odl.tomo.Parallel3dAxisGeometry(apart, dpart, axis=[0, 0, 1])
rot_mat = geom.rotation_matrix(np.pi / 2)
assert all_almost_equal(rot_mat.dot(coords),
[[0, -1, 0], [1, 0, 0], [0, 0, 1]])
# rotation axis
geom = odl.tomo.Parallel3dAxisGeometry(apart, dpart, axis=[1, 0, 0])
assert all_equal(geom.axis, np.array([1, 0, 0]))
geom = odl.tomo.Parallel3dAxisGeometry(apart, dpart, axis=[0, 1, 0])
assert all_equal(geom.axis, np.array([0, 1, 0]))
geom = odl.tomo.Parallel3dAxisGeometry(apart, dpart, axis=[0, 0, 1])
assert all_equal(geom.axis, np.array([0, 0, 1]))
geom = odl.tomo.Parallel3dAxisGeometry(apart, dpart, axis=[1, 2, 3])
assert all_equal(geom.axis,
np.array([1, 2, 3]) / np.linalg.norm([1, 2, 3]))
with pytest.raises(ValueError):
odl.tomo.Parallel3dAxisGeometry(apart, dpart, axis=(1, ))
with pytest.raises(ValueError):
odl.tomo.Parallel3dAxisGeometry(apart, dpart, axis=(1, 2))
with pytest.raises(ValueError):
odl.tomo.Parallel3dAxisGeometry(apart, dpart, axis=(1, 2, 3, 4))
# check str and repr work without crashing and return something
assert str(geom)
assert repr(geom)
def _build_forward_op(self, upscale_shape, impl, num_angles):
reco_space = self.space
if self.inner_circle:
space = odl.uniform_discr(min_pt=reco_space.min_pt,
max_pt=reco_space.max_pt,
shape=(upscale_shape, upscale_shape),
dtype=np.float32)
min_pt = reco_space.min_pt
max_pt = reco_space.max_pt
proj_space = odl.uniform_discr(
min_pt,
max_pt,
2 * (2 * int(reco_space.max_pt[0]) - 1, ),
dtype=np.float32)
detector_length = get_detector_length(proj_space)
det_partition = odl.uniform_partition(
-np.sqrt((reco_space.shape[0] / 2.)**2 / 2),
np.sqrt((reco_space.shape[0] / 2.)**2 / 2), detector_length)
else:
space = odl.uniform_discr(min_pt=reco_space.min_pt,
max_pt=reco_space.max_pt,
shape=(upscale_shape, upscale_shape),
dtype=np.float32)
min_pt = reco_space.min_pt
max_pt = reco_space.max_pt
proj_space = odl.uniform_discr(min_pt,
max_pt,
2 * (reco_space.shape[0], ),
dtype=np.float32)
detector_length = get_detector_length(proj_space)
det_partition = odl.uniform_partition(-reco_space.shape[0] / 2.,
reco_space.shape[0] / 2.,
detector_length)
angle_partition = odl.uniform_partition(0, np.pi, num_angles)
reco_geometry = odl.tomo.Parallel2dGeometry(angle_partition,
det_partition)
ray_trafo = odl.tomo.RayTransform(space, reco_geometry, impl=impl)
def get_reco_ray_trafo(**kwargs):
return odl.tomo.RayTransform(reco_space, reco_geometry, **kwargs)
reco_ray_trafo = get_reco_ray_trafo(impl=impl)
class _ResizeOperator(odl.Operator):
def __init__(self):
super().__init__(reco_space, space)
def _call(self, x, out, **kwargs):
out.assign(
space.element(
resize(x, (upscale_shape, upscale_shape), order=1)))
# forward operator
resize_op = _ResizeOperator()
forward_op = ray_trafo * resize_op
return forward_op, get_reco_ray_trafo, reco_ray_trafo
def __init__(self, data_obj, data_struct=True, **kwargs):
# %% Store the input in the object
# BE F*****G CONSISTENT WITH RENAMING ETC.
self.pix = data_obj.voxels[0]
self.angles = data_obj.angles
self.src_rad = data_obj.src_rad
self.det_rad = data_obj.det_rad
self.magn = self.src_rad / (self.src_rad + self.det_rad)
self.data_struct = data_struct
self.rec_methods = []
# %% Set up the geometry
self.phantom = data_obj
# Make the reconstruction space
self.reco_space = self.phantom.reco_space
voxels = self.phantom.voxels
factor = 2
dpix = [int(factor * voxels[0]), voxels[1]]
self.w_detu = (2 * self.phantom.detecsize[0]) / dpix[0]
self.w_detv = (2 * self.phantom.detecsize[1]) / dpix[1]
if self.phantom.data_type == 'simulated':
self.PH = data_obj.PH
self.noise = data_obj.noise
# Do we need a mask?
src_radius = self.src_rad * self.phantom.volumesize[0] * 2
det_radius = self.det_rad * self.phantom.volumesize[0] * 2
# Make a circular scanning geometry
angle_partition = odl.uniform_partition(0, 2 * np.pi, self.angles)
self.angle_space = odl.uniform_discr_frompartition(angle_partition)
# Make a flat detector space
det_partition = odl.uniform_partition(-self.phantom.detecsize,
self.phantom.detecsize, dpix)
self.det_space = odl.uniform_discr_frompartition(det_partition,
dtype='float32')
# Create geometry
self.geometry = odl.tomo.ConeFlatGeometry(angle_partition,
det_partition,
src_radius=src_radius,
det_radius=det_radius,
axis=[0, 0, 1])
else:
src_radius = self.phantom.src_rad
det_radius = self.phantom.det_rad
self.pix_size = self.phantom.pix_size
self.angle_space = self.phantom.angle_space
self.angles = np.size(self.angle_space)
self.det_space = self.phantom.det_space
self.geometry = self.phantom.geometry
# %% Create the FP and BP and the data
# Forward Projection
self.FwP = odl.tomo.RayTransform(self.reco_space,
self.geometry,
use_cache=False)
self.rs_detu = int(2**(np.ceil(np.log2(dpix[0])) + 1))
self.g = self.phantom.g
def test_astra_projection_geometry():
"""Create ASTRA projection geometry from geometry objects."""
with pytest.raises(TypeError):
odl.tomo.astra_projection_geometry(None)
apart = odl.uniform_partition(0, 2 * np.pi, 5)
dpart = odl.uniform_partition(-40, 40, 10)
# motion sampling grid, detector sampling grid but not uniform
dpart_0 = odl.RectPartition(odl.IntervalProd(0, 3), odl.RectGrid([0, 1,
3]))
geom_p2d = odl.tomo.Parallel2dGeometry(apart, dpart=dpart_0)
with pytest.raises(ValueError):
odl.tomo.astra_projection_geometry(geom_p2d)
# detector sampling grid, motion sampling grid
geom_p2d = odl.tomo.Parallel2dGeometry(apart, dpart)
odl.tomo.astra_projection_geometry(geom_p2d)
# Parallel 2D geometry
geom_p2d = odl.tomo.Parallel2dGeometry(apart, dpart)
astra_geom = odl.tomo.astra_projection_geometry(geom_p2d)
assert astra_geom['type'] == 'parallel'
# Fan flat
src_rad = 10
det_rad = 5
geom_ff = odl.tomo.FanFlatGeometry(apart, dpart, src_rad, det_rad)
astra_geom = odl.tomo.astra_projection_geometry(geom_ff)
assert astra_geom['type'] == 'fanflat_vec'
dpart = odl.uniform_partition([-40, -3], [40, 3], (10, 5))
# Parallel 3D geometry
geom_p3d = odl.tomo.Parallel3dAxisGeometry(apart, dpart)
odl.tomo.astra_projection_geometry(geom_p3d)
astra_geom = odl.tomo.astra_projection_geometry(geom_p3d)
assert astra_geom['type'] == 'parallel3d_vec'
# Circular conebeam flat
geom_ccf = odl.tomo.ConeFlatGeometry(apart, dpart, src_rad, det_rad)
astra_geom = odl.tomo.astra_projection_geometry(geom_ccf)
assert astra_geom['type'] == 'cone_vec'
# Helical conebeam flat
pitch = 1
geom_hcf = odl.tomo.ConeFlatGeometry(apart,
dpart,
src_rad,
det_rad,
pitch=pitch)
astra_geom = odl.tomo.astra_projection_geometry(geom_hcf)
assert astra_geom['type'] == 'cone_vec'
def test_detector_shifts_2d():
"""Check that detector shifts are handled correctly.
We forward project a cubic phantom and check that ray transform
and back-projection with and without detector shifts are
numerically close (the error depends on domain discretization).
"""
if not odl.tomo.ASTRA_AVAILABLE:
pytest.skip(msg='ASTRA not available, skipping 2d test')
d = 10
space = odl.uniform_discr([-1] * 2, [1] * 2, [d] * 2)
phantom = odl.phantom.cuboid(space, [-1 / 3] * 2, [1 / 3] * 2)
full_angle = 2 * np.pi
n_angles = 2 * 10
src_rad = 2
det_rad = 2
apart = odl.uniform_partition(0, full_angle, n_angles)
dpart = odl.uniform_partition(-4, 4, 8 * d)
geom = odl.tomo.FanBeamGeometry(apart, dpart, src_rad, det_rad)
k = 3
shift = k * dpart.cell_sides[0]
geom_shift = odl.tomo.FanBeamGeometry(
apart, dpart, src_rad, det_rad,
det_shift_func=lambda angle: [0.0, shift]
)
assert all_almost_equal(geom.angles, geom_shift.angles)
angles = geom.angles
assert all_almost_equal(geom.src_position(angles),
geom_shift.src_position(angles))
assert all_almost_equal(geom.det_axis(angles),
geom_shift.det_axis(angles))
assert all_almost_equal(geom.det_refpoint(angles),
geom_shift.det_refpoint(angles)
+ shift * geom_shift.det_axis(angles))
# check ray transform
op = odl.tomo.RayTransform(space, geom)
op_shift = odl.tomo.RayTransform(space, geom_shift)
y = op(phantom).asarray()
y_shift = op_shift(phantom).asarray()
# projection on the shifted detector is shifted regular projection
data_error = np.max(np.abs(y[:, :-k] - y_shift[:, k:]))
assert data_error < space.cell_volume
# check back-projection
im = op.adjoint(y).asarray()
im_shift = op_shift.adjoint(y_shift).asarray()
error = np.abs(im_shift - im)
rel_error = np.max(error[im > 0] / im[im > 0])
assert rel_error < space.cell_volume
def test_partition_byaxis():
"""Test indexing a partition along the axes."""
part = odl.uniform_partition([-1, -2, -3, -4], [1, 2, 3, 4], (1, 2, 4, 5))
assert part.byaxis[0] == odl.uniform_partition(-1, 1, 1)
assert part.byaxis[1:3] == odl.uniform_partition([-2, -3], [2, 3], (2, 4))
assert (part.byaxis[[1, 3,
1]] == odl.uniform_partition([-2, -4, -2], [2, 4, 2],
(2, 5, 2)))
assert part.byaxis[[1]] == part.byaxis[1]
assert part.byaxis[...] == part
assert part.byaxis[:] == part
def test_detector_shifts_3d():
"""Check that detector shifts are handled correctly.
We forward project a cubic phantom and check that ray transform
and back-projection with and without detector shifts are
numerically close (the error depends on domain discretization).
"""
if not odl.tomo.ASTRA_AVAILABLE:
pytest.skip(msg='ASTRA not available, skipping 2d test')
d = 100
space = odl.uniform_discr([-1] * 3, [1] * 3, [d] * 3)
phantom = odl.phantom.cuboid(space, [-1/3] * 3, [1/3] * 3)
full_angle = 2 * np.pi
n_angles = 2 * 100
src_rad = 2
det_rad = 2
apart = odl.uniform_partition(0, full_angle, n_angles)
dpart = odl.uniform_partition([-4] * 2, [4] * 2, [8 * d] * 2)
geom = odl.tomo.ConeBeamGeometry(apart, dpart, src_rad, det_rad)
k = 3
l = 2
shift = np.array([0, k, l]) * dpart.cell_sides[0]
geom_shift = odl.tomo.ConeBeamGeometry(apart, dpart, src_rad, det_rad,
det_shift_func=lambda angle: shift)
angles = geom.angles
assert all_almost_equal(angles, geom_shift.angles)
assert all_almost_equal(geom.src_position(angles),
geom_shift.src_position(angles))
assert all_almost_equal(geom.det_axes(angles),
geom_shift.det_axes(angles))
assert all_almost_equal(geom.det_refpoint(angles),
geom_shift.det_refpoint(angles)
+ geom_shift.det_axes(angles)[:, 0] * shift[1]
- geom_shift.det_axes(angles)[:, 1] * shift[2])
# check forward pass
op = odl.tomo.RayTransform(space, geom)
op_shift = odl.tomo.RayTransform(space, geom_shift)
y = op(phantom).asarray()
y_shift = op_shift(phantom).asarray()
data_error = np.max(np.abs(y[:, :-k, l:] - y_shift[:, k:, :-l]))
assert data_error < 1e-3
# check back-projection
im = op.adjoint(y).asarray()
im_shift = op_shift.adjoint(y_shift).asarray()
error = np.max(np.abs(im_shift-im))
assert error < 1e-3
def limited_view_parallel_beam_geometry(space, beam_num_angle):
corners = space.domain.corners()[:, :2]
rho = np.max(np.linalg.norm(corners, axis=1))
min_side = min(space.partition.cell_sides[:2])
omega = np.pi / min_side
num_px_horiz = 2 * int(np.ceil(rho * omega / np.pi)) + 1
det_min_pt = -rho
det_max_pt = rho
det_shape = num_px_horiz
angle_partition = odl.uniform_partition(0, beam_num_angle * (np.pi / 180),
beam_num_angle)
det_partition = odl.uniform_partition(det_min_pt, det_max_pt, det_shape)
return odl.tomo.Parallel2dGeometry(angle_partition, det_partition)
def generate_data(self, voxels_up, reco_space_up, f_up, **kwargs):
factor = 2
dpix_up = [factor * voxels_up[0], voxels_up[1]]
dpix = [int(factor * self.voxels[0]), self.voxels[0]]
src_radius = self.src_rad * self.volumesize[0] * 2
det_radius = self.det_rad * self.volumesize[0] * 2
# Make a circular scanning geometry
angle_partition = odl.uniform_partition(0, 2 * np.pi, self.angles)
# Make a flat detector space
det_partition = odl.uniform_partition(-self.detecsize, self.detecsize,
dpix_up)
# Create data_space_up and data_space
data_space = odl.uniform_discr((0, *-self.detecsize),
(2 * np.pi, *self.detecsize),
[self.angles, *dpix],
dtype='float32')
data_space_up = odl.uniform_discr((0, *-self.detecsize),
(2 * np.pi, *self.detecsize),
[self.angles, *dpix_up],
dtype='float32')
# Create geometry
geometry = odl.tomo.ConeFlatGeometry(angle_partition,
det_partition,
src_radius=src_radius,
det_radius=det_radius,
axis=[0, 0, 1])
FP = odl.tomo.RayTransform(reco_space_up, geometry, use_cache=False)
resamp = odl.Resampling(data_space_up, data_space)
if 'load_data_g' in kwargs:
if type(kwargs['load_data_g']) == str:
self.g = data_space.element(np.load(kwargs['load_data_g']))
else:
self.g = data_space.element(kwargs['load_data_g'])
else:
self.g = resamp(FP(f_up))
if self.noise == None:
pass
elif self.noise[0] == 'Gaussian':
self.g += data_space.element(
odl.phantom.white_noise(resamp.range) * \
np.mean(self.g) * self.noise[1])
elif self.noise[0] == 'Poisson':
# 2**8 seems to be the minimal accepted I_0
self.g = data_space.element(
self.add_poisson_noise(self.noise[1]))
else:
raise ValueError('unknown `noise type` ({})'
''.format(self.noise[0]))
def operators_smooth():
size = 512
space = odl.uniform_discr([-256, -256], [256, 256], [size, size],
dtype='float32',
weighting=1.0)
angle_partition = odl.uniform_partition(0, 2 * np.pi, 1000)
detector_partition = odl.uniform_partition(-360, 360, 1000)
geometry = odl.tomo.Parallel2dGeometry(angle_partition, detector_partition)
T = odl.tomo.RayTransform(space, geometry)
fbp = odl.tomo.fbp_op(T, frequency_scaling=0.45, filter_type='Hann')
T_norm = T.norm(estimate=True)
T = (1 / T_norm) * T
W = odl.Gradient(space)
return [T, W]
def test_spect():
det_nx_pix = 64
det_ny_pix = 64
det_nx_mm = 4
det_radius = 200
n_proj = 180
det_param = det_nx_mm * det_nx_pix
dpart = odl.uniform_partition([-det_param, -det_param],
[det_param, det_param],
[det_nx_pix, det_ny_pix])
apart = odl.uniform_partition(0, 2 * np.pi, n_proj)
geom = ParallelHoleCollimatorGeometry(apart, dpart, det_radius)
assert isinstance(geom.detector, odl.tomo.Flat2dDetector)
assert all_equal(geom.det_radius, det_radius)
def test_proj_geom_parallel_2d():
"""Create ASTRA 2D projection geometry."""
apart = odl.uniform_partition(0, 2, 5)
dpart = odl.uniform_partition(-1, 1, 10)
geom = odl.tomo.Parallel2dGeometry(apart, dpart)
proj_geom = astra_projection_geometry(geom)
correct_subdict = {
'type': 'parallel',
'DetectorCount': 10, 'DetectorWidth': 0.2}
assert is_subdict(correct_subdict, proj_geom)
assert 'ProjectionAngles' in proj_geom
def xray(nviews=15, ndectectors=100):
gtruth = resolution_phantom(case=1, nsamples=200, highres=800)
sinfo = resolution_phantom(case=2, nsamples=200, highres=800)
angle_partition = odl.uniform_partition(0, np.pi, nviews)
detector_partition = odl.uniform_partition(-1.5, 1.5, ndectectors)
geometry = odl.tomo.Parallel2dGeometry(angle_partition, detector_partition)
operator = odl.tomo.RayTransform(gtruth.space, geometry, impl='astra_cpu')
data = odl.phantom.salt_pepper_noise(operator(gtruth),
fraction=0.05,
seed=10)
return gtruth, sinfo, operator, data
