def test_uniform_discr_fromdiscr_two_attrs():
# Change 2 attributes -> resize and translate
discr = odl.uniform_discr([0, -1], [1, 1], [10, 5])
# csides = [0.1, 0.4]
new_min_pt = [-2, 1]
new_max_pt = [4, 2]
true_new_csides = [0.6, 0.2]
new_discr = odl.uniform_discr_fromdiscr(discr,
min_pt=new_min_pt,
max_pt=new_max_pt)
assert all_almost_equal(new_discr.min_pt, new_min_pt)
assert all_almost_equal(new_discr.max_pt, new_max_pt)
assert all_equal(new_discr.shape, discr.shape)
assert all_almost_equal(new_discr.cell_sides, true_new_csides)
new_min_pt = [-2, 1]
new_shape = (5, 20)
true_new_max_pt = [-1.5, 9]
new_discr = odl.uniform_discr_fromdiscr(discr,
min_pt=new_min_pt,
shape=new_shape)
assert all_almost_equal(new_discr.min_pt, new_min_pt)
assert all_almost_equal(new_discr.max_pt, true_new_max_pt)
assert all_equal(new_discr.shape, new_shape)
assert all_almost_equal(new_discr.cell_sides, discr.cell_sides)
new_min_pt = [-2, 1]
new_csides = [0.6, 0.2]
true_new_max_pt = [4, 2]
new_discr = odl.uniform_discr_fromdiscr(discr,
min_pt=new_min_pt,
cell_sides=new_csides)
assert all_almost_equal(new_discr.min_pt, new_min_pt)
assert all_almost_equal(new_discr.max_pt, true_new_max_pt)
assert all_equal(new_discr.shape, discr.shape)
assert all_almost_equal(new_discr.cell_sides, new_csides)
new_max_pt = [4, 2]
new_shape = (5, 20)
true_new_min_pt = [3.5, -6]
new_discr = odl.uniform_discr_fromdiscr(discr,
max_pt=new_max_pt,
shape=new_shape)
assert all_almost_equal(new_discr.min_pt, true_new_min_pt)
assert all_almost_equal(new_discr.max_pt, new_max_pt)
assert all_equal(new_discr.shape, new_shape)
assert all_almost_equal(new_discr.cell_sides, discr.cell_sides)
new_max_pt = [4, 2]
new_csides = [0.6, 0.2]
true_new_min_pt = [-2, 1]
new_discr = odl.uniform_discr_fromdiscr(discr,
max_pt=new_max_pt,
cell_sides=new_csides)
assert all_almost_equal(new_discr.min_pt, true_new_min_pt)
assert all_almost_equal(new_discr.max_pt, new_max_pt)
assert all_equal(new_discr.shape, discr.shape)
assert all_almost_equal(new_discr.cell_sides, new_csides)
def test_uniform_discr_fromdiscr_two_attrs():
# Change 2 attributes -> resize and translate
discr = odl.uniform_discr([0, -1], [1, 1], [10, 5])
# csides = [0.1, 0.4]
new_min_pt = [-2, 1]
new_max_pt = [4, 2]
true_new_csides = [0.6, 0.2]
new_discr = odl.uniform_discr_fromdiscr(discr, min_pt=new_min_pt,
max_pt=new_max_pt)
assert all_almost_equal(new_discr.min_pt, new_min_pt)
assert all_almost_equal(new_discr.max_pt, new_max_pt)
assert all_equal(new_discr.shape, discr.shape)
assert all_almost_equal(new_discr.cell_sides, true_new_csides)
new_min_pt = [-2, 1]
new_shape = (5, 20)
true_new_max_pt = [-1.5, 9]
new_discr = odl.uniform_discr_fromdiscr(discr, min_pt=new_min_pt,
shape=new_shape)
assert all_almost_equal(new_discr.min_pt, new_min_pt)
assert all_almost_equal(new_discr.max_pt, true_new_max_pt)
assert all_equal(new_discr.shape, new_shape)
assert all_almost_equal(new_discr.cell_sides, discr.cell_sides)
new_min_pt = [-2, 1]
new_csides = [0.6, 0.2]
true_new_max_pt = [4, 2]
new_discr = odl.uniform_discr_fromdiscr(discr, min_pt=new_min_pt,
cell_sides=new_csides)
assert all_almost_equal(new_discr.min_pt, new_min_pt)
assert all_almost_equal(new_discr.max_pt, true_new_max_pt)
assert all_equal(new_discr.shape, discr.shape)
assert all_almost_equal(new_discr.cell_sides, new_csides)
new_max_pt = [4, 2]
new_shape = (5, 20)
true_new_min_pt = [3.5, -6]
new_discr = odl.uniform_discr_fromdiscr(discr, max_pt=new_max_pt,
shape=new_shape)
assert all_almost_equal(new_discr.min_pt, true_new_min_pt)
assert all_almost_equal(new_discr.max_pt, new_max_pt)
assert all_equal(new_discr.shape, new_shape)
assert all_almost_equal(new_discr.cell_sides, discr.cell_sides)
new_max_pt = [4, 2]
new_csides = [0.6, 0.2]
true_new_min_pt = [-2, 1]
new_discr = odl.uniform_discr_fromdiscr(discr, max_pt=new_max_pt,
cell_sides=new_csides)
assert all_almost_equal(new_discr.min_pt, true_new_min_pt)
assert all_almost_equal(new_discr.max_pt, new_max_pt)
assert all_equal(new_discr.shape, discr.shape)
assert all_almost_equal(new_discr.cell_sides, new_csides)
def test_uniform_discr_fromdiscr_per_axis():
discr = odl.uniform_discr([0, -1], [1, 1], [10, 5])
# csides = [0.1, 0.4]
new_min_pt = [-2, None]
new_max_pt = [4, 2]
new_shape = (None, 20)
new_csides = [None, None]
true_new_min_pt = [-2, -6]
true_new_max_pt = [4, 2]
true_new_shape = (10, 20)
true_new_csides = [0.6, 0.4]
new_discr = odl.uniform_discr_fromdiscr(discr,
min_pt=new_min_pt,
max_pt=new_max_pt,
shape=new_shape,
cell_sides=new_csides)
assert all_almost_equal(new_discr.min_pt, true_new_min_pt)
assert all_almost_equal(new_discr.max_pt, true_new_max_pt)
assert all_equal(new_discr.shape, true_new_shape)
assert all_almost_equal(new_discr.cell_sides, true_new_csides)
new_min_pt = None
new_max_pt = [None, 2]
new_shape = (5, None)
new_csides = [None, 0.2]
true_new_min_pt = [0, 1]
true_new_max_pt = [1, 2]
true_new_shape = (5, 5)
true_new_csides = [0.2, 0.2]
new_discr = odl.uniform_discr_fromdiscr(discr,
min_pt=new_min_pt,
max_pt=new_max_pt,
shape=new_shape,
cell_sides=new_csides)
assert all_almost_equal(new_discr.min_pt, true_new_min_pt)
assert all_almost_equal(new_discr.max_pt, true_new_max_pt)
assert all_equal(new_discr.shape, true_new_shape)
assert all_almost_equal(new_discr.cell_sides, true_new_csides)
def test_uniform_discr_fromdiscr_one_attr():
# Change 1 attribute
discr = odl.uniform_discr([0, -1], [1, 1], [10, 5])
# csides = [0.1, 0.4]
# min_pt -> translate, keep cells
new_min_pt = [3, 7]
true_new_max_pt = [4, 9]
new_discr = odl.uniform_discr_fromdiscr(discr, min_pt=new_min_pt)
assert all_almost_equal(new_discr.min_pt, new_min_pt)
assert all_almost_equal(new_discr.max_pt, true_new_max_pt)
assert all_equal(new_discr.shape, discr.shape)
assert all_almost_equal(new_discr.cell_sides, discr.cell_sides)
# max_pt -> translate, keep cells
new_max_pt = [3, 7]
true_new_min_pt = [2, 5]
new_discr = odl.uniform_discr_fromdiscr(discr, max_pt=new_max_pt)
assert all_almost_equal(new_discr.min_pt, true_new_min_pt)
assert all_almost_equal(new_discr.max_pt, new_max_pt)
assert all_equal(new_discr.shape, discr.shape)
assert all_almost_equal(new_discr.cell_sides, discr.cell_sides)
# shape -> resize cells, keep corners
new_shape = (5, 20)
true_new_csides = [0.2, 0.1]
new_discr = odl.uniform_discr_fromdiscr(discr, shape=new_shape)
assert all_almost_equal(new_discr.min_pt, discr.min_pt)
assert all_almost_equal(new_discr.max_pt, discr.max_pt)
assert all_equal(new_discr.shape, new_shape)
assert all_almost_equal(new_discr.cell_sides, true_new_csides)
# cell_sides -> resize cells, keep corners
new_csides = [0.5, 0.2]
true_new_shape = (2, 10)
new_discr = odl.uniform_discr_fromdiscr(discr, cell_sides=new_csides)
assert all_almost_equal(new_discr.min_pt, discr.min_pt)
assert all_almost_equal(new_discr.max_pt, discr.max_pt)
assert all_equal(new_discr.shape, true_new_shape)
assert all_almost_equal(new_discr.cell_sides, new_csides)
def test_uniform_discr_fromdiscr_one_attr():
# Change 1 attribute
discr = odl.uniform_discr([0, -1], [1, 1], [10, 5])
# csides = [0.1, 0.4]
# min_pt -> translate, keep cells
new_min_pt = [3, 7]
true_new_max_pt = [4, 9]
new_discr = odl.uniform_discr_fromdiscr(discr, min_pt=new_min_pt)
assert all_almost_equal(new_discr.min_pt, new_min_pt)
assert all_almost_equal(new_discr.max_pt, true_new_max_pt)
assert all_equal(new_discr.shape, discr.shape)
assert all_almost_equal(new_discr.cell_sides, discr.cell_sides)
# max_pt -> translate, keep cells
new_max_pt = [3, 7]
true_new_min_pt = [2, 5]
new_discr = odl.uniform_discr_fromdiscr(discr, max_pt=new_max_pt)
assert all_almost_equal(new_discr.min_pt, true_new_min_pt)
assert all_almost_equal(new_discr.max_pt, new_max_pt)
assert all_equal(new_discr.shape, discr.shape)
assert all_almost_equal(new_discr.cell_sides, discr.cell_sides)
# shape -> resize cells, keep corners
new_shape = (5, 20)
true_new_csides = [0.2, 0.1]
new_discr = odl.uniform_discr_fromdiscr(discr, shape=new_shape)
assert all_almost_equal(new_discr.min_pt, discr.min_pt)
assert all_almost_equal(new_discr.max_pt, discr.max_pt)
assert all_equal(new_discr.shape, new_shape)
assert all_almost_equal(new_discr.cell_sides, true_new_csides)
# cell_sides -> resize cells, keep corners
new_csides = [0.5, 0.2]
true_new_shape = (2, 10)
new_discr = odl.uniform_discr_fromdiscr(discr, cell_sides=new_csides)
assert all_almost_equal(new_discr.min_pt, discr.min_pt)
assert all_almost_equal(new_discr.max_pt, discr.max_pt)
assert all_equal(new_discr.shape, true_new_shape)
assert all_almost_equal(new_discr.cell_sides, new_csides)
def test_uniform_discr_fromdiscr_one_attr():
# Change 1 attribute
discr = odl.uniform_discr([0, -1], [1, 1], [10, 5])
# csides = [0.1, 0.4]
# min_corner -> translate, keep cells
new_min_corner = [3, 7]
true_new_end = [4, 9]
new_discr = odl.uniform_discr_fromdiscr(discr, min_corner=new_min_corner)
assert all_almost_equal(new_discr.min_corner, new_min_corner)
assert all_almost_equal(new_discr.max_corner, true_new_end)
assert all_equal(new_discr.shape, discr.shape)
assert all_almost_equal(new_discr.cell_sides, discr.cell_sides)
# max_corner -> translate, keep cells
new_max_corner = [3, 7]
true_new_begin = [2, 5]
new_discr = odl.uniform_discr_fromdiscr(discr, max_corner=new_max_corner)
assert all_almost_equal(new_discr.min_corner, true_new_begin)
assert all_almost_equal(new_discr.max_corner, new_max_corner)
assert all_equal(new_discr.shape, discr.shape)
assert all_almost_equal(new_discr.cell_sides, discr.cell_sides)
# nsamples -> resize cells, keep corners
new_nsamples = (5, 20)
true_new_csides = [0.2, 0.1]
new_discr = odl.uniform_discr_fromdiscr(discr, nsamples=new_nsamples)
assert all_almost_equal(new_discr.min_corner, discr.min_corner)
assert all_almost_equal(new_discr.max_corner, discr.max_corner)
assert all_equal(new_discr.shape, new_nsamples)
assert all_almost_equal(new_discr.cell_sides, true_new_csides)
# cell_sides -> resize cells, keep corners
new_csides = [0.5, 0.2]
true_new_nsamples = (2, 10)
new_discr = odl.uniform_discr_fromdiscr(discr, cell_sides=new_csides)
assert all_almost_equal(new_discr.min_corner, discr.min_corner)
assert all_almost_equal(new_discr.max_corner, discr.max_corner)
assert all_equal(new_discr.shape, true_new_nsamples)
assert all_almost_equal(new_discr.cell_sides, new_csides)
def test_uniform_discr_fromdiscr_per_axis():
discr = odl.uniform_discr([0, -1], [1, 1], [10, 5])
# csides = [0.1, 0.4]
new_min_pt = [-2, None]
new_max_pt = [4, 2]
new_shape = (None, 20)
new_csides = [None, None]
true_new_min_pt = [-2, -6]
true_new_max_pt = [4, 2]
true_new_shape = (10, 20)
true_new_csides = [0.6, 0.4]
new_discr = odl.uniform_discr_fromdiscr(
discr, min_pt=new_min_pt, max_pt=new_max_pt,
shape=new_shape, cell_sides=new_csides)
assert all_almost_equal(new_discr.min_pt, true_new_min_pt)
assert all_almost_equal(new_discr.max_pt, true_new_max_pt)
assert all_equal(new_discr.shape, true_new_shape)
assert all_almost_equal(new_discr.cell_sides, true_new_csides)
new_min_pt = None
new_max_pt = [None, 2]
new_shape = (5, None)
new_csides = [None, 0.2]
true_new_min_pt = [0, 1]
true_new_max_pt = [1, 2]
true_new_shape = (5, 5)
true_new_csides = [0.2, 0.2]
new_discr = odl.uniform_discr_fromdiscr(
discr, min_pt=new_min_pt, max_pt=new_max_pt,
shape=new_shape, cell_sides=new_csides)
assert all_almost_equal(new_discr.min_pt, true_new_min_pt)
assert all_almost_equal(new_discr.max_pt, true_new_max_pt)
assert all_equal(new_discr.shape, true_new_shape)
assert all_almost_equal(new_discr.cell_sides, true_new_csides)
insert_min_pt1,
insert_max_pt1)
coarse_mask2 = multigrid.operators.MaskingOperator(coarse_discr,
insert_min_pt2,
insert_max_pt2)
# Define the forward operator of the masked coarse grid
coarse_ray_trafo = odl.tomo.RayTransform(coarse_discr,
geometry,
impl='astra_cuda')
masked_coarse_ray_trafo = coarse_ray_trafo * coarse_mask1 * coarse_mask2
# Define insert discretization (ROI discretization) using the fine cell sizes
# but the insert min and max points
insert_discr1 = odl.uniform_discr_fromdiscr(fine_discr,
min_pt=insert_min_pt1,
max_pt=insert_max_pt1,
cell_sides=fine_discr.cell_sides)
insert_discr2 = odl.uniform_discr_fromdiscr(fine_discr,
min_pt=insert_min_pt2,
max_pt=insert_max_pt2,
cell_sides=fine_discr.cell_sides)
# Ray trafo on the insert discretization only
insert_ray_trafo1 = odl.tomo.RayTransform(insert_discr1,
geometry,
impl='astra_cuda')
insert_ray_trafo2 = odl.tomo.RayTransform(insert_discr2,
geometry,
impl='astra_cuda')
impl='astra_cuda')
masked_coarse_ray_trafo = coarse_ray_trafo * coarse_mask
ray_trafo_fine = odl.tomo.RayTransform(fine_discr,
geometry,
impl='astra_cuda')
# Phantom
phantom_c = odl.phantom.shepp_logan(coarse_discr, modified=True)
phantom_f = odl.phantom.shepp_logan(fine_discr, modified=True)
# Define insert discretization using the fine cell sizes but the insert
# min and max points
insert_discr = odl.uniform_discr_fromdiscr(
fine_discr,
min_pt=insert_min_pt,
max_pt=insert_max_pt,
cell_sides=fine_discr.cell_sides)
# Restrict the phantom to the insert discr
resizing_operator = odl.ResizingOperator(fine_discr, insert_discr)
phantom_insert = resizing_operator(phantom_f)
# Ray trafo on the insert discretization only
insert_ray_trafo = odl.tomo.RayTransform(insert_discr,
geometry,
impl='astra_cuda')
# Forward operator = sum of masked coarse ray trafo and insert ray trafo
sum_ray_trafo = odl.ReductionOperator(masked_coarse_ray_trafo,
insert_ray_trafo)
R22(X2.one()).show('ROI footprint')
# %% Make phantoms
# Merged low-resolution phantom
f1 = odl.phantom.shepp_logan(X1, modified=True)
f1 += odl.phantom.shepp_logan(X1,
modified=True,
min_pt=X2.min_pt,
max_pt=X2.max_pt)
f1.show('f1 -- low-res full phantom')
f1.show('low-res ROI part in f1', coords=[X2.min_pt, X2.max_pt])
# High-resolution full phantom (for data generation)
X1_hires = odl.uniform_discr_fromdiscr(X1, cell_sides=X2.cell_sides)
f1_hires = odl.phantom.shepp_logan(X1_hires, modified=True)
f1_hires += odl.phantom.shepp_logan(X1_hires,
modified=True,
min_pt=X2.min_pt,
max_pt=X2.max_pt)
f1_hires.show('f1_hires -- hi-res full phantom')
# ROI high-resolution phantom
f2 = odl.phantom.shepp_logan(X2, modified=True)
f2.show('f2 -- hi-res ROI part')
# %% Generate projection data
# Full data from low-resolution phantom
# Initialize data as ODL space element and display it, clipping to a
# somewhat reasonable range
data = ray_trafo_fbp.range.element(log_data_arr)
data.show('Sinogram', clim=[0, 4.5])
# Compute FBP reco for a good initial guess and for reference
fbp = odl.tomo.fbp_op(ray_trafo_fbp,
padding=True,
filter_type='Hamming',
frequency_scaling=0.8)
reco_fbp = fbp(data)
reco_fbp.show('FBP reconstruction', clim=[0.019, 0.023])
# Low-resolution space covering the same domain
space_lowres = odl.uniform_discr_fromdiscr(space_fbp, shape=(64, 64))
# Define the high-resolution space for the detail region.
# Find partition indices closest to the desired min and max points, such
# that there is no overlap.
detail_min_pt = [-39, -55]
detail_max_pt = [41, 25]
detail_min_pt_idx = np.floor(
(detail_min_pt - space_lowres.min_pt) / space_lowres.cell_sides)
detail_min_pt_idx = detail_min_pt_idx.astype(int)
detail_max_pt_idx = np.ceil(
(detail_max_pt - space_lowres.min_pt) / space_lowres.cell_sides)
detail_max_pt_idx = detail_max_pt_idx.astype(int)
detail_shape_coarse = detail_max_pt_idx - detail_min_pt_idx
detail_min_pt = (space_lowres.min_pt +
detail_min_pt_idx * space_lowres.cell_sides)
