def find_center(tomo,
theta,
ind=None,
emission=True,
init=None,
tol=0.5,
mask=True,
ratio=1.):
"""
Find rotation axis location.
The function exploits systematic artifacts in reconstructed images
due to shifts in the rotation center. It uses image entropy
as the error metric and ''Nelder-Mead'' routine (of the scipy
optimization module) as the optimizer :cite:`Donath:06`.
Parameters
----------
tomo : ndarray
3D tomographic data.
theta : array
Projection angles in radian.
ind : int, optional
Index of the slice to be used for reconstruction.
emission : bool, optional
Determines whether data is emission or transmission type.
init : float
Initial guess for the center.
tol : scalar
Desired sub-pixel accuracy.
mask : bool, optional
If ``True``, apply a circular mask to the reconstructed image to
limit the analysis into a circular region.
ratio : float, optional
The ratio of the radius of the circular mask to the edge of the
reconstructed image.
Returns
-------
float
Rotation axis location.
"""
tomo = dtype.as_float32(tomo)
theta = dtype.as_float32(theta)
if ind is None:
ind = tomo.shape[1] // 2
if init is None:
init = tomo.shape[2] // 2
hmin, hmax = _adjust_hist_limits(tomo[:, ind:ind + 1, :], theta, ind, mask,
emission)
# Magic is ready to happen...
res = minimize(_find_center_cost,
init,
args=(tomo, theta, ind, hmin, hmax, mask, ratio, emission),
method='Nelder-Mead',
tol=tol)
return res.x
def project(obj, theta, center=None, emission=True, sinogram_order=False, ncore=None, nchunk=None):
"""
Project x-rays through a given 3D object.
Parameters
----------
obj : ndarray
Voxelized 3D object.
theta : array
Projection angles in radian.
center: array, optional
Location of rotation axis.
emission : bool, optional
Determines whether output data is emission or transmission type.
sinogram_order: bool, optional
Determins whether output data is a stack of sinograms (True, y-axis first axis)
or a stack of radiographs (False, theta first axis).
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
3D tomographic data.
"""
obj = dtype.as_float32(obj)
theta = dtype.as_float32(theta)
# Estimate data dimensions.
oy, ox, oz = obj.shape
dt = theta.size
dy = oy
dx = _round_to_even(np.sqrt(ox * ox + oz * oz) + 2)
shape = dy, dt, dx
tomo = dtype.empty_shared_array(shape)
tomo[:] = 0.0
center = get_center(shape, center)
tomo = mproc.distribute_jobs(
(obj, center, tomo),
func=extern.c_project,
args=(theta,),
axis=0,
ncore=ncore,
nchunk=nchunk)
# NOTE: returns sinogram order with emmission=True
if not emission:
# convert data to be transmission type
np.exp(-tomo, tomo)
if not sinogram_order:
# rotate to radiograph order
tomo = np.swapaxes(tomo, 0, 1) #doesn't copy data
# copy data to sharedmem
tomo = dtype.as_sharedmem(tomo, copy=True)
return tomo
def find_center(
tomo, theta, ind=None, emission=True, init=None,
tol=0.5, mask=True, ratio=1.):
"""
Find rotation axis location.
The function exploits systematic artifacts in reconstructed images
due to shifts in the rotation center. It uses image entropy
as the error metric and ''Nelder-Mead'' routine (of the scipy
optimization module) as the optimizer :cite:`Donath:06`.
Parameters
----------
tomo : ndarray
3D tomographic data.
theta : array
Projection angles in radian.
ind : int, optional
Index of the slice to be used for reconstruction.
emission : bool, optional
Determines whether data is emission or transmission type.
init : float
Initial guess for the center.
tol : scalar
Desired sub-pixel accuracy.
mask : bool, optional
If ``True``, apply a circular mask to the reconstructed image to
limit the analysis into a circular region.
ratio : float, optional
The ratio of the radius of the circular mask to the edge of the
reconstructed image.
Returns
-------
float
Rotation axis location.
"""
tomo = dtype.as_float32(tomo)
theta = dtype.as_float32(theta)
if ind is None:
ind = tomo.shape[1] // 2
if init is None:
init = tomo.shape[2] // 2
print (ind, tomo.shape)
hmin, hmax = _adjust_hist_limits(
tomo[:, ind:ind + 1, :], theta, ind, mask, emission)
# Magic is ready to happen...
res = minimize(
_find_center_cost, init,
args=(tomo, theta, ind, hmin, hmax, mask, ratio, emission),
method='Nelder-Mead',
tol=tol)
return res.x
def remove_outlier(arr, dif, size=3, axis=0, ncore=None, out=None):
"""
Remove high intensity bright spots from a N-dimensional array by chunking
along the specified dimension, and performing (N-1)-dimensional median
filtering along the other dimensions.
Parameters
----------
arr : ndarray
Input array.
dif : float
Expected difference value between outlier value and
the median value of the array.
size : int
Size of the median filter.
axis : int, optional
Axis along which to chunk.
ncore : int, optional
Number of cores that will be assigned to jobs.
out : ndarray, optional
Output array for result. If same as arr, process
will be done in-place.
Returns
-------
ndarray
Corrected array.
"""
tmp = np.empty_like(arr)
ncore, chnk_slices = mproc.get_ncore_slices(arr.shape[axis], ncore=ncore)
filt_size = [size] * arr.ndim
filt_size[axis] = 1
with cf.ThreadPoolExecutor(ncore) as e:
slc = [slice(None)] * arr.ndim
for i in range(ncore):
slc[axis] = chnk_slices[i]
e.submit(scipy.ndimage.median_filter,
arr[tuple(slc)],
size=filt_size,
output=tmp[tuple(slc)])
arr = dtype.as_float32(arr)
tmp = dtype.as_float32(tmp)
dif = np.float32(dif)
with mproc.set_numexpr_threads(ncore):
out = ne.evaluate('where(arr-tmp>=dif,tmp,arr)', out=out)
return out
def find_center_vo(tomo,
ind=None,
smin=-50,
smax=50,
srad=6,
step=0.5,
ratio=0.5,
drop=20):
"""
Find rotation axis location using Nghia Vo's method. :cite:`Vo:14`.
Parameters
----------
tomo : ndarray
3D tomographic data.
ind : int, optional
Index of the slice to be used for reconstruction.
smin, smax : int, optional
Coarse search radius. Reference to the horizontal center of the sinogram.
srad : float, optional
Fine search radius.
step : float, optional
Step of fine searching.
ratio : float, optional
The ratio between the FOV of the camera and the size of object.
It's used to generate the mask.
drop : int, optional
Drop lines around vertical center of the mask.
Returns
-------
float
Rotation axis location.
"""
tomo = dtype.as_float32(tomo)
if ind is None:
ind = tomo.shape[1] // 2
_tomo = tomo[:, ind, :]
# Enable cache for FFTW.
pyfftw.interfaces.cache.enable()
# Reduce noise by smooth filters. Use different filters for coarse and fine search
_tomo_cs = ndimage.filters.gaussian_filter(_tomo, (3, 1))
_tomo_fs = ndimage.filters.median_filter(_tomo, (2, 2))
# Coarse and fine searches for finding the rotation center.
if _tomo.shape[0] * _tomo.shape[1] > 4e6: # If data is large (>2kx2k)
_tomo_coarse = downsample(np.expand_dims(_tomo_cs, 1), level=2)[:,
0, :]
init_cen = _search_coarse(_tomo_coarse, smin, smax, ratio, drop)
fine_cen = _search_fine(_tomo_fs, srad, step, init_cen * 4, ratio,
drop)
else:
init_cen = _search_coarse(_tomo_cs, smin, smax, ratio, drop)
fine_cen = _search_fine(_tomo_fs, srad, step, init_cen, ratio, drop)
logger.debug('Rotation center search finished: %i', fine_cen)
return fine_cen
def remove_stripe_sf(tomo, size=5, ncore=None, nchunk=None):
"""
Normalize raw projection data using a smoothing filter approach.
Parameters
----------
tomo : ndarray
3D tomographic data.
size : int, optional
Size of the smoothing filter.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
Corrected 3D tomographic data.
"""
tomo = dtype.as_float32(tomo)
dx, dy, dz = tomo.shape
arr = mproc.distribute_jobs(
tomo,
func=extern.c_remove_stripe_sf,
args=(dx, dy, dz, size),
axis=1,
ncore=ncore,
nchunk=nchunk)
return arr
def find_center_vo(tomo, ind=None, smin=-50, smax=50, srad=6, step=0.25,
ratio=0.5, drop=20):
"""
Find rotation axis location using Nghia Vo's method. :cite:`Vo:14`.
Parameters
----------
tomo : ndarray
3D tomographic data.
ind : int, optional
Index of the slice to be used for reconstruction.
smin, smax : int, optional
Coarse search radius. Reference to the horizontal center of the sinogram.
srad : float, optional
Fine search radius.
step : float, optional
Step of fine searching.
ratio : float, optional
The ratio between the FOV of the camera and the size of object.
It's used to generate the mask.
drop : int, optional
Drop lines around vertical center of the mask.
Returns
-------
float
Rotation axis location.
"""
tomo = dtype.as_float32(tomo)
(depth, height, width) = tomo.shape
if ind is None:
ind = height // 2
if height > 10:
# Averaging sinograms to improve SNR
_tomo = np.mean(tomo[:, ind - 5:ind + 5, :], axis=1)
else:
_tomo = tomo[:, ind, :]
else:
_tomo = tomo[:, ind, :]
# Denoising
# There's a critical reason to use different window sizes
# between coarse and fine search.
_tomo_cs = ndimage.filters.gaussian_filter(_tomo, (3, 1))
_tomo_fs = ndimage.filters.gaussian_filter(_tomo, (2, 2))
# Coarse and fine searches for finding the rotation center.
if _tomo.shape[0] * _tomo.shape[1] > 4e6: # If data is large (>2kx2k)
_tomo_coarse = downsample(
np.expand_dims(_tomo_cs, 1), level=2)[:, 0, :]
init_cen = _search_coarse(
_tomo_coarse, smin / 4.0, smax / 4.0, ratio, drop)
fine_cen = _search_fine(_tomo_fs, srad, step,
init_cen * 4, ratio, drop)
else:
init_cen = _search_coarse(_tomo_cs, smin, smax, ratio, drop)
fine_cen = _search_fine(_tomo_fs, srad, step, init_cen, ratio, drop)
logger.debug('Rotation center search finished: %i', fine_cen)
return fine_cen
def circ_mask(arr, axis, ratio=1, val=0., ncore=None):
"""
Apply circular mask to a 3D array.
Parameters
----------
arr : ndarray
Arbitrary 3D array.
axis : int
Axis along which mask will be performed.
ratio : int, optional
Ratio of the mask's diameter in pixels to
the smallest edge size along given axis.
val : int, optional
Value for the masked region.
Returns
-------
ndarray
Masked array.
"""
arr = dtype.as_float32(arr)
val = np.float32(val)
_arr = arr.swapaxes(0, axis)
dx, dy, dz = _arr.shape
mask = _get_mask(dy, dz, ratio)
with mproc.set_numexpr_threads(ncore):
ne.evaluate('where(mask, _arr, val)', out=_arr)
return _arr.swapaxes(0, axis)
def circ_mask(arr, axis, ratio=1, val=0., ncore=None):
"""
Apply circular mask to a 3D array.
Parameters
----------
arr : ndarray
Arbitrary 3D array.
axis : int
Axis along which mask will be performed.
ratio : int, optional
Ratio of the mask's diameter in pixels to
the smallest edge size along given axis.
val : int, optional
Value for the masked region.
Returns
-------
ndarray
Masked array.
"""
arr = dtype.as_float32(arr)
val = np.float32(val)
_arr = arr.swapaxes(0, axis)
dx, dy, dz = _arr.shape
mask = _get_mask(dy, dz, ratio)
with mproc.set_numexpr_threads(ncore):
ne.evaluate('where(mask, _arr, val)', out=_arr)
return _arr.swapaxes(0, axis)
def remove_stripe_sf(tomo, size=5, ncore=None, nchunk=None):
"""
Normalize raw projection data using a smoothing filter approach.
Parameters
----------
tomo : ndarray
3D tomographic data.
size : int, optional
Size of the smoothing filter.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
Corrected 3D tomographic data.
"""
tomo = dtype.as_float32(tomo)
arr = mproc.distribute_jobs(
tomo,
func=extern.c_remove_stripe_sf,
args=(size,),
axis=1,
ncore=ncore,
nchunk=nchunk)
return arr
def normalize_bg(tomo, air=1, ncore=None, nchunk=None):
"""
Normalize 3D tomgraphy data based on background intensity.
Weight sinogram such that the left and right image boundaries
(i.e., typically the air region around the object) are set to one
and all intermediate values are scaled linearly.
Parameters
----------
tomo : ndarray
3D tomographic data.
air : int, optional
Number of pixels at each boundary to calculate the scaling factor.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
Corrected 3D tomographic data.
"""
tomo = dtype.as_float32(tomo)
air = dtype.as_int32(air)
dx, dy, dz = tomo.shape
arr = mproc.distribute_jobs(tomo,
func=extern.c_normalize_bg,
args=(dx, dy, dz, air),
axis=0,
ncore=ncore,
nchunk=nchunk)
return arr
def median_filter(arr, size=3, axis=0, ncore=None, nchunk=None):
"""
Apply median filter to 3D array along specified axis.
Parameters
----------
arr : ndarray
Input array.
size : int, optional
The size of the filter.
axis : int, optional
Axis along which median filtering is performed.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
Median filtered 3D array.
"""
arr = dtype.as_float32(arr)
arr = mproc.distribute_jobs(arr.swapaxes(0, axis),
func=_median_filter,
args=(size, ),
axis=axis,
ncore=ncore,
nchunk=nchunk)
return arr.swapaxes(0, axis)
def remove_nan(arr, val=0., ncore=None):
"""
Replace NaN values in array with a given value.
Parameters
----------
arr : ndarray
Input array.
val : float, optional
Values to be replaced with NaN values in array.
ncore : int, optional
Number of cores that will be assigned to jobs.
Returns
-------
ndarray
Corrected array.
"""
arr = dtype.as_float32(arr)
val = np.float32(val)
with mproc.set_numexpr_threads(ncore):
ne.evaluate('where(arr!=arr, val, arr)', out=arr)
return arr
def remove_nan(arr, val=0., ncore=None):
"""
Replace NaN values in array with a given value.
Parameters
----------
arr : ndarray
Input array.
val : float, optional
Values to be replaced with NaN values in array.
ncore : int, optional
Number of cores that will be assigned to jobs.
Returns
-------
ndarray
Corrected array.
"""
arr = dtype.as_float32(arr)
val = np.float32(val)
with mproc.set_numexpr_threads(ncore):
ne.evaluate('where(arr!=arr, val, arr)', out=arr)
return arr
def circ_mask(arr, axis, ratio=1, val=0.):
"""
Apply circular mask to a 3D array.
Parameters
----------
arr : ndarray
Arbitrary 3D array.
axis : int
Axis along which mask will be performed.
ratio : int, optional
Ratio of the mask's diameter in pixels to
the smallest edge size along given axis.
val : int, optional
Value for the masked region.
Returns
-------
ndarray
Masked array.
"""
arr = dtype.as_float32(arr)
_arr = arr.swapaxes(0, axis)
dx, dy, dz = _arr.shape
mask = _get_mask(dy, dz, ratio)
for m in range(dx):
_arr[m, ~mask] = val
return _arr.swapaxes(0, axis)
def vector(tomo, theta, center=None, num_iter=1):
tomo = dtype.as_float32(tomo)
theta = dtype.as_float32(theta)
# Initialize tomography data.
tomo = init_tomo(tomo, sinogram_order=False, sharedmem=False)
recon_shape = (tomo.shape[0], tomo.shape[2], tomo.shape[2])
recon1 = np.zeros(recon_shape, dtype=np.float32)
recon2 = np.zeros(recon_shape, dtype=np.float32)
center_arr = get_center(tomo.shape, center)
extern.c_vector(tomo, center_arr, recon1, recon2, theta,
num_gridx=tomo.shape[2], num_gridy=tomo.shape[2], num_iter=num_iter)
return recon1, recon2
def median_filter(arr, size=3, axis=0, ncore=None):
"""
Apply median filter to 3D array along specified axis.
Parameters
----------
arr : ndarray
Input array.
size : int, optional
The size of the filter.
axis : int, optional
Axis along which median filtering is performed.
ncore : int, optional
Number of cores that will be assigned to jobs.
Returns
-------
ndarray
Median filtered 3D array.
"""
arr = dtype.as_float32(arr)
out = np.empty_like(arr)
if ncore is None:
ncore = mproc.mp.cpu_count()
with cf.ThreadPoolExecutor(ncore) as e:
slc = [slice(None)]*arr.ndim
for i in range(arr.shape[axis]):
slc[axis] = i
e.submit(filters.median_filter, arr[tuple(slc)], size=(size, size),
output=out[tuple(slc)])
return out
def remove_outlier(arr, dif, size=3, axis=0, ncore=None, nchunk=None):
"""
Remove high intensity bright spots from a 3D array along specified
dimension.
Parameters
----------
arr : ndarray
Input array.
dif : float
Expected difference value between outlier value and
the median value of the array.
size : int
Size of the median filter.
axis : int, optional
Axis along which median filtering is performed.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
Corrected array.
"""
arr = dtype.as_float32(arr)
arr = mproc.distribute_jobs(arr.swapaxes(0, axis),
func=_remove_outlier,
args=(dif, size),
axis=0,
ncore=ncore,
nchunk=nchunk)
return arr.swapaxes(0, axis)
def normalize_roi(arr, roi=[0, 0, 10, 10], ncore=None):
"""
Normalize raw projection data using an average of a selected window
on projection images.
Parameters
----------
arr : ndarray
3D tomographic data.
roi: list of int, optional
[top-left, top-right, bottom-left, bottom-right] pixel coordinates.
ncore : int, optional
Number of cores that will be assigned to jobs.
Returns
-------
ndarray
Normalized 3D tomographic data.
"""
arr = dtype.as_float32(arr)
arr = mproc.distribute_jobs(arr,
func=_normalize_roi,
args=(roi, ),
axis=0,
ncore=ncore,
nchunk=0)
return arr
def sobel_filter(arr, axis=0, ncore=None, nchunk=None):
"""
Apply Sobel filter to 3D array along specified axis.
Parameters
----------
arr : ndarray
Input array.
axis : int, optional
Axis along which sobel filtering is performed.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
3D array of same shape as input.
"""
arr = dtype.as_float32(arr)
arr = mproc.distribute_jobs(arr.swapaxes(0, axis),
func=_sobel_filter,
axis=axis,
ncore=ncore,
nchunk=nchunk)
return arr.swapaxes(0, axis)
def remove_outlier(arr, dif, size=3, axis=0, ncore=None):
"""
Remove high intensity bright spots from a 3D array along specified
dimension.
Parameters
----------
arr : ndarray
Input array.
dif : float
Expected difference value between outlier value and
the median value of the array.
size : int
Size of the median filter.
axis : int, optional
Axis along which median filtering is performed.
ncore : int, optional
Number of cores that will be assigned to jobs.
Returns
-------
ndarray
Corrected array.
"""
arr = dtype.as_float32(arr)
arr = mproc.distribute_jobs(
arr,
func=_remove_outlier_from_img,
args=(dif, size),
axis=axis,
ncore=ncore,
nchunk=0)
return arr
def sobel_filter(arr, axis=0, ncore=None):
"""
Apply Sobel filter to 3D array along specified axis.
Parameters
----------
arr : ndarray
Input array.
axis : int, optional
Axis along which sobel filtering is performed.
ncore : int, optional
Number of cores that will be assigned to jobs.
Returns
-------
ndarray
3D array of same shape as input.
"""
arr = dtype.as_float32(arr)
out = np.empty_like(arr)
if ncore is None:
ncore = mproc.mp.cpu_count()
with cf.ThreadPoolExecutor(ncore) as e:
slc = [slice(None)]*arr.ndim
for i in range(arr.shape[axis]):
slc[axis] = i
e.submit(filters.sobel, arr[slc], output=out[slc])
return out
def median_filter(arr, size=3, axis=0, ncore=None):
"""
Apply median filter to 3D array along specified axis.
Parameters
----------
arr : ndarray
Input array.
size : int, optional
The size of the filter.
axis : int, optional
Axis along which median filtering is performed.
ncore : int, optional
Number of cores that will be assigned to jobs.
Returns
-------
ndarray
Median filtered 3D array.
"""
arr = dtype.as_float32(arr)
arr = mproc.distribute_jobs(
arr,
func=filters.median_filter,
args=((size, size),),
axis=axis,
ncore=ncore,
nchunk=0)
return arr
def sobel_filter(arr, axis=0, ncore=None):
"""
Apply Sobel filter to 3D array along specified axis.
Parameters
----------
arr : ndarray
Input array.
axis : int, optional
Axis along which sobel filtering is performed.
ncore : int, optional
Number of cores that will be assigned to jobs.
Returns
-------
ndarray
3D array of same shape as input.
"""
arr = dtype.as_float32(arr)
arr = mproc.distribute_jobs(
arr,
func=filters.sobel,
axis=axis,
ncore=ncore,
nchunk=0)
return arr
def normalize_bg(tomo, air=1, ncore=None, nchunk=None):
"""
Normalize 3D tomgraphy data based on background intensity.
Weight sinogram such that the left and right image boundaries
(i.e., typically the air region around the object) are set to one
and all intermediate values are scaled linearly.
Parameters
----------
tomo : ndarray
3D tomographic data.
air : int, optional
Number of pixels at each boundary to calculate the scaling factor.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
Corrected 3D tomographic data.
"""
tomo = dtype.as_float32(tomo)
air = dtype.as_int32(air)
arr = mproc.distribute_jobs(
tomo,
func=extern.c_normalize_bg,
args=(air,),
axis=0,
ncore=ncore,
nchunk=nchunk)
return arr
def median_filter(arr, size=3, axis=0, ncore=None):
"""
Apply median filter to 3D array along specified axis.
Parameters
----------
arr : ndarray
Input array.
size : int, optional
The size of the filter.
axis : int, optional
Axis along which median filtering is performed.
ncore : int, optional
Number of cores that will be assigned to jobs.
Returns
-------
ndarray
Median filtered 3D array.
"""
arr = dtype.as_float32(arr)
out = np.empty_like(arr)
if ncore is None:
ncore = mproc.mp.cpu_count()
with cf.ThreadPoolExecutor(ncore) as e:
slc = [slice(None)]*arr.ndim
for i in range(arr.shape[axis]):
slc[axis] = i
e.submit(filters.median_filter, arr[tuple(slc)], size=(size, size),
output=out[tuple(slc)])
return out
def sobel_filter(arr, axis=0, ncore=None):
"""
Apply Sobel filter to 3D array along specified axis.
Parameters
----------
arr : ndarray
Input array.
axis : int, optional
Axis along which sobel filtering is performed.
ncore : int, optional
Number of cores that will be assigned to jobs.
Returns
-------
ndarray
3D array of same shape as input.
"""
arr = dtype.as_float32(arr)
out = np.empty_like(arr)
if ncore is None:
ncore = mproc.mp.cpu_count()
with cf.ThreadPoolExecutor(ncore) as e:
slc = [slice(None)]*arr.ndim
for i in range(arr.shape[axis]):
slc[axis] = i
e.submit(filters.sobel, arr[slc], output=out[slc])
return out
def normalize_roi(tomo, roi=[0, 0, 10, 10], ncore=None, nchunk=None):
"""
Normalize raw projection data using an average of a selected window
on projection images.
Parameters
----------
tomo : ndarray
3D tomographic data.
roi: list of int, optional
[top-left, top-right, bottom-left, bottom-right] pixel coordinates.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
Normalized 3D tomographic data.
"""
tomo = dtype.as_float32(tomo)
arr = mproc.distribute_jobs(
tomo,
func=_normalize_roi,
args=(roi, ),
axis=0,
ncore=ncore,
nchunk=nchunk)
return arr
def remove_ring(rec, center_x=None, center_y=None, thresh=300.0,
thresh_max=300.0, thresh_min=-100.0, theta_min=30,
rwidth=30, ncore=None, nchunk=None):
"""
Remove ring artifacts from images in the reconstructed domain.
Descriptions of parameters need to be more clear for sure.
Parameters
----------
arr : ndarray
Array of reconstruction data
center_x : float, optional
abscissa location of center of rotation
center_y : float, optional
ordinate location of center of rotation
thresh : float, optional
maximum value of an offset due to a ring artifact
thresh_max : float, optional
max value for portion of image to filter
thresh_min : float, optional
min value for portion of image to filer
theta_min : int, optional
minimum angle in degrees (int) to be considered ring artifact
rwidth : int, optional
Maximum width of the rings to be filtered in pixels
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
Corrected reconstruction data
"""
rec = dtype.as_float32(rec)
dz, dy, dx = rec.shape
if center_x is None:
center_x = (dx - 1.0)/2.0
if center_y is None:
center_y = (dy - 1.0)/2.0
args = (center_x, center_y, dx, dy, dz, thresh_max, thresh_min,
thresh, theta_min, rwidth)
rec = mproc.distribute_jobs(
rec,
func=extern.c_remove_ring,
args=args,
axis=0,
ncore=ncore,
nchunk=nchunk)
return rec
def project(obj, theta, center=None, ncore=None, nchunk=None):
"""
Project x-rays through a given 3D object.
Parameters
----------
obj : ndarray
Voxelized 3D object.
theta : array
Projection angles in radian.
center: array, optional
Location of rotation axis.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
3D tomographic data.
"""
obj = dtype.as_float32(obj)
theta = dtype.as_float32(theta)
# Estimate data dimensions.
ox, oy, oz = obj.shape
dx = theta.size
dy = ox
dz = np.ceil(np.sqrt(oy * oy + oz * oz)).astype('int')
shape = dx, dy, dz
tomo = np.zeros(shape, dtype='float32')
center = get_center(shape, center)
mproc.init_obj(obj)
arr = mproc.distribute_jobs(
tomo,
func=extern.c_project,
args=(ox, oy, oz, theta, center, dx, dy, dz),
axis=0,
ncore=ncore,
nchunk=nchunk)
return arr
def project(obj, theta, center=None, ncore=None, nchunk=None):
"""
Project x-rays through a given 3D object.
Parameters
----------
obj : ndarray
Voxelized 3D object.
theta : array
Projection angles in radian.
center: array, optional
Location of rotation axis.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
3D tomographic data.
"""
obj = dtype.as_float32(obj)
theta = dtype.as_float32(theta)
# Estimate data dimensions.
ox, oy, oz = obj.shape
dx = theta.size
dy = ox
dz = np.ceil(np.sqrt(oy * oy + oz * oz)).astype('int')
shape = dx, dy, dz
tomo = np.zeros(shape, dtype='float32')
center = get_center(shape, center)
mproc.init_obj(obj)
arr = mproc.distribute_jobs(tomo,
func=extern.c_project,
args=(ox, oy, oz, theta, center, dx, dy, dz),
axis=0,
ncore=ncore,
nchunk=nchunk)
return arr
def trim_sinogram(data, center, x, y, diameter):
"""
Provide sinogram corresponding to a circular region of interest
by trimming the complete sinogram of a compact object.
Parameters
----------
data : ndarray
Input 3D data.
center : float
Rotation center location.
x, y : int, int
x and y coordinates in pixels (image center is (0, 0))
diameter : float
Diameter of the circle of the region of interest.
Returns
-------
ndarray
Output 3D data.
"""
data = dtype.as_float32(data.copy())
dx, dy, dz = data.shape
rad = np.sqrt(x * x + y * y)
alpha = np.arctan2(x, y)
l1 = center - diameter / 2
l2 = center - diameter / 2 + rad
roidata = np.ones((dx, dy, diameter), dtype='float32')
delphi = np.pi / dx
for m in range(dx):
# Calculate start end coordinates for each row of the sinogram.
ind1 = np.ceil(np.cos(alpha - m * delphi) * (l2 - l1) + l1)
ind2 = np.floor(np.cos(alpha - m * delphi) * (l2 - l1) + l1 + diameter)
# Make sure everythin is inside the frame.
if ind1 < 0:
ind1 = 0
if ind1 > dz:
ind1 = dz
if ind2 < 0:
ind2 = 0
if ind2 > dz:
ind2 = dz
roidata[m, :, 0:(ind2 - ind1)] = data[m:m + 1, :, ind1:ind2]
return roidata
def _sample(arr, level, axis, mode):
arr = dtype.as_float32(arr)
dx, dy, dz = arr.shape
if mode == 0:
dim = arr.shape[axis] / np.power(2, level)
if mode == 1:
dim = arr.shape[axis] * np.power(2, level)
out = _init_out(arr, axis, dim)
return extern.c_sample(mode, arr, dx, dy, dz, level, axis, out)
def _sample(arr, level, axis, mode):
arr = dtype.as_float32(arr)
dx, dy, dz = arr.shape
if mode == 0:
dim = arr.shape[axis] / np.power(2, level)
if mode == 1:
dim = arr.shape[axis] * np.power(2, level)
out = _init_out(arr, axis, dim)
return extern.c_sample(mode, arr, dx, dy, dz, level, axis, out)
def trim_sinogram(data, center, x, y, diameter):
"""
Provide sinogram corresponding to a circular region of interest
by trimming the complete sinogram of a compact object.
Parameters
----------
data : ndarray
Input 3D data.
center : float
Rotation center location.
x, y : int, int
x and y coordinates in pixels (image center is (0, 0))
diameter : float
Diameter of the circle of the region of interest.
Returns
-------
ndarray
Output 3D data.
"""
data = dtype.as_float32(data.copy())
dx, dy, dz = data.shape
rad = np.sqrt(x * x + y * y)
alpha = np.arctan2(x, y)
l1 = center - diameter / 2
l2 = center - diameter / 2 + rad
roidata = np.ones((dx, dy, diameter), dtype='float32')
delphi = np.pi / dx
for m in range(dx):
# Calculate start end coordinates for each row of the sinogram.
ind1 = np.ceil(np.cos(alpha - m * delphi) * (l2 - l1) + l1)
ind2 = np.floor(np.cos(alpha - m * delphi) * (l2 - l1) + l1 + diameter)
# Make sure everythin is inside the frame.
if ind1 < 0:
ind1 = 0
if ind1 > dz:
ind1 = dz
if ind2 < 0:
ind2 = 0
if ind2 > dz:
ind2 = dz
roidata[m, :, 0:(ind2 - ind1)] = data[m:m+1, :, ind1:ind2]
return roidata
def _sample(arr, level, axis, mode):
arr = dtype.as_float32(arr.copy())
dx, dy, dz = arr.shape
# Determine the new size, dim, of the down-/up-sampled dimension
if mode == 0:
dim = int(arr.shape[axis] / np.power(2, level))
if mode == 1:
dim = int(arr.shape[axis] * np.power(2, level))
out = _init_out(arr, axis, dim)
return extern.c_sample(mode, arr, dx, dy, dz, level, axis, out)
def init_tomo(tomo, sinogram_order, sharedmem=True):
tomo = dtype.as_float32(tomo)
if not sinogram_order:
tomo = np.swapaxes(tomo, 0, 1) # doesn't copy data
if sharedmem:
# copy data to sharedmem (if not already or not contiguous)
tomo = dtype.as_sharedmem(tomo, copy=not dtype.is_contiguous(tomo))
else:
# ensure contiguous
tomo = np.require(tomo, requirements="AC")
return tomo
def _sample(arr, level, axis, mode):
arr = dtype.as_float32(arr.copy())
dx, dy, dz = arr.shape
# Determine the new size, dim, of the down-/up-sampled dimension
if mode == 0:
dim = int(arr.shape[axis] / np.power(2, level))
if mode == 1:
dim = int(arr.shape[axis] * np.power(2, level))
out = _init_out(arr, axis, dim)
return extern.c_sample(mode, arr, dx, dy, dz, level, axis, out)
def remove_outlier1d(arr, dif, size=3, axis=0, ncore=None, out=None):
"""
Remove high intensity bright spots from an array, using a one-dimensional
median filter along the specified axis.
Parameters
----------
arr : ndarray
Input array.
dif : float
Expected difference value between outlier value and
the median value of the array.
size : int
Size of the median filter.
axis : int, optional
Axis along which median filtering is performed.
ncore : int, optional
Number of cores that will be assigned to jobs.
out : ndarray, optional
Output array for result. If same as arr, process
will be done in-place.
Returns
-------
ndarray
Corrected array.
"""
arr = dtype.as_float32(arr)
dif = np.float32(dif)
tmp = np.empty_like(arr)
other_axes = [i for i in range(arr.ndim) if i != axis]
largest = np.argmax([arr.shape[i] for i in other_axes])
lar_axis = other_axes[largest]
ncore, chnk_slices = mproc.get_ncore_slices(arr.shape[lar_axis],
ncore=ncore)
filt_size = [1] * arr.ndim
filt_size[axis] = size
with cf.ThreadPoolExecutor(ncore) as e:
slc = [slice(None)] * arr.ndim
for i in range(ncore):
slc[lar_axis] = chnk_slices[i]
e.submit(filters.median_filter,
arr[slc],
size=filt_size,
output=tmp[slc],
mode='mirror')
with mproc.set_numexpr_threads(ncore):
out = ne.evaluate('where(arr-tmp>=dif,tmp,arr)', out=out)
return out
def init_tomo(tomo, sinogram_order, sharedmem=True):
tomo = dtype.as_float32(tomo)
if not sinogram_order:
tomo = np.swapaxes(tomo, 0, 1) #doesn't copy data
if sharedmem:
# copy data to sharedmem (if not already or not contiguous)
tomo = dtype.as_sharedmem(tomo, copy=not dtype.is_contiguous(tomo))
else:
# ensure contiguous
tomo = np.require(tomo, requirements="AC")
return tomo
def vector2(tomo1,
tomo2,
theta1,
theta2,
center1=None,
center2=None,
num_iter=1,
axis1=1,
axis2=2):
tomo1 = dtype.as_float32(tomo1)
tomo2 = dtype.as_float32(tomo2)
theta1 = dtype.as_float32(theta1)
theta2 = dtype.as_float32(theta2)
# Initialize tomography data.
tomo1 = init_tomo(tomo1, sinogram_order=False, sharedmem=False)
tomo2 = init_tomo(tomo2, sinogram_order=False, sharedmem=False)
recon_shape = (tomo1.shape[0], tomo1.shape[2], tomo1.shape[2])
recon1 = np.zeros(recon_shape, dtype=np.float32)
recon2 = np.zeros(recon_shape, dtype=np.float32)
recon3 = np.zeros(recon_shape, dtype=np.float32)
center_arr1 = get_center(tomo1.shape, center1)
center_arr2 = get_center(tomo2.shape, center2)
extern.c_vector2(tomo1,
tomo2,
center_arr1,
center_arr2,
recon1,
recon2,
recon3,
theta1,
theta2,
num_gridx=tomo1.shape[2],
num_gridy=tomo1.shape[2],
num_iter=num_iter,
axis1=axis1,
axis2=axis2)
return recon1, recon2, recon3
def find_center_vo(tomo,
ind=None,
smin=-50,
smax=50,
srad=3,
tol=0.5,
ratio=2.,
drop=20):
"""
Find rotation axis location using Nghia Vo's method. :cite:`Vo:14`.
Parameters
----------
tomo : ndarray
3D tomographic data.
ind : int, optional
Index of the slice to be used for reconstruction.
smin, smax : int, optional
Reference to the horizontal center of the sinogram.
srad : float, optional
Initial guess for the center.
tol : scalar, optional
Desired sub-pixel accuracy.
ratio : float, optional
The ratio between the size of object and FOV of the camera.
It's used to generate the mask.
drop : int, optional
Drop lines around vertical center of the mask.
Returns
-------
float
Rotation axis location.
Warning
-------
Not tested yet.
"""
tomo = dtype.as_float32(tomo)
if ind is None:
ind = tomo.shape[1] // 2
if init is None:
init = tomo.shape[2] // 2
# Reduce noise by smooth filtering.
tomo = ndimage.filters.gaussian_filter(tomo, sigma=(3, 1))
# Coarse search for finiding the roataion center.
init_cen = _search_coarse(tomo, smin, smax, ratio, drop)
# Fine search for finiding the roataion center.
return _search_fine(tomo, srad, step, init_cen, ratio, drop)
def vector2(tomo1, tomo2, theta1, theta2, center1=None, center2=None, num_iter=1, axis1=1, axis2=2):
tomo1 = dtype.as_float32(tomo1)
tomo2 = dtype.as_float32(tomo2)
theta1 = dtype.as_float32(theta1)
theta2 = dtype.as_float32(theta2)
# Initialize tomography data.
tomo1 = init_tomo(tomo1, sinogram_order=False, sharedmem=False)
tomo2 = init_tomo(tomo2, sinogram_order=False, sharedmem=False)
recon_shape = (tomo1.shape[0], tomo1.shape[2], tomo1.shape[2])
recon1 = np.zeros(recon_shape, dtype=np.float32)
recon2 = np.zeros(recon_shape, dtype=np.float32)
recon3 = np.zeros(recon_shape, dtype=np.float32)
center_arr1 = get_center(tomo1.shape, center1)
center_arr2 = get_center(tomo2.shape, center2)
extern.c_vector2(tomo1, tomo2, center_arr1, center_arr2, recon1, recon2, recon3, theta1, theta2,
num_gridx=tomo1.shape[2], num_gridy=tomo1.shape[2], num_iter=num_iter, axis1=axis1, axis2=axis2)
return recon1, recon2, recon3
def vector(tomo, theta, center=None, num_iter=1, axis=0):
tomo = dtype.as_float32(tomo)
theta = dtype.as_float32(theta)
# Initialize tomography data.
tomo = init_tomo(tomo, sinogram_order=False, sharedmem=False)
recon_shape = (tomo.shape[0], tomo.shape[2], tomo.shape[2])
recon = np.zeros(recon_shape, dtype=np.float32)
center_arr = get_center(tomo.shape, center)
extern.c_vector(tomo,
center_arr,
recon,
theta,
num_gridx=tomo.shape[2],
num_gridy=tomo.shape[2],
num_iter=num_iter,
axis=axis)
return recon
def normalize(arr, flat, dark, cutoff=None, ncore=None, out=None):
"""
Normalize raw projection data using the flat and dark field projections.
Parameters
----------
arr : ndarray
3D stack of projections.
flat : ndarray
3D flat field data.
dark : ndarray
3D dark field data.
cutoff : float, optional
Permitted maximum vaue for the normalized data.
ncore : int, optional
Number of cores that will be assigned to jobs.
out : ndarray, optional
Output array for result. If same as arr, process will be done in-place.
Returns
-------
ndarray
Normalized 3D tomographic data.
"""
arr = dtype.as_float32(arr)
flat = dtype.as_float32(flat)
dark = dtype.as_float32(dark)
flat = flat.mean(axis=0)
dark = dark.mean(axis=0)
arr = mproc.distribute_jobs(
arr,
func=_normalize,
args=(flat, dark, cutoff),
axis=0,
ncore=ncore,
nchunk=0,
out=out)
return arr
def find_center_vo(tomo, ind=None, smin=-50, smax=50, srad=6, step=0.5,
ratio=0.5, drop=20):
"""
Find rotation axis location using Nghia Vo's method. :cite:`Vo:14`.
Parameters
----------
tomo : ndarray
3D tomographic data.
ind : int, optional
Index of the slice to be used for reconstruction.
smin, smax : int, optional
Coarse search radius. Reference to the horizontal center of the sinogram.
srad : float, optional
Fine search radius.
step : float, optional
Step of fine searching.
ratio : float, optional
The ratio between the FOV of the camera and the size of object.
It's used to generate the mask.
drop : int, optional
Drop lines around vertical center of the mask.
Returns
-------
float
Rotation axis location.
"""
tomo = dtype.as_float32(tomo)
if ind is None:
ind = tomo.shape[1] // 2
_tomo = tomo[:, ind, :]
# Enable cache for FFTW.
pyfftw.interfaces.cache.enable()
# Reduce noise by smooth filters. Use different filters for coarse and fine search
_tomo_cs = ndimage.filters.gaussian_filter(_tomo, (3, 1))
_tomo_fs = ndimage.filters.median_filter(_tomo, (2, 2))
# Coarse and fine searches for finding the rotation center.
if _tomo.shape[0] * _tomo.shape[1] > 4e6: # If data is large (>2kx2k)
_tomo_coarse = downsample(np.expand_dims(_tomo_cs,1), level=2)[:, 0, :]
init_cen = _search_coarse(_tomo_coarse, smin / 4.0, smax / 4.0, ratio, drop)
fine_cen = _search_fine(_tomo_fs, srad, step, init_cen*4, ratio, drop)
else:
init_cen = _search_coarse(_tomo_cs, smin, smax, ratio, drop)
fine_cen = _search_fine(_tomo_fs, srad, step, init_cen, ratio, drop)
logger.debug('Rotation center search finished: %i', fine_cen)
return fine_cen
def normalize(arr, flat, dark, cutoff=None, ncore=None, out=None):
"""
Normalize raw projection data using the flat and dark field projections.
Parameters
----------
arr : ndarray
3D stack of projections.
flat : ndarray
3D flat field data.
dark : ndarray
3D dark field data.
cutoff : float, optional
Permitted maximum vaue for the normalized data.
ncore : int, optional
Number of cores that will be assigned to jobs.
out : ndarray, optional
Output array for result. If same as arr, process will be done in-place.
Returns
-------
ndarray
Normalized 3D tomographic data.
"""
arr = dtype.as_float32(arr)
flat = dtype.as_float32(flat)
dark = dtype.as_float32(dark)
flat = flat.mean(axis=0)
dark = dark.mean(axis=0)
arr = mproc.distribute_jobs(arr,
func=_normalize,
args=(flat, dark, cutoff),
axis=0,
ncore=ncore,
nchunk=0,
out=out)
return arr
def normalize(tomo, flat, dark, cutoff=None, ncore=None, nchunk=None):
"""
Normalize raw projection data using the flat and dark field projections.
Parameters
----------
tomo : ndarray
3D tomographic data.
flat : ndarray
3D flat field data.
dark : ndarray
3D dark field data.
cutoff : float, optional
Permitted maximum vaue for the normalized data.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
Normalized 3D tomographic data.
"""
tomo = dtype.as_float32(tomo)
flat = dtype.as_float32(flat)
dark = dtype.as_float32(dark)
flat = flat.mean(axis=0)
dark = dark.mean(axis=0)
arr = mproc.distribute_jobs(
tomo,
func=_normalize,
args=(flat, dark, cutoff),
axis=0,
ncore=ncore,
nchunk=nchunk)
return arr
def remove_outlier1d(arr, dif, size=3, axis=0, ncore=None, out=None):
"""
Remove high intensity bright spots from an array, using a one-dimensional
median filter along the specified axis.
Parameters
----------
arr : ndarray
Input array.
dif : float
Expected difference value between outlier value and
the median value of the array.
size : int
Size of the median filter.
axis : int, optional
Axis along which median filtering is performed.
ncore : int, optional
Number of cores that will be assigned to jobs.
out : ndarray, optional
Output array for result. If same as arr, process
will be done in-place.
Returns
-------
ndarray
Corrected array.
"""
arr = dtype.as_float32(arr)
dif = np.float32(dif)
tmp = np.empty_like(arr)
other_axes = [i for i in range(arr.ndim) if i != axis]
largest = np.argmax([arr.shape[i] for i in other_axes])
lar_axis = other_axes[largest]
ncore, chnk_slices = mproc.get_ncore_slices(
arr.shape[lar_axis], ncore=ncore)
filt_size = [1]*arr.ndim
filt_size[axis] = size
with cf.ThreadPoolExecutor(ncore) as e:
slc = [slice(None)]*arr.ndim
for i in range(ncore):
slc[lar_axis] = chnk_slices[i]
e.submit(filters.median_filter, arr[slc], size=filt_size,
output=tmp[slc], mode='mirror')
with mproc.set_numexpr_threads(ncore):
out = ne.evaluate('where(arr-tmp>=dif,tmp,arr)', out=out)
return out
def normalize(tomo, flat, dark, cutoff=None, ncore=None, nchunk=None):
"""
Normalize raw projection data using the flat and dark field projections.
Parameters
----------
tomo : ndarray
3D tomographic data.
flat : ndarray
3D flat field data.
dark : ndarray
3D dark field data.
cutoff : float, optional
Permitted maximum vaue for the normalized data.
ncore : int, optional
Number of cores that will be assigned to jobs.
nchunk : int, optional
Chunk size for each core.
Returns
-------
ndarray
Normalized 3D tomographic data.
"""
tomo = dtype.as_float32(tomo)
flat = dtype.as_float32(flat)
dark = dtype.as_float32(dark)
flat = flat.mean(axis=0)
dark = dark.mean(axis=0)
arr = mproc.distribute_jobs(tomo,
func=_normalize,
args=(flat, dark, cutoff),
axis=0,
ncore=ncore,
nchunk=nchunk)
return arr
def remove_outlier(arr, dif, size=3, axis=0, ncore=None, out=None):
"""
Remove high intensity bright spots from a N-dimensional array by chunking
along the specified dimension, and performing (N-1)-dimensional median
filtering along the other dimensions.
Parameters
----------
arr : ndarray
Input array.
dif : float
Expected difference value between outlier value and
the median value of the array.
size : int
Size of the median filter.
axis : int, optional
Axis along which to chunk.
ncore : int, optional
Number of cores that will be assigned to jobs.
out : ndarray, optional
Output array for result. If same as arr, process
will be done in-place.
Returns
-------
ndarray
Corrected array.
"""
arr = dtype.as_float32(arr)
dif = np.float32(dif)
tmp = np.empty_like(arr)
ncore, chnk_slices = mproc.get_ncore_slices(arr.shape[axis], ncore=ncore)
filt_size = [size]*arr.ndim
filt_size[axis] = 1
with cf.ThreadPoolExecutor(ncore) as e:
slc = [slice(None)]*arr.ndim
for i in range(ncore):
slc[axis] = chnk_slices[i]
e.submit(filters.median_filter, arr[tuple(slc)], size=filt_size,
output=tmp[tuple(slc)])
with mproc.set_numexpr_threads(ncore):
out = ne.evaluate('where(arr-tmp>=dif,tmp,arr)', out=out)
return out
def find_center_vo(tomo, ind=None, smin=-40, smax=40, srad=10, step=1,
ratio=2., drop=20):
"""
Find rotation axis location using Nghia Vo's method. :cite:`Vo:14`.
Parameters
----------
tomo : ndarray
3D tomographic data.
ind : int, optional
Index of the slice to be used for reconstruction.
smin, smax : int, optional
Reference to the horizontal center of the sinogram.
srad : float, optional
Fine search radius.
step : float, optional
Step of fine searching.
ratio : float, optional
The ratio between the FOV of the camera and the size of object.
It's used to generate the mask.
drop : int, optional
Drop lines around vertical center of the mask.
Returns
-------
float
Rotation axis location.
"""
tomo = dtype.as_float32(tomo)
if ind is None:
ind = tomo.shape[1] // 2
_tomo = tomo[:, ind, :]
# Reduce noise by smooth filtering.
_tomo = ndimage.filters.gaussian_filter(_tomo, sigma=(3, 1))
# Coarse search for finiding the roataion center.
if _tomo.shape[0] * _tomo.shape[1] > 4e6: # If data is large (>2kx2k)
_tomo_coarse = downsample(tomo, level=2)[:, ind, :]
init_cen = _search_coarse(_tomo_coarse, smin, smax, ratio, drop)
else:
init_cen = _search_coarse(_tomo, smin, smax, ratio, drop)
# Fine search for finiding the roataion center.
fine_cen = _search_fine(_tomo, srad, step, init_cen*4, ratio, drop)
logger.debug('Rotation center search finished: %i', fine_cen)
return fine_cen
def minus_log(arr):
"""
In-place computation of the minus log of a given array.
Parameters
----------
arr : ndarray
3D stack of projections.
Returns
-------
none
"""
arr = dtype.as_float32(arr)
np.log(arr, arr) # in-place
np.negative(arr, arr) # in-place
def remove_outlier(arr, dif, size=3, axis=0, ncore=None, out=None):
"""
Remove high intensity bright spots from a 3D array along specified
dimension.
Parameters
----------
arr : ndarray
Input array.
dif : float
Expected difference value between outlier value and
the median value of the array.
size : int
Size of the median filter.
axis : int, optional
Axis along which median filtering is performed.
ncore : int, optional
Number of cores that will be assigned to jobs.
out : ndarray, optional
Output array for result. If same as arr, process will be done in-place.
Returns
-------
ndarray
Corrected array.
"""
arr = dtype.as_float32(arr)
dif = np.float32(dif)
tmp = np.empty_like(arr)
if ncore is None:
ncore = mproc.mp.cpu_count()
e = cf.ThreadPoolExecutor(ncore)
slc = [slice(None)]*len(arr.shape)
for i in range(arr.shape[axis]):
slc[axis] = i
e.submit(filters.median_filter, arr[slc], size=(size, size),
output=tmp[slc])
e.shutdown()
with mproc.set_numexpr_threads(ncore):
out = ne.evaluate('where(arr-tmp>=dif,tmp,arr)', out=out)
return out
def find_center_vo(tomo, ind=None, smin=-50, smax=50, srad=3,
tol=0.5, ratio=2., drop=20):
"""
Find rotation axis location using Nghia Vo's method. :cite:`Vo:14`.
Parameters
----------
tomo : ndarray
3D tomographic data.
ind : int, optional
Index of the slice to be used for reconstruction.
smin, smax : int, optional
Reference to the horizontal center of the sinogram.
srad : float, optional
Initial guess for the center.
tol : scalar, optional
Desired sub-pixel accuracy.
ratio : float, optional
The ratio between the size of object and FOV of the camera.
It's used to generate the mask.
drop : int, optional
Drop lines around vertical center of the mask.
Returns
-------
float
Rotation axis location.
Warning
-------
Not tested yet.
"""
tomo = dtype.as_float32(tomo)
if ind is None:
ind = tomo.shape[1] // 2
if init is None:
init = tomo.shape[2] // 2
# Reduce noise by smooth filtering.
tomo = ndimage.filters.gaussian_filter(tomo, sigma=(3, 1))
# Coarse search for finiding the roataion center.
init_cen = _search_coarse(tomo, smin, smax, ratio, drop)
# Fine search for finiding the roataion center.
return _search_fine(tomo, srad, step, init_cen, ratio, drop)
def normalize(arr, flat, dark, cutoff=None, ncore=None, out=None):
"""
Normalize raw projection data using the flat and dark field projections.
Parameters
----------
arr : ndarray
3D stack of projections.
flat : ndarray
3D flat field data.
dark : ndarray
3D dark field data.
cutoff : float, optional
Permitted maximum vaue for the normalized data.
ncore : int, optional
Number of cores that will be assigned to jobs.
out : ndarray, optional
Output array for result. If same as arr,
process will be done in-place.
Returns
-------
ndarray
Normalized 3D tomographic data.
"""
arr = dtype.as_float32(arr)
l = np.float32(1e-6)
flat = np.mean(flat, axis=0, dtype=np.float32)
dark = np.mean(dark, axis=0, dtype=np.float32)
with mproc.set_numexpr_threads(ncore):
#denom = ne.evaluate('flat-dark')
#ne.evaluate('where(denom<l,l,denom)', out=denom)
#out = ne.evaluate('arr-dark', out=out)
denom = flat - dark
denom[denom < l] = l
out = arr - dark
out[out < l] = l
out[:] /= denom
#ne.evaluate('out/denom', out=out, truediv=True)
if cutoff is not None:
cutoff = np.float32(cutoff)
out[out > cutoff] = cutoff
#ne.evaluate('where(out>cutoff,cutoff,out)', out=out)
return out
def gaussian_filter(arr, sigma=3, order=0, axis=0, ncore=None):
"""
Apply Gaussian filter to 3D array along specified axis.
Parameters
----------
arr : ndarray
Input array.
sigma : scalar or sequence of scalars
Standard deviation for Gaussian kernel. The standard deviations
of the Gaussian filter are given for each axis as a sequence, or
as a single number, in which case it is equal for all axes.
order : {0, 1, 2, 3} or sequence from same set, optional
Order of the filter along each axis is given as a sequence
of integers, or as a single number. An order of 0 corresponds
to convolution with a Gaussian kernel. An order of 1, 2, or 3
corresponds to convolution with the first, second or third
derivatives of a Gaussian. Higher order derivatives are not
implemented
axis : int, optional
Axis along which median filtering is performed.
ncore : int, optional
Number of cores that will be assigned to jobs.
Returns
-------
ndarray
3D array of same shape as input.
"""
arr = dtype.as_float32(arr)
out = np.empty_like(arr)
if ncore is None:
ncore = mproc.mp.cpu_count()
with cf.ThreadPoolExecutor(ncore) as e:
slc = [slice(None)] * arr.ndim
for i in range(arr.shape[axis]):
slc[axis] = i
e.submit(filters.gaussian_filter,
arr[tuple(slc)],
sigma,
order=order,
output=out[tuple(slc)])
return out
def remove_nan(arr, val=0.):
"""
Replace NaN values in array with a given value.
Parameters
----------
arr : ndarray
Input array.
val : float, optional
Values to be replaced with NaN values in array.
Returns
-------
ndarray
Corrected array.
"""
arr = dtype.as_float32(arr)
arr[np.isnan(arr)] = val
return arr
def remove_neg(arr, val=0.):
"""
Replace negative values in array with a given value.
Parameters
----------
arr : ndarray
Input array.
val : float, optional
Values to be replaced with negative values in array.
Returns
-------
ndarray
Corrected array.
"""
arr = dtype.as_float32(arr)
arr[arr < 0.0] = val
return arr
