def __init__(self,
acquisition_scheme,
model,
x0_vector=None,
sh_order=8,
unity_constraint=True,
lambda_lb=0.):
self.model = model
self.acquisition_scheme = acquisition_scheme
self.sh_order = sh_order
self.Ncoef = int((sh_order + 2) * (sh_order + 1) // 2)
self.Nmodels = len(self.model.models)
self.lambda_lb = lambda_lb
self.unity_constraint = unity_constraint
self.sphere_jacobian = 2 * np.sqrt(np.pi)
sphere = get_sphere('symmetric724')
hemisphere = HemiSphere(phi=sphere.phi, theta=sphere.theta)
self.L_positivity = real_sym_sh_mrtrix(self.sh_order, hemisphere.theta,
hemisphere.phi)[0]
x0_single_voxel = np.reshape(x0_vector, (-1, x0_vector.shape[-1]))[0]
if np.all(np.isnan(x0_single_voxel)):
self.single_convolution_kernel = True
self.A = self._construct_convolution_kernel(x0_single_voxel)
else:
self.single_convolution_kernel = False
self.Ncoef_total = 0
vf_array = []
if self.model.volume_fractions_fixed:
self.sh_start = 0
self.Ncoef_total = self.Ncoef
self.vf_indices = np.array([0])
else:
for model in self.model.models:
if 'orientation' in model.parameter_types.values():
self.sh_start = self.Ncoef_total
sh_model = np.zeros(self.Ncoef)
sh_model[0] = 1
vf_array.append(sh_model)
self.Ncoef_total += self.Ncoef
else:
vf_array.append(1)
self.Ncoef_total += 1
self.vf_indices = np.where(np.hstack(vf_array))[0]
sh_l = sph_harm_ind_list(sh_order)[1]
lb_weights = sh_l**2 * (sh_l + 1)**2 # laplace-beltrami
if self.model.volume_fractions_fixed:
self.R_smoothness = np.diag(lb_weights)
else:
diagonal = np.zeros(self.Ncoef_total)
diagonal[self.sh_start:self.sh_start + self.Ncoef] = lb_weights
self.R_smoothness = np.diag(diagonal)
def __init__(self,
acquisition_scheme,
model,
x0_vector=None,
sh_order=8,
lambda_pos=1.,
lambda_lb=5e-4,
tau=0.1,
max_iter=50,
unity_constraint=True,
init_sh_order=4):
self.model = model
self.acquisition_scheme = acquisition_scheme
self.sh_order = sh_order
self.Ncoef = int((sh_order + 2) * (sh_order + 1) // 2)
self.Ncoef4 = int((init_sh_order + 2) * (init_sh_order + 1) // 2)
self.Nmodels = len(self.model.models)
self.lambda_pos = lambda_pos
self.lambda_lb = lambda_lb
self.tau = tau
self.max_iter = max_iter
self.unity_constraint = unity_constraint
self.sphere_jacobian = 1 / (2 * np.sqrt(np.pi))
# step 1: prepare positivity grid on sphere
sphere = get_sphere('symmetric724')
hemisphere = HemiSphere(phi=sphere.phi, theta=sphere.theta)
self.L_positivity = real_sym_sh_mrtrix(self.sh_order, hemisphere.theta,
hemisphere.phi)[0]
sh_l = sph_harm_ind_list(sh_order)[1]
self.R_smoothness = np.diag(sh_l**2 * (sh_l + 1)**2)
# check if there is only one model. If so, precompute rh array.
if self.model.volume_fractions_fixed:
x0_single_voxel = np.reshape(x0_vector,
(-1, x0_vector.shape[-1]))[0]
if np.all(np.isnan(x0_single_voxel)):
self.single_convolution_kernel = True
parameters_dict = self.model.parameter_vector_to_parameters(
x0_single_voxel)
self.A = self.model._construct_convolution_kernel(
**parameters_dict)
self.AT_A = np.dot(self.A.T, self.A)
else:
self.single_convolution_kernel = False
else:
msg = "This CSD optimizer cannot estimate volume fractions."
raise ValueError(msg)
def __init__(self,
acquisition_scheme,
model,
x0_vector=None,
sh_order=8,
unity_constraint=True):
self.model = model
self.acquisition_scheme = acquisition_scheme
self.sh_order = sh_order
self.Ncoef = int((sh_order + 2) * (sh_order + 1) // 2)
self.Nmodels = len(self.model.models)
self.unity_constraint = unity_constraint
# step 1: prepare positivity grid on sphere
sphere = get_sphere('symmetric724')
hemisphere = HemiSphere(phi=sphere.phi, theta=sphere.theta)
self.sh_matrix_positivity = real_sym_sh_mrtrix(self.sh_order,
hemisphere.theta,
hemisphere.phi)[0]
# check if there is only one model. If so, precompute rh array.
if self.Nmodels == 1:
# also needs to check if x0 is not changing.
self.prepared_computation = True
x0_shape = x0_vector.shape
x0_dummy = np.reshape(x0_vector, (-1, x0_shape[-1]))[0]
rh_matrix = self.recover_rotational_harmonics(x0_dummy)[0]
self.prepared_rh_coef = np.zeros([rh_matrix.shape[0], self.Ncoef])
for i, shell_index in enumerate(
acquisition_scheme.unique_dwi_indices):
rh_order = int(acquisition_scheme.shell_sh_orders[shell_index])
prepared_rh_shell = self.prepare_rotational_harmonics(
rh_matrix[i], rh_order)
if sh_order >= rh_order:
self.prepared_rh_coef[i, :len(prepared_rh_shell)] = (
prepared_rh_shell)
else:
self.prepared_rh_coef[i] = prepared_rh_shell[:self.Ncoef]
else:
self.prepared_computation = False
from __future__ import division
import pkg_resources
from os.path import join
import numpy as np
from scipy import stats
from scipy import special
from dipy.reconst.shm import real_sym_sh_mrtrix
from dmipy.utils import utils
from scipy import interpolate
from dmipy.core.modeling_framework import ModelProperties
from dipy.utils.optpkg import optional_package
from dipy.data import get_sphere, HemiSphere
sphere = get_sphere('symmetric724')
hemisphere = HemiSphere(phi=sphere.phi, theta=sphere.theta)
numba, have_numba, _ = optional_package("numba")
GRADIENT_TABLES_PATH = pkg_resources.resource_filename('dmipy',
'data/gradient_tables')
SIGNAL_MODELS_PATH = pkg_resources.resource_filename('dmipy', 'signal_models')
DATA_PATH = pkg_resources.resource_filename('dmipy', 'data')
SPHERE_CARTESIAN = np.loadtxt(join(GRADIENT_TABLES_PATH,
'sphere_with_cap.txt'))
SPHERE_SPHERICAL = utils.cart2sphere(SPHERE_CARTESIAN)
log_bingham_normalization_splinefit = np.load(join(
DATA_PATH, "bingham_normalization_splinefit.npz"),
encoding='bytes')['arr_0']
inverse_sh_matrix_kernel = {
def main():
parser = _build_args_parser()
args = parser.parse_args()
if args.isVerbose:
logging.basicConfig(level=logging.DEBUG)
assert_inputs_exist(parser, [
args.sh_file, args.seed_file, args.map_include_file,
args.map_exclude_file
])
assert_outputs_exist(parser, args, [args.output_file])
if not nib.streamlines.is_supported(args.output_file):
parser.error('Invalid output streamline file format (must be trk or ' +
'tck): {0}'.format(args.output_file))
if not args.min_length > 0:
parser.error('minL must be > 0, {}mm was provided.'.format(
args.min_length))
if args.max_length < args.min_length:
parser.error(
'maxL must be > than minL, (minL={}mm, maxL={}mm).'.format(
args.min_length, args.max_length))
if args.compress:
if args.compress < 0.001 or args.compress > 1:
logging.warning(
'You are using an error rate of {}.\nWe recommend setting it '
'between 0.001 and 1.\n0.001 will do almost nothing to the '
'tracts while 1 will higly compress/linearize the tracts'.
format(args.compress))
if args.particles <= 0:
parser.error('--particles must be >= 1.')
if args.back_tracking <= 0:
parser.error('PFT backtracking distance must be > 0.')
if args.forward_tracking <= 0:
parser.error('PFT forward tracking distance must be > 0.')
if args.npv and args.npv <= 0:
parser.error('Number of seeds per voxel must be > 0.')
if args.nt and args.nt <= 0:
parser.error('Total number of seeds must be > 0.')
fodf_sh_img = nib.load(args.sh_file)
fodf_sh_img = nib.load(args.sh_file)
if not np.allclose(np.mean(fodf_sh_img.header.get_zooms()[:3]),
fodf_sh_img.header.get_zooms()[0],
atol=1.e-3):
parser.error(
'SH file is not isotropic. Tracking cannot be ran robustly.')
tracking_sphere = HemiSphere.from_sphere(get_sphere('repulsion724'))
# Check if sphere is unit, since we couldn't find such check in Dipy.
if not np.allclose(np.linalg.norm(tracking_sphere.vertices, axis=1), 1.):
raise RuntimeError('Tracking sphere should be unit normed.')
sh_basis = args.sh_basis
if args.algo == 'det':
dgklass = DeterministicMaximumDirectionGetter
else:
dgklass = ProbabilisticDirectionGetter
theta = get_theta(args.theta, args.algo)
# Reminder for the future:
# pmf_threshold == clip pmf under this
# relative_peak_threshold is for initial directions filtering
# min_separation_angle is the initial separation angle for peak extraction
dg = dgklass.from_shcoeff(fodf_sh_img.get_data().astype(np.double),
max_angle=theta,
sphere=tracking_sphere,
basis_type=sh_basis,
pmf_threshold=args.sf_threshold,
relative_peak_threshold=args.sf_threshold_init)
map_include_img = nib.load(args.map_include_file)
map_exclude_img = nib.load(args.map_exclude_file)
voxel_size = np.average(map_include_img.get_header()['pixdim'][1:4])
tissue_classifier = None
if not args.act:
tissue_classifier = CmcTissueClassifier(map_include_img.get_data(),
map_exclude_img.get_data(),
step_size=args.step_size,
average_voxel_size=voxel_size)
else:
tissue_classifier = ActTissueClassifier(map_include_img.get_data(),
map_exclude_img.get_data())
if args.npv:
nb_seeds = args.npv
seed_per_vox = True
elif args.nt:
nb_seeds = args.nt
seed_per_vox = False
else:
nb_seeds = 1
seed_per_vox = True
voxel_size = fodf_sh_img.header.get_zooms()[0]
vox_step_size = args.step_size / voxel_size
seed_img = nib.load(args.seed_file)
seeds = track_utils.random_seeds_from_mask(
seed_img.get_data(),
seeds_count=nb_seeds,
seed_count_per_voxel=seed_per_vox,
random_seed=args.seed)
# Note that max steps is used once for the forward pass, and
# once for the backwards. This doesn't, in fact, control the real
# max length
max_steps = int(args.max_length / args.step_size) + 1
pft_streamlines = ParticleFilteringTracking(
dg,
tissue_classifier,
seeds,
np.eye(4),
max_cross=1,
step_size=vox_step_size,
maxlen=max_steps,
pft_back_tracking_dist=args.back_tracking,
pft_front_tracking_dist=args.forward_tracking,
particle_count=args.particles,
return_all=args.keep_all,
random_seed=args.seed)
scaled_min_length = args.min_length / voxel_size
scaled_max_length = args.max_length / voxel_size
filtered_streamlines = (
s for s in pft_streamlines
if scaled_min_length <= length(s) <= scaled_max_length)
if args.compress:
filtered_streamlines = (compress_streamlines(s, args.compress)
for s in filtered_streamlines)
tractogram = LazyTractogram(lambda: filtered_streamlines,
affine_to_rasmm=seed_img.affine)
filetype = nib.streamlines.detect_format(args.output_file)
header = create_header_from_anat(seed_img, base_filetype=filetype)
# Use generator to save the streamlines on-the-fly
nib.streamlines.save(tractogram, args.output_file, header=header)
def white_matter_response_tournier13(acquisition_scheme,
data,
max_iter=5,
sh_order=10,
N_candidate_voxels=300,
peak_ratio_setting='mrtrix'):
"""
Iterative model-free white matter response function estimation according to
[1]_. Quoting the paper, the steps are the following:
- 1) The 300 brain voxels with the highest FA were identified within a
brain mask (eroded by three voxels to remove any noisy voxels at the
brain edges).
- 2) The single-fibre 'response function' was estimated within these
voxels, and used to compute the fibre orientation distribution (FOD)
employing constrained spherical deconvolution (CSD) up to lmax = 10.
- 3) Within each voxel, a peak-finding procedure was used to identify the
two largest FOD peaks, and their amplitude ratio was computed.
- 4) The 300 voxels with the lowest second to first peak amplitude ratios
were identified, and used as the current estimate of the set of
'single-fibre' voxels. It should be noted that these voxels were not
required to be a subset of the original set of 'single-fibre' voxels.
- 5) To ensure minimal bias from the initial estimate of the 'response
function', steps (2) to (4) were re-iterated until convergence (no
difference in the set of 'single-fibre' voxels). It should be noted
that, in practice, convergence was achieved within a single iteration
in all cases.
Parameters
----------
acquisition_scheme : DmipyAcquisitionScheme instance,
An acquisition scheme that has been instantiated using dMipy.
data : NDarray,
Measured diffusion signal array.
max_iter : Positive integer,
Defines the maximum amount of iterations to be done for the single-
fibre response kernel.
sh_order : Positive even integer,
Maximum spherical harmonics order to be used in the FOD estimation for
the single-fibre response kernel.
N_candidate_voxels : integer,
Number of voxels to be included in the final white matter response
estimation. Default is 300 following [1]_.
peak_ratio_setting : string,
Can be either 'ratio' or 'mrtrix', meaning the 'ratio' parameter
between two peaks is actually calculated as the ratio, or a more
complicated version as 1 / sqrt(peak1 * (1 - peak2 / peak1)) ** 2, to
avoid favouring small, yet low SNR FODs [2]_.
Returns
-------
S0_wm : positive float,
Estimated S0 tissue response value.
TR2_wm_model : Dmipy Anisotropic ModelFree Model
ModelFree representation of white matter response.
selected_indices : array of size (N_candidate_voxels,),
indices of selected voxels for white matter response.
References
----------
.. [1] Tournier, J-Donald, Fernando Calamante, and Alan Connelly.
"Determination of the appropriate b value and number of gradient
directions for high-angular-resolution diffusion-weighted imaging."
NMR in Biomedicine 26.12 (2013): 1775-1786.
.. [2] MRtrix 3.0 readthedocs
"""
data_shape = np.atleast_2d(data).shape
N_voxels = int(np.prod(data_shape[:-1]))
if N_voxels < N_candidate_voxels:
msg = "The parameter N_candidate voxels is set to {} but only ".format(
N_candidate_voxels)
msg += "{} voxels are given. N_candidate_voxels".format(N_voxels)
msg += " reset to number of voxels given."
print(msg)
N_candidate_voxels = N_voxels
ratio_settings = ['ratio', 'mrtrix']
if peak_ratio_setting not in ratio_settings:
msg = 'peak_ratio_setting must be in {}'.format(ratio_settings)
raise ValueError(msg)
if data.ndim == 4:
# calculate brain mask on 4D data (x, y, z, DWI)
b0_mask, mask = median_otsu(data, 2, 1)
# needs to be eroded 3 times.
mask_eroded = binary_erosion(mask, iterations=3)
data_to_fit = data[mask_eroded]
else:
# can't calculate brain mask on other than 4D data.
# assume the data was prepared.
data_to_fit = data.reshape([-1, data_shape[-1]])
gtab = gtab_dmipy2dipy(acquisition_scheme)
tenmod = dti.TensorModel(gtab)
tenfit = tenmod.fit(data_to_fit)
fa = tenfit.fa
# selected based on FA
selected_indices = np.argsort(fa)[-N_candidate_voxels:]
sphere = get_sphere('symmetric724')
hemisphere = HemiSphere(theta=sphere.theta, phi=sphere.phi)
# iterate until convergence
it = 0
while True:
print('Tournier13 white matter response iteration {}'.format(it + 1))
selected_data = data_to_fit[selected_indices]
S0_wm, TR2_wm_model = estimate_TR2_anisotropic_tissue_response_model(
acquisition_scheme, selected_data)
sh_model = MultiCompartmentSphericalHarmonicsModel([TR2_wm_model],
sh_order=sh_order)
sh_fit = sh_model.fit(acquisition_scheme,
data_to_fit,
solver='csd_tournier07',
use_parallel_processing=False,
lambda_lb=0.)
peaks, values, indices = sh_fit.peaks_directions(
hemisphere, max_peaks=2, relative_peak_threshold=0.)
if peak_ratio_setting == 'ratio':
ratio = values[..., 1] / values[..., 0]
elif peak_ratio_setting == 'mrtrix':
ratio = 1. / np.sqrt(values[..., 0] *
(1 - values[..., 1] / values[..., 0]))**2
selected_indices_old = selected_indices
selected_indices = np.argsort(ratio)[:N_candidate_voxels]
percentage_overlap = 100 * float(
len(np.intersect1d(selected_indices,
selected_indices_old))) / N_candidate_voxels
print('{:.1f} percent candidate voxel overlap.'.format(
percentage_overlap))
if percentage_overlap == 100.:
print('White matter response converged')
break
it += 1
if it > max_iter:
print('Maximum iterations reached without convergence')
break
return S0_wm, TR2_wm_model, selected_indices
