def _sort_eigensystem(parameters_dict):
"""Sort the eigensystem of the Tensor parameterized by eigen values and vectors.
Args:
parameters_dict (dict): the results from optimization. This expects each value to be a (n, ...) array with
for each voxel either a scalar or a vector.
Returns:
tuple: the sorted eigenvalues,
"""
eigenvectors = np.stack(tensor_spherical_to_cartesian(np.squeeze(parameters_dict['theta']),
np.squeeze(parameters_dict['phi']),
np.squeeze(parameters_dict['psi'])), axis=0)
eigenvalues = np.atleast_2d(np.squeeze(np.dstack([parameters_dict['d'],
parameters_dict['dperp0'],
parameters_dict['dperp1']])))
ranking = np.atleast_2d(np.squeeze(np.argsort(eigenvalues, axis=1, kind='mergesort')[:, ::-1]))
voxels_range = np.arange(ranking.shape[0])
sorted_eigenvalues = np.concatenate([eigenvalues[voxels_range, ranking[:, ind], None]
for ind in range(ranking.shape[1])], axis=1)
sorted_eigenvectors = np.stack([eigenvectors[ranking[:, ind], voxels_range, :]
for ind in range(ranking.shape[1])])
return sorted_eigenvalues, sorted_eigenvectors, ranking
def extra_optimization_maps(results, input_data=None):
"""Return some interesting measures like FA, MD, RD and AD.
This function is meant to be used as a post processing routine in Tensor-like compartment models.
Args:
results (dict): Dictionary containing at least theta, phi, psi, d, dperp0 and dperp1
We will use this to generate some standard measures from the diffusion Tensor.
input_data (mdt.utils.MRIInputData): optionally, the input data used during the model fitting.
Returns:
dict: as keys typical elements like 'FA and 'MD' as interesting output and as per values the maps.
These maps are per voxel, and optionally per instance per voxel
"""
output = {
'FA':
DTIMeasures.fractional_anisotropy(results['d'], results['dperp0'],
results['dperp1']),
'MD': (results['d'] + results['dperp0'] + results['dperp1']) / 3.,
'AD':
results['d'],
'RD': (results['dperp0'] + results['dperp1']) / 2.0,
}
if all('{}.std'.format(el) in results
for el in ['d', 'dperp0', 'dperp1']):
output.update({
'FA.std':
DTIMeasures.fractional_anisotropy_std(results['d'],
results['dperp0'],
results['dperp1'],
results['d.std'],
results['dperp0.std'],
results['dperp1.std'],
covariances=results.get(
'covariances',
None)),
'MD.std':
np.sqrt(results['d.std'] + results['dperp0.std'] +
results['dperp1.std']) / 3.,
'AD.std':
results['d.std'],
'RD.std':
(results['dperp0.std'] + results['dperp1.std']) / 2.0,
})
if all(el in results for el in ['theta', 'phi', 'psi']):
eigenvectors = tensor_spherical_to_cartesian(
np.squeeze(results['theta']), np.squeeze(results['phi']),
np.squeeze(results['psi']))
for ind in range(3):
output.update({'vec{}'.format(ind): eigenvectors[ind]})
return output
def sort_eigensystem(parameters_dict):
eigenvectors = np.stack(tensor_spherical_to_cartesian(np.squeeze(parameters_dict['theta']),
np.squeeze(parameters_dict['phi']),
np.squeeze(parameters_dict['psi'])), axis=0)
eigenvalues = np.atleast_2d(np.squeeze(np.dstack([parameters_dict['d'],
parameters_dict['dperp0'],
parameters_dict['dperp1']])))
ranking = np.atleast_2d(np.squeeze(np.argsort(eigenvalues, axis=1, kind='mergesort')[:, ::-1]))
voxels_range = np.arange(ranking.shape[0])
sorted_eigenvalues = np.concatenate([eigenvalues[voxels_range, ranking[:, ind], None]
for ind in range(ranking.shape[1])], axis=1)
sorted_eigenvectors = np.stack([eigenvectors[ranking[:, ind], voxels_range, :]
for ind in range(ranking.shape[1])])
return sorted_eigenvalues, sorted_eigenvectors, ranking
def extra_optimization_maps(results):
"""Return some interesting measures like FA, MD, RD and AD.
Args:
results (dict): Dictionary containing at least theta, phi, psi, d, dperp0 and dperp1
We will use this to generate some standard measures from the diffusion Tensor.
Returns:
dict: as keys typical elements like 'FA and 'MD' as interesting output and as per values the maps.
These maps are per voxel, and optionally per instance per voxel
"""
output = {
'FA': DTIMeasures.fractional_anisotropy(results['d'], results['dperp0'], results['dperp1']),
'MD': (results['d'] + results['dperp0'] + results['dperp1']) / 3.,
'AD': results['d'],
'RD': (results['dperp0'] + results['dperp1']) / 2.0,
}
if all('{}.std'.format(el) in results for el in ['d', 'dperp0', 'dperp1']):
output.update({
'FA.std': DTIMeasures.fractional_anisotropy_std(
results['d'], results['dperp0'], results['dperp1'],
results['d.std'], results['dperp0.std'], results['dperp1.std']),
'MD.std': np.sqrt(results['d.std'] + results['dperp0.std'] + results['dperp1.std']) / 3.,
'AD.std': results['d.std'],
'RD.std': (results['dperp0.std'] + results['dperp1.std']) / 2.0,
})
if all(el in results for el in ['theta', 'phi', 'psi']):
eigenvectors = tensor_spherical_to_cartesian(np.squeeze(results['theta']),
np.squeeze(results['phi']),
np.squeeze(results['psi']))
for ind in range(3):
output.update({'vec{}'.format(ind): eigenvectors[ind]})
return output