def get_spherical_harmonics_coefficients(dwi, bvals, bvecs, sh_order=8, smooth=0.006, first=False, mean_centering=True):
""" Compute coefficients of the spherical harmonics basis.
Parameters
-----------
dwi : `nibabel.NiftiImage` object
Diffusion signal as weighted images (4D).
bvals : ndarray shape (N,)
B-values used with each direction.
bvecs : ndarray shape (N, 3)
Directions of the diffusion signal. Directions are
assumed to be only on the hemisphere.
sh_order : int, optional
SH order. Default: 8
smooth : float, optional
Lambda-regularization in the SH fit. Default: 0.006.
mean_centering : bool
If True, signal will have zero mean in each direction for all nonzero voxels
Returns
-------
sh_coeffs : ndarray of shape (X, Y, Z, #coeffs)
Spherical harmonics coefficients at every voxel. The actual number of
coeffs depends on `sh_order`.
"""
bvals = np.asarray(bvals)
bvecs = np.asarray(bvecs)
dwi_weights = dwi.get_data().astype("float32")
# Exract the averaged b0.
b0_idx = bvals == 0
b0 = dwi_weights[..., b0_idx].mean(axis=3)
# Extract diffusion weights and normalize by the b0.
bvecs = bvecs[np.logical_not(b0_idx)]
weights = dwi_weights[..., np.logical_not(b0_idx)]
weights = normalize_dwi(weights, b0)
# Assuming all directions are on the hemisphere.
raw_sphere = HemiSphere(xyz=bvecs)
# Fit SH to signal
sph_harm_basis = sph_harm_lookup.get('mrtrix')
Ba, m, n = sph_harm_basis(sh_order, raw_sphere.theta, raw_sphere.phi)
L = -n * (n + 1)
invB = smooth_pinv(Ba, np.sqrt(smooth) * L)
data_sh = np.dot(weights, invB.T)
if mean_centering:
# Normalization in each direction (zero mean)
idx = data_sh.sum(axis=-1).nonzero()
means = data_sh[idx].mean(axis=0)
data_sh[idx] -= means
return data_sh
def displaySphericalHist(odf, pts, minmax=False):
# assumes pts and odf are hemisphere
fullsphere = HemiSphere(xyz=pts).mirror()
fullodf = np.concatenate((odf, odf), axis=0)
r = fvtk.ren()
if minmax:
a = fvtk.sphere_funcs(fullodf - fullodf.min(), fullsphere)
else:
a = fvtk.sphere_funcs(fullodf, fullsphere)
fvtk.add(r, a)
fvtk.show(r)
def create_repulsion_sphere(n_points, n_iter):
""" Create a sphere using electrostatic repulsion.
params:
npoints: number of points in the electrostatic repulsion
n_iter: number of iterations to optimise energy
return: HemiSphere object with n points vertices
"""
theta = np.pi * np.random.rand(n_points)
phi = 2 * np.pi * np.random.rand(n_points)
hsph_initial = HemiSphere(theta=theta, phi=phi)
hsph_updated, energy = disperse_charges(hsph_initial, iters=n_iter)
sph = hsph_updated
return sph
def create_symmetric_repulsion_sphere(n_points, n_iter):
"""
Create a full Sphere object using electrostatic repulsion.
params:
npoints: number of points in the electrostatic repulsion
n_iter: number of iterations to optimise energy
return: Sphere object with 2*npoints vertices
"""
theta = np.pi * np.random.rand(n_points)
phi = 2 * np.pi * np.random.rand(n_points)
hsph_initial = HemiSphere(theta=theta, phi=phi)
hsph_updated, energy = disperse_charges(hsph_initial, iters=n_iter)
sph = Sphere(xyz=np.vstack((hsph_updated.vertices,
-hsph_updated.vertices)))
return sph
def get_spherical_harmonics_coefficients(self,
dwi_weights,
bvals,
bvecs,
sh_order=8,
smooth=0.006):
""" Compute coefficients of the spherical harmonics basis.
Parameters
-----------
dwi_weights : `nibabel.NiftiImage` object
Diffusion signal as weighted images (4D).
bvals : ndarray shape (N,)
B-values used with each direction.
bvecs : ndarray shape (N, 3)
Directions of the diffusion signal. Directions are
assumed to be only on the hemisphere.
sh_order : int, optional
SH order. Default: 8
smooth : float, optional
Lambda-regularization in the SH fit. Default: 0.006.
Returns
-------
sh_coeffs : ndarray of shape (X, Y, Z, #coeffs)
Spherical harmonics coefficients at every voxel. The actual number of
coeffs depends on `sh_order`.
"""
# Exract the averaged b0.
b0_idx = bvals == 0
b0 = dwi_weights[..., b0_idx].mean(axis=3) + 1e-10
# Extract diffusion weights and normalize by the b0.
bvecs = bvecs[np.logical_not(b0_idx)]
weights = dwi_weights[..., np.logical_not(b0_idx)]
weights = self.normalize_dwi(weights, b0)
# Assuming all directions are on the hemisphere.
raw_sphere = HemiSphere(xyz=bvecs)
# Fit SH to signal
sph_harm_basis = sph_harm_lookup.get("tournier07")
Ba, m, n = sph_harm_basis(sh_order, raw_sphere.theta, raw_sphere.phi)
L = -n * (n + 1)
invB = smooth_pinv(Ba, np.sqrt(smooth) * L)
data_sh = np.dot(weights, invB.T)
return data_sh