def _optim_hparcel(feature, domain, graphs, nb_parcel, lamb=1., dmax=10.,
niter=5, initial_mask=None, chunksize=1.e5, verbose=0):
""" Core function of the heirrachical parcellation procedure.
Parameters
----------
feature: list of subject-related feature arrays
Pa : parcellation instance that is updated
graphs: graph that represents the topology of the parcellation
anat_coord: array of shape (nvox,3) space defining set of coordinates
nb_parcel: int
the number of desrired parcels
lamb=1.0: parameter to weight position
and feature impact on the algorithm
dmax = 10: locality parameter (in the space of anat_coord)
to limit surch volume (CPU save)
chunksize = int, optional
niter = 5: number of iterations in the algorithm
verbose=0: verbosity level
Returns
-------
U: list of arrays of length nsubj
subject-dependent parcellations
Proto_anat: array of shape (nvox) labelling of the common space
(template parcellation)
"""
nb_subj = len(feature)
# a1. perform a rough clustering of the data to make prototype
indiv_coord = np.array([domain.coord[initial_mask[:, s] > - 1]
for s in range(nb_subj)])
reduced_anat, reduced_feature = _reduce_and_concatenate(
indiv_coord, feature, chunksize)
_, labs, _ = kmeans(reduced_feature, nb_parcel, Labels=None, maxiter=10)
proto_anat = [np.mean(reduced_anat[labs == k], 0)
for k in range(nb_parcel)]
proto_anat = np.array(proto_anat)
proto = [np.mean(reduced_feature[labs == k], 0) for k in range(nb_parcel)]
proto = np.array(proto)
# a2. topological model of the parcellation
# group-level part
spatial_proto = Field(nb_parcel)
spatial_proto.set_field(proto_anat)
spatial_proto.voronoi_diagram(proto_anat, domain.coord)
spatial_proto.set_gaussian(proto_anat)
spatial_proto.normalize()
for git in range(niter):
LP = []
LPA = []
U = []
Energy = 0
for s in range(nb_subj):
# b.subject-specific instances of the model
# b.0 subject-specific information
Fs = feature[s]
lac = indiv_coord[s]
target = proto_anat.copy()
lseeds = np.zeros(nb_parcel, np.int)
aux = np.argsort(rand(nb_parcel))
toto = np.zeros(lac.shape[0])
for j in range(nb_parcel):
# b.1 speed-up :only take a small ball
i = aux[j]
dx = lac - target[i]
iz = np.nonzero(np.sum(dx ** 2, 1) < dmax ** 2)
iz = np.reshape(iz, np.size(iz))
if np.size(iz) == 0:
iz = np.array([np.argmin(np.sum(dx ** 2, 1))])
# b.2: anatomical constraints
lanat = np.reshape(lac[iz], (np.size(iz),
domain.coord.shape[1]))
pot = np.zeros(np.size(iz))
JM, rmin = _exclusion_map(i, spatial_proto, target, lanat)
pot[JM < 0] = np.inf
pot[JM >= 0] = - JM[JM >= 0]
# b.3: add feature discrepancy
df = Fs[iz] - proto[i]
df = np.reshape(df, (np.size(iz), proto.shape[1]))
pot += lamb * np.sum(df ** 2, 1)
# b.4: solution
if np.sum(np.isinf(pot)) == np.size(pot):
pot = np.sum(dx[iz] ** 2, 1)
sol = iz[np.argmin(pot)]
target[i] = lac[sol]
lseeds[i] = sol
toto[sol] = 1
if verbose > 1:
jm = _field_gradient_jac(spatial_proto, target)
print jm.min(), jm.max(), np.sum(toto > 0)
# c.subject-specific parcellation
g = graphs[s]
f = Field(g.V, g.edges, g.weights, Fs)
U.append(f.constrained_voronoi(lseeds))
Energy += np.sum((Fs - proto[U[-1]]) ** 2) / \
np.sum(initial_mask[:, s] > - 1)
# recompute the prototypes
# (average in subject s)
lproto = [np.mean(Fs[U[-1] == k], 0) for k in range(nb_parcel)]
lproto = np.array(lproto)
lproto_anat = np.array([np.mean(lac[U[-1] == k], 0)
for k in range(nb_parcel)])
LP.append(lproto)
LPA.append(lproto_anat)
# recompute the prototypes across subjects
proto_mem = proto.copy()
proto = np.mean(np.array(LP), 0)
proto_anat = np.mean(np.array(LPA), 0)
displ = np.sqrt(np.sum((proto_mem - proto) ** 2, 1).max())
if verbose:
print 'energy', Energy, 'displacement', displ
# recompute the topological model
spatial_proto.set_field(proto_anat)
spatial_proto.voronoi_diagram(proto_anat, domain.coord)
spatial_proto.set_gaussian(proto_anat)
spatial_proto.normalize()
if displ < 1.e-4 * dmax:
break
return U, proto_anat
def _optim_hparcel(feature,
domain,
graphs,
nb_parcel,
lamb=1.,
dmax=10.,
niter=5,
initial_mask=None,
chunksize=1.e5,
verbose=0):
""" Core function of the heirrachical parcellation procedure.
Parameters
----------
feature: list of subject-related feature arrays
Pa : parcellation instance that is updated
graphs: graph that represents the topology of the parcellation
anat_coord: array of shape (nvox,3) space defining set of coordinates
nb_parcel: int
the number of desrired parcels
lamb=1.0: parameter to weight position
and feature impact on the algorithm
dmax = 10: locality parameter (in the space of anat_coord)
to limit surch volume (CPU save)
chunksize = int, optional
niter = 5: number of iterations in the algorithm
verbose=0: verbosity level
Returns
-------
U: list of arrays of length nsubj
subject-dependent parcellations
Proto_anat: array of shape (nvox) labelling of the common space
(template parcellation)
"""
nb_subj = len(feature)
# a1. perform a rough clustering of the data to make prototype
indiv_coord = np.array(
[domain.coord[initial_mask[:, s] > -1] for s in range(nb_subj)])
reduced_anat, reduced_feature = _reduce_and_concatenate(
indiv_coord, feature, chunksize)
_, labs, _ = kmeans(reduced_feature, nb_parcel, Labels=None, maxiter=10)
proto_anat = [
np.mean(reduced_anat[labs == k], 0) for k in range(nb_parcel)
]
proto_anat = np.array(proto_anat)
proto = [np.mean(reduced_feature[labs == k], 0) for k in range(nb_parcel)]
proto = np.array(proto)
# a2. topological model of the parcellation
# group-level part
spatial_proto = Field(nb_parcel)
spatial_proto.set_field(proto_anat)
spatial_proto.voronoi_diagram(proto_anat, domain.coord)
spatial_proto.set_gaussian(proto_anat)
spatial_proto.normalize()
for git in range(niter):
LP = []
LPA = []
U = []
Energy = 0
for s in range(nb_subj):
# b.subject-specific instances of the model
# b.0 subject-specific information
Fs = feature[s]
lac = indiv_coord[s]
target = proto_anat.copy()
lseeds = np.zeros(nb_parcel, np.int)
aux = np.argsort(rand(nb_parcel))
toto = np.zeros(lac.shape[0])
for j in range(nb_parcel):
# b.1 speed-up :only take a small ball
i = aux[j]
dx = lac - target[i]
iz = np.nonzero(np.sum(dx**2, 1) < dmax**2)
iz = np.reshape(iz, np.size(iz))
if np.size(iz) == 0:
iz = np.array([np.argmin(np.sum(dx**2, 1))])
# b.2: anatomical constraints
lanat = np.reshape(lac[iz],
(np.size(iz), domain.coord.shape[1]))
pot = np.zeros(np.size(iz))
JM, rmin = _exclusion_map(i, spatial_proto, target, lanat)
pot[JM < 0] = np.inf
pot[JM >= 0] = -JM[JM >= 0]
# b.3: add feature discrepancy
df = Fs[iz] - proto[i]
df = np.reshape(df, (np.size(iz), proto.shape[1]))
pot += lamb * np.sum(df**2, 1)
# b.4: solution
if np.sum(np.isinf(pot)) == np.size(pot):
pot = np.sum(dx[iz]**2, 1)
sol = iz[np.argmin(pot)]
target[i] = lac[sol]
lseeds[i] = sol
toto[sol] = 1
if verbose > 1:
jm = _field_gradient_jac(spatial_proto, target)
print jm.min(), jm.max(), np.sum(toto > 0)
# c.subject-specific parcellation
g = graphs[s]
f = Field(g.V, g.edges, g.weights, Fs)
U.append(f.constrained_voronoi(lseeds))
Energy += np.sum((Fs - proto[U[-1]]) ** 2) / \
np.sum(initial_mask[:, s] > - 1)
# recompute the prototypes
# (average in subject s)
lproto = [np.mean(Fs[U[-1] == k], 0) for k in range(nb_parcel)]
lproto = np.array(lproto)
lproto_anat = np.array(
[np.mean(lac[U[-1] == k], 0) for k in range(nb_parcel)])
LP.append(lproto)
LPA.append(lproto_anat)
# recompute the prototypes across subjects
proto_mem = proto.copy()
proto = np.mean(np.array(LP), 0)
proto_anat = np.mean(np.array(LPA), 0)
displ = np.sqrt(np.sum((proto_mem - proto)**2, 1).max())
if verbose:
print 'energy', Energy, 'displacement', displ
# recompute the topological model
spatial_proto.set_field(proto_anat)
spatial_proto.voronoi_diagram(proto_anat, domain.coord)
spatial_proto.set_gaussian(proto_anat)
spatial_proto.normalize()
if displ < 1.e-4 * dmax:
break
return U, proto_anat
