def isolated(XYZ, k=18):
"""
Outputs an index I of isolated points from their integer coordinates,
XYZ (3, n), and under k-connectivity, k = 6, 18 or 26.
"""
label = wgraph_from_3d_grid(XYZ.T, k).cc()
# Isolated points
ncc = label.max() + 1
p = XYZ.shape[1]
size = np.zeros(ncc, float)
ones = np.ones((p, 1), float)
add_lines(ones, size.reshape(ncc, 1), label)
return np.where(size[label] == 1)[0]
def isolated(XYZ, k=18):
"""
Outputs an index I of isolated points from their integer coordinates,
XYZ (3, n), and under k-connectivity, k = 6, 18 or 26.
"""
label = wgraph_from_3d_grid(XYZ.T, k).cc()
# Isolated points
ncc = label.max() + 1
p = XYZ.shape[1]
size = np.zeros(ncc, float)
ones = np.ones((p, 1), float)
add_lines(ones, size.reshape(ncc, 1), label)
return np.where(size[label] == 1)[0]
def test_onesample_graph(self):
data, vardata, XYZ = make_data()
G = wgraph_from_3d_grid(XYZ.T)
# rfx calibration
P = pt.permutation_test_onesample_graph(data, G, ndraws=ndraws)
c = [(P.random_Tvalues[P.ndraws * (0.95)], None)]
r = np.ones(data.shape[1], int)
r[data.shape[1] / 2:] *= 10
# mfx calibration
P = pt.permutation_test_onesample_graph(
data, G, vardata=vardata, stat_id="student_mfx", ndraws=ndraws)
p_values, cluster_results, region_results = P.calibrate(
nperms=nperms, clusters=c, regions=[r])
def test_onesample_graph(self):
data, vardata, XYZ = make_data()
G = wgraph_from_3d_grid(XYZ.T)
# rfx calibration
P = pt.permutation_test_onesample_graph(data, G, ndraws=ndraws)
c = [(P.random_Tvalues[P.ndraws*(0.95)],None)]
r = np.ones(data.shape[1],int)
r[data.shape[1]/2:] *= 10
#p_values, cluster_results, region_results = P.calibrate(nperms=100, clusters=c, regions=[r])
# mfx calibration
P = pt.permutation_test_onesample_graph(
data, G, vardata=vardata, stat_id="student_mfx", ndraws=ndraws)
p_values, cluster_results, region_results = P.calibrate(
nperms=nperms, clusters=c, regions=[r])
def smatrix_from_3d_idx(ijk, nn=18):
"""Create a sparse adjacency matrix from 3d index system
Parameters
----------
idx:array of shape (n_samples, 3), type int
indexes of certain positions in a 3d space
nn: int, optional
3d neighboring system to be chosen within {6, 18, 26}
Returns
-------
coo_mat: a sparse coo matrix,
adjacency of the neighboring system
"""
G = wgraph_from_3d_grid(ijk, nn)
return G.to_coo_matrix()
def extract_clusters_from_thresh(T, XYZ, th, k=18):
"""
Extract clusters from statistical map
above specified threshold
In: T (p) statistical map
XYZ (3,p) voxels coordinates
th <float> threshold
k <int> the number of neighbours considered. (6,18 or 26)
Out: labels (p) cluster labels
"""
labels = -np.ones(len(T), int)
I = np.where(T >= th)[0]
if len(I) > 0:
SupraThreshXYZ = XYZ[:, I]
CC_label = wgraph_from_3d_grid(SupraThreshXYZ.T, k).cc()
labels[I] = CC_label
return labels
def extract_clusters_from_thresh(T, XYZ, th, k=18):
"""
Extract clusters from statistical map
above specified threshold
In: T (p) statistical map
XYZ (3,p) voxels coordinates
th <float> threshold
k <int> the number of neighbours considered. (6,18 or 26)
Out: labels (p) cluster labels
"""
labels = -np.ones(len(T), int)
I = np.where(T >= th)[0]
if len(I) > 0:
SupraThreshXYZ = XYZ[:, I]
CC_label = wgraph_from_3d_grid(SupraThreshXYZ.T, k).cc()
labels[I] = CC_label
return labels
def smatrix_from_3d_idx(ijk, nn=18):
"""Create a sparse adjacency matrix from 3d index system
Parameters
----------
idx:array of shape (n_samples, 3), type int
indexes of certain positions in a 3d space
nn: int, optional
3d neighboring system to be chosen within {6, 18, 26}
Returns
-------
coo_mat: a sparse coo matrix,
adjacency of the neighboring system
"""
G = wgraph_from_3d_grid(ijk, nn)
return G.to_coo_matrix()
def _extract_clusters_from_diam(labels, T, XYZ, th, diam, k, nCC, CClabels):
"""
This recursive function modifies the `labels` input array.
"""
clust_label = 0
for i in range(nCC):
# print "Searching connected component ", i, " out of ", nCC
I = np.where(CClabels == i)[0]
extCC = len(I)
if extCC <= (diam + 1) ** 3:
diamCC = max_dist(XYZ, I, I)
else:
diamCC = diam + 1
if diamCC <= diam:
labels[I] = np.zeros(extCC, int) + clust_label
# print "cluster ", clust_label, ", diam = ", diamCC
# print "ext = ", len(I), ", diam = ", max_dist(XYZ,I,I)
clust_label += 1
else:
# build the field
p = len(T[I])
F = field_from_graph_and_data(wgraph_from_3d_grid(XYZ[:, I].T, k), np.reshape(T[I], (p, 1)))
# compute the blobs
idx, parent, label = F.threshold_bifurcations(0, th)
nidx = np.size(idx)
height = np.array([np.ceil(np.sum(label == i) ** (1.0 / 3)) for i in np.arange(nidx)])
# root = nidx-1
root = np.where(np.arange(nidx) == parent)[0]
# Can constraint be met within current region?
Imin = I[T[I] >= height[root]]
extmin = len(Imin)
if extmin <= (diam + 1) ** 3:
dmin = max_dist(XYZ, Imin, Imin)
else:
dmin = diam + 1
if dmin <= diam: # If so, search for the largest cluster meeting the constraint
Iclust = Imin # Smallest cluster
J = I[T[I] < height[root]] # Remaining voxels
argsortTJ = np.argsort(T[J])[::-1] # Sorted by decreasing T values
l = 0
L = np.array([J[argsortTJ[l]]], int)
diameter = dmin
new_diameter = max(dmin, max_dist(XYZ, Iclust, L))
while new_diameter <= diam:
# print "diameter = " + str(new_diameter)
# sys.stdout.flush()
Iclust = np.concatenate((Iclust, L))
diameter = new_diameter
# print "diameter = ", diameter
l += 1
L = np.array([J[argsortTJ[l]]], int)
new_diameter = max(diameter, max_dist(XYZ, Iclust, L))
labels[Iclust] = np.zeros(len(Iclust), int) + clust_label
# print "cluster ", clust_label, ", diam = ", diameter
# print "ext = ", len(Iclust), ", diam = ", max_dist(XYZ,Iclust,Iclust)
clust_label += 1
else: # If not, search inside sub-regions
# print "Searching inside sub-regions "
Irest = I[T[I] > height[root]]
rest_labels = extract_clusters_from_diam(T[Irest], XYZ[:, Irest], th, diam, k)
rest_labels[rest_labels >= 0] += clust_label
clust_label = rest_labels.max() + 1
labels[Irest] = rest_labels
return labels
def extract_clusters_from_diam(T, XYZ, th, diam, k=18):
"""
Extract clusters from a statistical map
under diameter constraint
and above given threshold
In: T (p) statistical map
XYZ (3,p) voxels coordinates
th <float> minimum threshold
diam <int> maximal diameter (in voxels)
k <int> the number of neighbours considered. (6,18 or 26)
Out: labels (p) cluster labels
"""
CClabels = extract_clusters_from_thresh(T, XYZ, th, k)
nCC = CClabels.max() + 1
labels = -np.ones(len(CClabels), int)
clust_label = 0
for i in xrange(nCC):
#print "Searching connected component ", i, " out of ", nCC
I = np.where(CClabels == i)[0]
extCC = len(I)
if extCC <= (diam + 1)**3:
diamCC = max_dist(XYZ, I, I)
else:
diamCC = diam + 1
if diamCC <= diam:
labels[I] = np.zeros(extCC, int) + clust_label
#print "cluster ", clust_label, ", diam = ", diamCC
#print "ext = ", len(I), ", diam = ", max_dist(XYZ,I,I)
clust_label += 1
else:
# build the field
p = len(T[I])
F = field_from_graph_and_data(wgraph_from_3d_grid(XYZ[:, I].T, k),
np.reshape(T[I], (p, 1)))
# compute the blobs
idx, parent, label = F.threshold_bifurcations(0, th)
nidx = np.size(idx)
height = np.array([
np.ceil(np.sum(label == i)**(1. / 3)) for i in np.arange(nidx)
])
#root = nidx-1
root = np.where(np.arange(nidx) == parent)[0]
# Can constraint be met within current region?
Imin = I[T[I] >= height[root]]
extmin = len(Imin)
if extmin <= (diam + 1)**3:
dmin = max_dist(XYZ, Imin, Imin)
else:
dmin = diam + 1
if dmin <= diam: # If so, search for the largest cluster meeting the constraint
Iclust = Imin # Smallest cluster
J = I[T[I] < height[root]] # Remaining voxels
argsortTJ = np.argsort(
T[J])[::-1] # Sorted by decreasing T values
l = 0
L = np.array([J[argsortTJ[l]]], int)
diameter = dmin
new_diameter = max(dmin, max_dist(XYZ, Iclust, L))
while new_diameter <= diam:
#print "diameter = " + str(new_diameter)
#sys.stdout.flush()
Iclust = np.concatenate((Iclust, L))
diameter = new_diameter
#print "diameter = ", diameter
l += 1
L = np.array([J[argsortTJ[l]]], int)
new_diameter = max(diameter, max_dist(XYZ, Iclust, L))
labels[Iclust] = np.zeros(len(Iclust), int) + clust_label
#print "cluster ", clust_label, ", diam = ", diameter
#print "ext = ", len(Iclust), ", diam = ", max_dist(XYZ,Iclust,Iclust)
clust_label += 1
else: # If not, search inside sub-regions
#print "Searching inside sub-regions "
Irest = I[T[I] > height[root]]
rest_labels = extract_clusters_from_diam(
T[Irest], XYZ[:, Irest], th, diam, k)
rest_labels[rest_labels >= 0] += clust_label
clust_label = rest_labels.max() + 1
labels[Irest] = rest_labels
return labels
def _extract_clusters_from_diam(labels, T, XYZ, th, diam, k,
nCC, CClabels):
"""
This recursive function modifies the `labels` input array.
"""
clust_label = 0
for i in range(nCC):
#print "Searching connected component ", i, " out of ", nCC
I = np.where(CClabels==i)[0]
extCC = len(I)
if extCC <= (diam+1)**3:
diamCC = max_dist(XYZ,I,I)
else:
diamCC = diam+1
if diamCC <= diam:
labels[I] = np.zeros(extCC,int) + clust_label
#print "cluster ", clust_label, ", diam = ", diamCC
#print "ext = ", len(I), ", diam = ", max_dist(XYZ,I,I)
clust_label += 1
else:
# build the field
p = len(T[I])
F = field_from_graph_and_data(
wgraph_from_3d_grid(XYZ[:, I].T, k), np.reshape(T[I],(p,1)))
# compute the blobs
idx, parent,label = F.threshold_bifurcations(0,th)
nidx = np.size(idx)
height = np.array([np.ceil(np.sum(label == i) ** (1./3))
for i in np.arange(nidx)])
#root = nidx-1
root = np.where(np.arange(nidx)==parent)[0]
# Can constraint be met within current region?
Imin = I[T[I]>=height[root]]
extmin = len(Imin)
if extmin <= (diam+1)**3:
dmin = max_dist(XYZ,Imin,Imin)
else:
dmin = diam+1
if dmin <= diam:# If so, search for the largest cluster meeting the constraint
Iclust = Imin # Smallest cluster
J = I[T[I]<height[root]] # Remaining voxels
argsortTJ = np.argsort(T[J])[::-1] # Sorted by decreasing T values
l = 0
L = np.array([J[argsortTJ[l]]],int)
diameter = dmin
new_diameter = max(dmin,max_dist(XYZ,Iclust,L))
while new_diameter <= diam:
#print "diameter = " + str(new_diameter)
#sys.stdout.flush()
Iclust = np.concatenate((Iclust,L))
diameter = new_diameter
#print "diameter = ", diameter
l += 1
L = np.array([J[argsortTJ[l]]],int)
new_diameter = max(diameter,max_dist(XYZ,Iclust,L))
labels[Iclust] = np.zeros(len(Iclust),int) + clust_label
#print "cluster ", clust_label, ", diam = ", diameter
#print "ext = ", len(Iclust), ", diam = ", max_dist(XYZ,Iclust,Iclust)
clust_label += 1
else:# If not, search inside sub-regions
#print "Searching inside sub-regions "
Irest = I[T[I]>height[root]]
rest_labels = extract_clusters_from_diam(T[Irest],XYZ[:,Irest],th,diam,k)
rest_labels[rest_labels>=0] += clust_label
clust_label = rest_labels.max() + 1
labels[Irest] = rest_labels
return labels
def extract_clusters_from_diam(T,XYZ,th,diam,k=18):
"""
Extract clusters from a statistical map
under diameter constraint
and above given threshold
In: T (p) statistical map
XYZ (3,p) voxels coordinates
th <float> minimum threshold
diam <int> maximal diameter (in voxels)
k <int> the number of neighbours considered. (6,18 or 26)
Out: labels (p) cluster labels
"""
CClabels = extract_clusters_from_thresh(T,XYZ,th,k)
nCC = CClabels.max() + 1
labels = -np.ones(len(CClabels),int)
clust_label = 0
for i in xrange(nCC):
#print "Searching connected component ", i, " out of ", nCC
I = np.where(CClabels==i)[0]
extCC = len(I)
if extCC <= (diam+1)**3:
diamCC = max_dist(XYZ,I,I)
else:
diamCC = diam+1
if diamCC <= diam:
labels[I] = np.zeros(extCC,int) + clust_label
#print "cluster ", clust_label, ", diam = ", diamCC
#print "ext = ", len(I), ", diam = ", max_dist(XYZ,I,I)
clust_label += 1
else:
# build the field
p = len(T[I])
F = field_from_graph_and_data(
wgraph_from_3d_grid(XYZ[:, I].T, k), np.reshape(T[I],(p,1)))
# compute the blobs
idx, parent,label = F.threshold_bifurcations(0,th)
nidx = np.size(idx)
height = np.array([np.ceil(np.sum(label == i) ** (1./3))
for i in np.arange(nidx)])
#root = nidx-1
root = np.where(np.arange(nidx)==parent)[0]
# Can constraint be met within current region?
Imin = I[T[I]>=height[root]]
extmin = len(Imin)
if extmin <= (diam+1)**3:
dmin = max_dist(XYZ,Imin,Imin)
else:
dmin = diam+1
if dmin <= diam:# If so, search for the largest cluster meeting the constraint
Iclust = Imin # Smallest cluster
J = I[T[I]<height[root]] # Remaining voxels
argsortTJ = np.argsort(T[J])[::-1] # Sorted by decreasing T values
l = 0
L = np.array([J[argsortTJ[l]]],int)
diameter = dmin
new_diameter = max(dmin,max_dist(XYZ,Iclust,L))
while new_diameter <= diam:
#print "diameter = " + str(new_diameter)
#sys.stdout.flush()
Iclust = np.concatenate((Iclust,L))
diameter = new_diameter
#print "diameter = ", diameter
l += 1
L = np.array([J[argsortTJ[l]]],int)
new_diameter = max(diameter,max_dist(XYZ,Iclust,L))
labels[Iclust] = np.zeros(len(Iclust),int) + clust_label
#print "cluster ", clust_label, ", diam = ", diameter
#print "ext = ", len(Iclust), ", diam = ", max_dist(XYZ,Iclust,Iclust)
clust_label += 1
else:# If not, search inside sub-regions
#print "Searching inside sub-regions "
Irest = I[T[I]>height[root]]
rest_labels = extract_clusters_from_diam(T[Irest],XYZ[:,Irest],th,diam,k)
rest_labels[rest_labels>=0] += clust_label
clust_label = rest_labels.max() + 1
labels[Irest] = rest_labels
return labels
