def spectrum_of_largest(points,
faces,
spectrum_size=10,
exclude_labels=[-1],
normalization="areaindex",
areas=None,
verbose=False):
"""
Compute Laplace-Beltrami spectrum on largest connected segment.
In case a surface patch is fragmented, we select the largest fragment,
remove extraneous triangular faces, and reindex indices.
Parameters
----------
points : list of lists of 3 floats
x,y,z coordinates for each vertex of the structure
faces : list of lists of 3 integers
3 indices to vertices that form a triangle on the mesh
spectrum_size : integer
number of eigenvalues to be computed (the length of the spectrum)
exclude_labels : list of integers
background values to exclude
normalization : string
the method used to normalize eigenvalues
if None, no normalization is used
if "area", use area of the 2D structure as in Reuter et al. 2006
if "index", divide eigenvalue by index to account for linear trend
if "areaindex", do both (default)
areas : numpy array or list of floats (or None)
surface area scalar values for all vertices
verbose : bool
print statements?
Returns
-------
spectrum : list
first spectrum_size eigenvalues for Laplace-Beltrami spectrum
Examples
--------
>>> # Spectrum for left postcentral + pars triangularis pial surfaces:
>>> import numpy as np
>>> from mindboggle.mio.vtks import read_scalars, read_vtk, write_vtk
>>> from mindboggle.guts.mesh import keep_faces, reindex_faces_points
>>> from mindboggle.shapes.laplace_beltrami import spectrum_of_largest
>>> from mindboggle.mio.fetch_data import prep_tests
>>> urls, fetch_data = prep_tests()
>>> label_file = fetch_data(urls['left_freesurfer_labels'], '', '.vtk')
>>> area_file = fetch_data(urls['left_area'], '', '.vtk')
>>> spectrum_size = 6
>>> exclude_labels = [-1]
>>> normalization = None
>>> points, indices, lines, faces, labels, f1, npoints, f2 = read_vtk(label_file,
... return_first=True, return_array=True)
>>> I20 = [i for i,x in enumerate(labels) if x==1020] # pars triangularis
>>> I22 = [i for i,x in enumerate(labels) if x==1022] # postcentral
>>> I22.extend(I20)
>>> faces = keep_faces(faces, I22)
>>> faces, points, o1 = reindex_faces_points(faces, points)
>>> areas, u1 = read_scalars(area_file, True, True)
>>> verbose = False
>>> spectrum = spectrum_of_largest(points, faces, spectrum_size,
... exclude_labels, normalization, areas, verbose)
>>> [np.float("{0:.{1}f}".format(x, 5)) for x in spectrum[1::]]
[0.00057, 0.00189, 0.00432, 0.00691, 0.00775]
View both segments (skip test):
>>> from mindboggle.mio.plots import plot_surfaces
>>> scalars = np.zeros(np.shape(labels))
>>> scalars[I22] = 1
>>> vtk_file = 'test_two_labels.vtk'
>>> write_vtk(vtk_file, points, indices, lines, faces,
... scalars, scalar_names='scalars', scalar_type='int')
>>> plot_surfaces(vtk_file) # doctest: +SKIP
"""
import numpy as np
#from scipy.sparse.linalg import eigsh, lobpcg
from mindboggle.guts.segment import select_largest
from mindboggle.shapes.laplace_beltrami import fem_laplacian
if isinstance(areas, list):
areas = np.array(areas)
# Check to see if there are enough points:
min_points_faces = spectrum_size
npoints = len(points)
if npoints < min_points_faces or len(faces) < min_points_faces:
raise IOError("The input size {0} ({1} faces) should be much larger "
"than spectrum_size ({2})".format(
npoints, len(faces), spectrum_size))
return None
else:
# --------------------------------------------------------------------
# Select the largest segment (connected set of indices):
# --------------------------------------------------------------------
points, faces = select_largest(points,
faces,
exclude_labels,
areas,
reindex=True)
# Alert if the number of indices is small:
if len(points) < min_points_faces:
raise IOError("The input size {0} is too small.".format(
len(points)))
return None
elif faces:
# ----------------------------------------------------------------
# Compute spectrum:
# ----------------------------------------------------------------
spectrum = fem_laplacian(points, faces, spectrum_size,
normalization, verbose)
return spectrum
else:
return None
def spectrum_per_label(vtk_file,
spectrum_size=10,
exclude_labels=[-1],
normalization='areaindex',
area_file='',
largest_segment=True,
verbose=False):
"""
Compute Laplace-Beltrami spectrum per labeled region in a file.
Parameters
----------
vtk_file : string
name of VTK surface mesh file containing index scalars (labels)
spectrum_size : integer
number of eigenvalues to be computed (the length of the spectrum)
exclude_labels : list of integers
labels to be excluded
normalization : string
the method used to normalize eigenvalues
if None, no normalization is used
if "area", use area of the 2D structure as in Reuter et al. 2006
if "index", divide eigenvalue by index to account for linear trend
if "areaindex", do both (default)
area_file : string (optional)
name of VTK file with surface area scalar values
largest_segment : bool
compute spectrum only for largest segment with a given label?
verbose : bool
print statements?
Returns
-------
spectrum_lists : list of lists
first eigenvalues for each label's Laplace-Beltrami spectrum
label_list : list of integers
list of unique labels for which spectra are obtained
Examples
--------
>>> # Uncomment "if label==22:" below to run example:
>>> # Spectrum for Twins-2-1 left postcentral (22) pial surface:
>>> import numpy as np
>>> from mindboggle.shapes.laplace_beltrami import spectrum_per_label
>>> from mindboggle.mio.fetch_data import prep_tests
>>> urls, fetch_data = prep_tests()
>>> vtk_file = fetch_data(urls['left_freesurfer_labels'], '', '.vtk')
>>> area_file = fetch_data(urls['left_area'], '', '.vtk')
>>> spectrum_size = 6
>>> exclude_labels = [0] #[-1]
>>> largest_segment = True
>>> verbose = False
>>> spectrum_lists, label_list = spectrum_per_label(vtk_file,
... spectrum_size, exclude_labels, None, area_file, largest_segment,
... verbose)
>>> [np.float("{0:.{1}f}".format(x, 5)) for x in spectrum_lists[0]]
[0.0, 0.00054, 0.00244, 0.00291, 0.00456, 0.00575]
>>> label_list[0:10]
[1029, 1005, 1011, 1021, 1008, 1025, 999, 1013, 1007, 1022]
"""
from mindboggle.mio.vtks import read_vtk, read_scalars
from mindboggle.guts.mesh import keep_faces, reindex_faces_points
from mindboggle.shapes.laplace_beltrami import fem_laplacian,\
spectrum_of_largest
# Read VTK surface mesh file:
points, indices, lines, faces, labels, scalar_names, npoints, \
input_vtk = read_vtk(vtk_file)
# Area file:
if area_file:
areas, u1 = read_scalars(area_file)
else:
areas = None
# Loop through labeled regions:
ulabels = []
[
ulabels.append(int(x)) for x in labels if x not in ulabels
if x not in exclude_labels
]
label_list = []
spectrum_lists = []
for label in ulabels:
#if label == 22:
# print("DEBUG: COMPUTE FOR ONLY ONE LABEL")
# Determine the indices per label:
Ilabel = [i for i, x in enumerate(labels) if x == label]
if verbose:
print('{0} vertices for label {1}'.format(len(Ilabel), label))
# Remove background faces:
pick_faces = keep_faces(faces, Ilabel)
pick_faces, pick_points, o1 = reindex_faces_points(pick_faces, points)
# Compute Laplace-Beltrami spectrum for the label:
if largest_segment:
exclude_labels_inner = [-1]
spectrum = spectrum_of_largest(pick_points, pick_faces,
spectrum_size, exclude_labels_inner,
normalization, areas, verbose)
else:
spectrum = fem_laplacian(pick_points, pick_faces, spectrum_size,
normalization, verbose)
# Append to a list of lists of spectra:
spectrum_lists.append(spectrum)
label_list.append(label)
return spectrum_lists, label_list
def spectrum_of_largest(points, faces, spectrum_size=10, exclude_labels=[-1],
normalization=None, areas=None):
"""
Compute Laplace-Beltrami spectrum on largest connected segment.
In case a surface patch is fragmented, we select the largest fragment,
remove extraneous triangular faces, and reindex indices.
Parameters
----------
points : list of lists of 3 floats
x,y,z coordinates for each vertex of the structure
faces : list of lists of 3 integers
3 indices to vertices that form a triangle on the mesh
spectrum_size : integer
number of eigenvalues to be computed (the length of the spectrum)
exclude_labels : list of integers
background values to exclude
normalization : string
the method used to normalize eigenvalues ('area' or None)
if "area", use area of the 2D structure as in Reuter et al. 2006
areas : numpy array or list of floats (or None)
surface area scalar values for all vertices
Returns
-------
spectrum : list
first spectrum_size eigenvalues for Laplace-Beltrami spectrum
Examples
--------
>>> # Spectrum for left postcentral + pars triangularis pial surfaces:
>>> import os
>>> import numpy as np
>>> from mindboggle.mio.vtks import read_scalars, read_vtk, write_vtk
>>> from mindboggle.guts.mesh import remove_faces, reindex_faces_points
>>> from mindboggle.shapes.laplace_beltrami import spectrum_of_largest
>>> path = os.environ['MINDBOGGLE_DATA']
>>> label_file = os.path.join(path, 'arno', 'labels', 'lh.labels.DKT31.manual.vtk')
>>> area_file = os.path.join(path, 'arno', 'shapes', 'lh.pial.area.vtk')
>>> spectrum_size = 6
>>> exclude_labels = [-1]
>>> normalization = None
>>> faces, lines, indices, points, u1, labels, u2,u3 = read_vtk(label_file,
>>> return_first=True, return_array=True)
>>> I20 = [i for i,x in enumerate(labels) if x==20] # pars triangularis
>>> I22 = [i for i,x in enumerate(labels) if x==22] # postcentral
>>> I22.extend(I20)
>>> faces = remove_faces(faces, I22)
>>> faces, points, o1 = reindex_faces_points(faces, points)
>>> areas, u1 = read_scalars(area_file, True, True)
>>> #
>>> spectrum_of_largest(points, faces, spectrum_size, exclude_labels,
>>> normalization, areas)
[6.3469513010430304e-18,
0.0005178862383467463,
0.0017434911095630772,
0.003667561767487686,
0.005429017880363784,
0.006309346984678924]
>>> # View both segments:
>>> from mindboggle.mio.plots import plot_surfaces
>>> scalars = np.zeros(np.shape(labels))
>>> scalars[I22] = 1
>>> vtk_file = 'test_two_labels.vtk'
>>> write_vtk(vtk_file, points, indices, lines, faces,
>>> scalars, scalar_names='scalars', scalar_type='int')
>>> plot_surfaces(vtk_file)
"""
from scipy.sparse.linalg import eigsh, lobpcg
import numpy as np
from mindboggle.guts.segment import select_largest
from mindboggle.shapes.laplace_beltrami import fem_laplacian
if isinstance(areas, list):
areas = np.array(areas)
# Check to see if there are enough points:
min_points_faces = spectrum_size
npoints = len(points)
if npoints < min_points_faces or len(faces) < min_points_faces:
print("The input size {0} ({1} faces) should be much larger "
"than spectrum_size ({2})".
format(npoints, len(faces), spectrum_size))
return None
else:
#---------------------------------------------------------------------
# Select the largest segment (connected set of indices):
#---------------------------------------------------------------------
points, faces = select_largest(points, faces, exclude_labels, areas,
reindex=True)
# Alert if the number of indices is small:
if len(points) < min_points_faces:
print("The input size {0} is too small.".format(len(points)))
return None
elif faces:
#-----------------------------------------------------------------
# Compute spectrum:
#-----------------------------------------------------------------
spectrum = fem_laplacian(points, faces, spectrum_size,
normalization)
return spectrum
else:
return None
def spectrum_per_label(vtk_file, spectrum_size=10, exclude_labels=[-1],
normalization='area', area_file='',
largest_segment=True):
"""
Compute Laplace-Beltrami spectrum per labeled region in a file.
Parameters
----------
vtk_file : string
name of VTK surface mesh file containing index scalars (labels)
spectrum_size : integer
number of eigenvalues to be computed (the length of the spectrum)
exclude_labels : list of integers
labels to be excluded
normalization : string
the method used to normalize eigenvalues ('area' or None)
if "area", use area of the 2D structure as in Reuter et al. 2006
area_file : string (optional)
name of VTK file with surface area scalar values
largest_segment : Boolean
compute spectrum only for largest segment with a given label?
Returns
-------
spectrum_lists : list of lists
first eigenvalues for each label's Laplace-Beltrami spectrum
label_list : list of integers
list of unique labels for which spectra are obtained
Examples
--------
>>> # Uncomment "if label==22:" below to run example:
>>> # Spectrum for Twins-2-1 left postcentral (22) pial surface:
>>> import os
>>> from mindboggle.shapes.laplace_beltrami import spectrum_per_label
>>> path = os.environ['MINDBOGGLE_DATA']
>>> vtk_file = os.path.join(path, 'arno', 'labels', 'lh.labels.DKT31.manual.vtk')
>>> area_file = os.path.join(path, 'arno', 'shapes', 'lh.pial.area.vtk')
>>> spectrum_size = 6
>>> exclude_labels = [0] #[-1]
>>> largest_segment = True
>>> spectrum_per_label(vtk_file, spectrum_size, exclude_labels, None,
>>> area_file, largest_segment)
([[6.3469513010430304e-18,
0.0005178862383467463,
0.0017434911095630772,
0.003667561767487686,
0.005429017880363784,
0.006309346984678924]],
[22])
"""
from mindboggle.mio.vtks import read_vtk, read_scalars
from mindboggle.guts.mesh import remove_faces, reindex_faces_points
from mindboggle.shapes.laplace_beltrami import fem_laplacian,\
spectrum_of_largest
# Read VTK surface mesh file:
faces, u1, u2, points, u4, labels, u5, u6 = read_vtk(vtk_file)
# Area file:
if area_file:
areas, u1 = read_scalars(area_file)
else:
areas = None
# Loop through labeled regions:
ulabels = []
[ulabels.append(int(x)) for x in labels if x not in ulabels
if x not in exclude_labels]
label_list = []
spectrum_lists = []
for label in ulabels:
#if label == 22:
# print("DEBUG: COMPUTE FOR ONLY ONE LABEL")
# Determine the indices per label:
Ilabel = [i for i,x in enumerate(labels) if x == label]
print('{0} vertices for label {1}'.format(len(Ilabel), label))
# Remove background faces:
pick_faces = remove_faces(faces, Ilabel)
pick_faces, pick_points, o1 = reindex_faces_points(pick_faces, points)
# Compute Laplace-Beltrami spectrum for the label:
if largest_segment:
exclude_labels_inner = [-1]
spectrum = spectrum_of_largest(pick_points, pick_faces,
spectrum_size,
exclude_labels_inner,
normalization, areas)
else:
spectrum = fem_laplacian(pick_points, pick_faces,
spectrum_size, normalization)
# Append to a list of lists of spectra:
spectrum_lists.append(spectrum)
label_list.append(label)
return spectrum_lists, label_list
def spectrum_per_label(vtk_file, spectrum_size=10, exclude_labels=[-1],
normalization='area', area_file='',
largest_segment=True, verbose=False):
"""
Compute Laplace-Beltrami spectrum per labeled region in a file.
Parameters
----------
vtk_file : string
name of VTK surface mesh file containing index scalars (labels)
spectrum_size : integer
number of eigenvalues to be computed (the length of the spectrum)
exclude_labels : list of integers
labels to be excluded
normalization : string
the method used to normalize eigenvalues ('area' or None)
if "area", use area of the 2D structure as in Reuter et al. 2006
area_file : string (optional)
name of VTK file with surface area scalar values
largest_segment : bool
compute spectrum only for largest segment with a given label?
verbose : bool
print statements?
Returns
-------
spectrum_lists : list of lists
first eigenvalues for each label's Laplace-Beltrami spectrum
label_list : list of integers
list of unique labels for which spectra are obtained
Examples
--------
>>> # Uncomment "if label==22:" below to run example:
>>> # Spectrum for Twins-2-1 left postcentral (22) pial surface:
>>> import numpy as np
>>> from mindboggle.shapes.laplace_beltrami import spectrum_per_label
>>> from mindboggle.mio.fetch_data import prep_tests
>>> urls, fetch_data = prep_tests()
>>> vtk_file = fetch_data(urls['left_freesurfer_labels'], '', '.vtk')
>>> area_file = fetch_data(urls['left_area'], '', '.vtk')
>>> spectrum_size = 6
>>> exclude_labels = [0] #[-1]
>>> largest_segment = True
>>> verbose = False
>>> spectrum_lists, label_list = spectrum_per_label(vtk_file,
... spectrum_size, exclude_labels, None, area_file, largest_segment,
... verbose)
>>> print(np.array_str(np.array(spectrum_lists[0][1::]),
... precision=5, suppress_small=True))
[ 0.00054 0.00244 0.00291 0.00456 0.00575]
>>> label_list[0:10]
[1029, 1005, 1011, 1021, 1008, 1025, 999, 1013, 1007, 1022]
"""
from mindboggle.mio.vtks import read_vtk, read_scalars
from mindboggle.guts.mesh import keep_faces, reindex_faces_points
from mindboggle.shapes.laplace_beltrami import fem_laplacian,\
spectrum_of_largest
# Read VTK surface mesh file:
points, indices, lines, faces, labels, scalar_names, npoints, \
input_vtk = read_vtk(vtk_file)
# Area file:
if area_file:
areas, u1 = read_scalars(area_file)
else:
areas = None
# Loop through labeled regions:
ulabels = []
[ulabels.append(int(x)) for x in labels if x not in ulabels
if x not in exclude_labels]
label_list = []
spectrum_lists = []
for label in ulabels:
#if label == 22:
# print("DEBUG: COMPUTE FOR ONLY ONE LABEL")
# Determine the indices per label:
Ilabel = [i for i,x in enumerate(labels) if x == label]
if verbose:
print('{0} vertices for label {1}'.format(len(Ilabel), label))
# Remove background faces:
pick_faces = keep_faces(faces, Ilabel)
pick_faces, pick_points, o1 = reindex_faces_points(pick_faces, points)
# Compute Laplace-Beltrami spectrum for the label:
if largest_segment:
exclude_labels_inner = [-1]
spectrum = spectrum_of_largest(pick_points, pick_faces,
spectrum_size,
exclude_labels_inner,
normalization, areas, verbose)
else:
spectrum = fem_laplacian(pick_points, pick_faces, spectrum_size,
normalization, verbose)
# Append to a list of lists of spectra:
spectrum_lists.append(spectrum)
label_list.append(label)
return spectrum_lists, label_list
def spectrum_of_largest(points, faces, spectrum_size=10, exclude_labels=[-1],
normalization=None, areas=None, verbose=False):
"""
Compute Laplace-Beltrami spectrum on largest connected segment.
In case a surface patch is fragmented, we select the largest fragment,
remove extraneous triangular faces, and reindex indices.
Parameters
----------
points : list of lists of 3 floats
x,y,z coordinates for each vertex of the structure
faces : list of lists of 3 integers
3 indices to vertices that form a triangle on the mesh
spectrum_size : integer
number of eigenvalues to be computed (the length of the spectrum)
exclude_labels : list of integers
background values to exclude
normalization : string
the method used to normalize eigenvalues ('area' or None)
if "area", use area of the 2D structure as in Reuter et al. 2006
areas : numpy array or list of floats (or None)
surface area scalar values for all vertices
verbose : bool
print statements?
Returns
-------
spectrum : list
first spectrum_size eigenvalues for Laplace-Beltrami spectrum
Examples
--------
>>> # Spectrum for left postcentral + pars triangularis pial surfaces:
>>> import numpy as np
>>> from mindboggle.mio.vtks import read_scalars, read_vtk, write_vtk
>>> from mindboggle.guts.mesh import keep_faces, reindex_faces_points
>>> from mindboggle.shapes.laplace_beltrami import spectrum_of_largest
>>> from mindboggle.mio.fetch_data import prep_tests
>>> urls, fetch_data = prep_tests()
>>> label_file = fetch_data(urls['left_freesurfer_labels'], '', '.vtk')
>>> area_file = fetch_data(urls['left_area'], '', '.vtk')
>>> spectrum_size = 6
>>> exclude_labels = [-1]
>>> normalization = None
>>> points, indices, lines, faces, labels, f1, npoints, f2 = read_vtk(label_file,
... return_first=True, return_array=True)
>>> I20 = [i for i,x in enumerate(labels) if x==1020] # pars triangularis
>>> I22 = [i for i,x in enumerate(labels) if x==1022] # postcentral
>>> I22.extend(I20)
>>> faces = keep_faces(faces, I22)
>>> faces, points, o1 = reindex_faces_points(faces, points)
>>> areas, u1 = read_scalars(area_file, True, True)
>>> verbose = False
>>> spectrum = spectrum_of_largest(points, faces, spectrum_size,
... exclude_labels, normalization, areas, verbose)
>>> print(np.array_str(np.array(spectrum[1::]),
... precision=5, suppress_small=True))
[ 0.00057 0.00189 0.00432 0.00691 0.00775]
View both segments (skip test):
>>> from mindboggle.mio.plots import plot_surfaces
>>> scalars = np.zeros(np.shape(labels))
>>> scalars[I22] = 1
>>> vtk_file = 'test_two_labels.vtk'
>>> write_vtk(vtk_file, points, indices, lines, faces,
... scalars, scalar_names='scalars', scalar_type='int')
>>> plot_surfaces(vtk_file) # doctest: +SKIP
"""
import numpy as np
#from scipy.sparse.linalg import eigsh, lobpcg
from mindboggle.guts.segment import select_largest
from mindboggle.shapes.laplace_beltrami import fem_laplacian
if isinstance(areas, list):
areas = np.array(areas)
# Check to see if there are enough points:
min_points_faces = spectrum_size
npoints = len(points)
if npoints < min_points_faces or len(faces) < min_points_faces:
raise IOError("The input size {0} ({1} faces) should be much larger "
"than spectrum_size ({2})".
format(npoints, len(faces), spectrum_size))
return None
else:
# --------------------------------------------------------------------
# Select the largest segment (connected set of indices):
# --------------------------------------------------------------------
points, faces = select_largest(points, faces, exclude_labels, areas,
reindex=True)
# Alert if the number of indices is small:
if len(points) < min_points_faces:
raise IOError("The input size {0} is too small.".
format(len(points)))
return None
elif faces:
# ----------------------------------------------------------------
# Compute spectrum:
# ----------------------------------------------------------------
spectrum = fem_laplacian(points, faces, spectrum_size,
normalization, verbose)
return spectrum
else:
return None
def spectrum_per_label(vtk_file, spectrum_size=10, exclude_labels=[-1],
normalization='area', area_file='',
largest_segment=True):
"""
Compute Laplace-Beltrami spectrum per labeled region in a file.
Parameters
----------
vtk_file : string
name of VTK surface mesh file containing index scalars (labels)
spectrum_size : integer
number of eigenvalues to be computed (the length of the spectrum)
exclude_labels : list of integers
labels to be excluded
normalization : string
the method used to normalize eigenvalues ('area' or None)
if "area", use area of the 2D structure as in Reuter et al. 2006
area_file : string
name of VTK file with surface area scalar values
largest_segment : Boolean
compute spectrum only for largest segment with a given label?
Returns
-------
spectrum_lists : list of lists
first eigenvalues for each label's Laplace-Beltrami spectrum
label_list : list of integers
list of unique labels for which spectra are obtained
Examples
--------
>>> # Uncomment "if label==22:" below to run example:
>>> # Spectrum for Twins-2-1 left postcentral (22) pial surface:
>>> import os
>>> from mindboggle.shapes.laplace_beltrami import spectrum_per_label
>>> path = os.environ['MINDBOGGLE_DATA']
>>> vtk_file = os.path.join(path, 'arno', 'labels', 'lh.labels.DKT31.manual.vtk')
>>> area_file = os.path.join(path, 'arno', 'shapes', 'lh.pial.area.vtk')
>>> spectrum_size = 6
>>> exclude_labels = [0] #[-1]
>>> largest_segment = True
>>> spectrum_per_label(vtk_file, spectrum_size, exclude_labels, None,
>>> area_file, largest_segment)
([[6.3469513010430304e-18,
0.0005178862383467463,
0.0017434911095630772,
0.003667561767487686,
0.005429017880363784,
0.006309346984678924]],
[22])
"""
from mindboggle.utils.io_vtk import read_vtk, read_scalars
from mindboggle.utils.mesh import remove_faces, reindex_faces_points
from mindboggle.shapes.laplace_beltrami import fem_laplacian,\
spectrum_of_largest
# Read VTK surface mesh file:
faces, u1, u2, points, u4, labels, u5, u6 = read_vtk(vtk_file)
# Area file:
if area_file:
areas, u1 = read_scalars(area_file)
else:
areas = None
# Loop through labeled regions:
ulabels = []
[ulabels.append(int(x)) for x in labels if x not in ulabels
if x not in exclude_labels]
label_list = []
spectrum_lists = []
for label in ulabels:
#if label == 22:
# print("DEBUG: COMPUTE FOR ONLY ONE LABEL")
# Determine the indices per label:
Ilabel = [i for i,x in enumerate(labels) if x == label]
print('{0} vertices for label {1}'.format(len(Ilabel), label))
# Remove background faces:
pick_faces = remove_faces(faces, Ilabel)
pick_faces, pick_points, o1 = reindex_faces_points(pick_faces, points)
# Compute Laplace-Beltrami spectrum for the label:
if largest_segment:
exclude_labels_inner = [-1]
spectrum = spectrum_of_largest(pick_points, pick_faces,
spectrum_size,
exclude_labels_inner,
normalization, areas)
else:
spectrum = fem_laplacian(pick_points, pick_faces,
spectrum_size, normalization)
# Append to a list of lists of spectra:
spectrum_lists.append(spectrum)
label_list.append(label)
return spectrum_lists, label_list
def spectrum_of_largest(points, faces, spectrum_size=10, exclude_labels=[-1],
normalization=None, areas=None):
"""
Compute Laplace-Beltrami spectrum on largest connected segment.
In case a surface patch is fragmented, we select the largest fragment,
remove extraneous triangular faces, and reindex indices.
Parameters
----------
points : list of lists of 3 floats
x,y,z coordinates for each vertex of the structure
faces : list of lists of 3 integers
3 indices to vertices that form a triangle on the mesh
spectrum_size : integer
number of eigenvalues to be computed (the length of the spectrum)
exclude_labels : list of integers
background values to exclude
normalization : string
the method used to normalize eigenvalues ('area' or None)
if "area", use area of the 2D structure as in Reuter et al. 2006
areas : numpy array or list of floats (or None)
surface area scalar values for all vertices
Returns
-------
spectrum : list
first spectrum_size eigenvalues for Laplace-Beltrami spectrum
Examples
--------
>>> # Spectrum for left postcentral + pars triangularis pial surfaces:
>>> import os
>>> import numpy as np
>>> from mindboggle.utils.io_vtk import read_scalars, read_vtk, write_vtk
>>> from mindboggle.utils.mesh import remove_faces, reindex_faces_points
>>> from mindboggle.shapes.laplace_beltrami import spectrum_of_largest
>>> path = os.environ['MINDBOGGLE_DATA']
>>> label_file = os.path.join(path, 'arno', 'labels', 'lh.labels.DKT31.manual.vtk')
>>> area_file = os.path.join(path, 'arno', 'shapes', 'lh.pial.area.vtk')
>>> spectrum_size = 6
>>> exclude_labels = [-1]
>>> normalization = None
>>> faces, lines, indices, points, u1, labels, u2,u3 = read_vtk(label_file,
>>> return_first=True, return_array=True)
>>> I20 = [i for i,x in enumerate(labels) if x==20] # pars triangularis
>>> I22 = [i for i,x in enumerate(labels) if x==22] # postcentral
>>> I22.extend(I20)
>>> faces = remove_faces(faces, I22)
>>> faces, points, o1 = reindex_faces_points(faces, points)
>>> areas, u1 = read_scalars(area_file, True, True)
>>> #
>>> spectrum_of_largest(points, faces, spectrum_size, exclude_labels,
>>> normalization, areas)
[6.3469513010430304e-18,
0.0005178862383467463,
0.0017434911095630772,
0.003667561767487686,
0.005429017880363784,
0.006309346984678924]
>>> # View both segments:
>>> from mindboggle.utils.plots import plot_surfaces
>>> scalars = np.zeros(np.shape(labels))
>>> scalars[I22] = 1
>>> vtk_file = 'test_two_labels.vtk'
>>> write_vtk(vtk_file, points, indices, lines, faces,
>>> scalars, scalar_names='scalars', scalar_type='int')
>>> plot_surfaces(vtk_file)
"""
from scipy.sparse.linalg import eigsh, lobpcg
import numpy as np
from mindboggle.utils.segment import select_largest
from mindboggle.shapes.laplace_beltrami import fem_laplacian
if isinstance(areas, list):
areas = np.array(areas)
# Check to see if there are enough points:
min_points_faces = spectrum_size
npoints = len(points)
if npoints < min_points_faces or len(faces) < min_points_faces:
print("The input size {0} ({1} faces) should be much larger "
"than spectrum_size ({2})".
format(npoints, len(faces), spectrum_size))
return None
else:
#---------------------------------------------------------------------
# Select the largest segment (connected set of indices):
#---------------------------------------------------------------------
points, faces = select_largest(points, faces, exclude_labels, areas,
reindex=True)
# Alert if the number of indices is small:
if len(points) < min_points_faces:
print("The input size {0} is too small.".format(len(points)))
return None
elif faces:
#-----------------------------------------------------------------
# Compute spectrum:
#-----------------------------------------------------------------
spectrum = fem_laplacian(points, faces, spectrum_size,
normalization)
return spectrum
else:
return None
def spectrum_of_largest(points, faces, n_eigenvalues=6, exclude_labels=[-1],
normalization=None, areas=None):
"""
Compute Laplace-Beltrami spectrum on largest connected segment.
In case a surface patch is fragmented, we select the largest fragment,
remove extraneous triangular faces, and reindex indices.
Parameters
----------
points : list of lists of 3 floats
x,y,z coordinates for each vertex of the structure
faces : list of lists of 3 integers
3 indices to vertices that form a triangle on the mesh
n_eigenvalues : integer
number of eigenvalues to be computed (the length of the spectrum)
exclude_labels : list of integers
background values to exclude
normalization : string
the method used to normalize eigenvalues ('area' or None)
if "area", use area of the 2D structure as in Reuter et al. 2006
areas : numpy array or list of floats (or None)
surface area scalar values for all vertices
Returns
-------
spectrum : list
first n_eigenvalues eigenvalues for Laplace-Beltrami spectrum
Examples
--------
>>> # Spectrum for one label (artificial composite), two fragments:
>>> import os
>>> import numpy as np
>>> from mindboggle.utils.io_vtk import read_scalars, read_vtk, write_vtk
>>> from mindboggle.utils.mesh import remove_faces
>>> from mindboggle.shapes.laplace_beltrami import spectrum_of_largest
>>> path = os.environ['MINDBOGGLE_DATA']
>>> label_file = os.path.join(path, 'arno', 'labels', 'lh.labels.DKT25.manual.vtk')
>>> area_file = os.path.join(path, 'arno', 'shapes', 'lh.pial.area.vtk')
>>> n_eigenvalues = 6
>>> exclude_labels = [0] #[-1]
>>> normalization = None
>>> faces, lines, indices, points, foo1, labels, foo2, foo3 = read_vtk(label_file,
>>> return_first=True, return_array=True)
>>> I2 = [i for i,x in enumerate(labels) if x==2] # cingulate
>>> I22 = [i for i,x in enumerate(labels) if x==22] # postcentral
>>> I2.extend(I22)
>>> faces = remove_faces(faces, I2)
>>> areas, u1 = read_scalars(area_file, True, True)
>>> #
>>> spectrum_of_largest(points, faces, n_eigenvalues, exclude_labels,
>>> normalization, areas)
>>> #
>>> # View:
>>> from mindboggle.utils.plots import plot_vtk
>>> scalars = np.zeros(np.shape(labels))
>>> scalars[I2] = 1
>>> vtk_file = 'test_two_labels.vtk'
>>> write_vtk(vtk_file, points, indices, lines, faces,
>>> scalars, scalar_names='scalars')
>>> plot_vtk(vtk_file)
Load "Labels" scalars from lh.labels.DKT25.manual.vtk
Reduced 290134 to 29728 triangular faces
Load "scalars" scalars from lh.pial.area.vtk
2 segments
Reduced 29728 to 14498 triangular faces
Compute linear FEM Laplace-Beltrami spectrum
[-8.764053090852845e-18,
0.00028121452203987146,
0.0010941205613292243,
0.0017301461686759188,
0.0034244633555606295,
0.004280982704174599]
"""
from scipy.sparse.linalg import eigsh, lobpcg
import numpy as np
from mindboggle.utils.mesh import find_neighbors, remove_faces, \
reindex_faces_points
from mindboggle.utils.segment import segment
from mindboggle.shapes.laplace_beltrami import fem_laplacian
# Areas:
use_area = False
if isinstance(areas, np.ndarray) and np.shape(areas):
use_area = True
elif isinstance(areas, list) and len(areas):
areas = np.array(areas)
use_area = True
# Check to see if there are enough points:
min_npoints = n_eigenvalues
npoints = len(points)
if npoints < min_npoints or len(faces) < min_npoints:
print("The input size {0} ({1} faces) should be much larger "
"than n_eigenvalues {2}".
format(npoints, len(faces), n_eigenvalues))
return None
else:
#---------------------------------------------------------------------
# Segment the indices into connected sets of indices:
#---------------------------------------------------------------------
# Construct neighbor lists:
neighbor_lists = find_neighbors(faces, npoints)
# Determine the indices:
indices = [x for sublst in faces for x in sublst]
# Segment:
segments = segment(indices, neighbor_lists, min_region_size=1,
seed_lists=[], keep_seeding=False, spread_within_labels=False,
labels=[], label_lists=[], values=[], max_steps='', verbose=False)
#---------------------------------------------------------------------
# Select the largest segment (connected set of indices):
#---------------------------------------------------------------------
unique_segments = [x for x in np.unique(segments)
if x not in exclude_labels]
if len(unique_segments) > 1:
select_indices = []
max_segment_area = 0
for segment_number in unique_segments:
segment_indices = [i for i,x in enumerate(segments)
if x == segment_number]
if use_area:
segment_area = np.sum(areas[segment_indices])
else:
segment_area = len(segment_indices)
if segment_area > max_segment_area:
select_indices = segment_indices
max_segment_area = len(select_indices)
print('Maximum size of {0} segments: {1} vertices'.
format(len(unique_segments), len(select_indices)))
#-----------------------------------------------------------------
# Extract points and renumber faces for the selected indices:
#-----------------------------------------------------------------
faces = remove_faces(faces, select_indices)
else:
select_indices = indices
# Alert if the number of indices is small:
if len(select_indices) < min_npoints:
print("The input size {0} is too small.".format(len(select_indices)))
return None
elif faces:
#-----------------------------------------------------------------
# Reindex indices in faces:
#-----------------------------------------------------------------
faces, points = reindex_faces_points(faces, points)
#-----------------------------------------------------------------
# Compute spectrum:
#-----------------------------------------------------------------
spectrum = fem_laplacian(points, faces, n_eigenvalues,
normalization)
return spectrum
else:
return None