/usr/lib/python2.7/dist-packages/mne/surface.py is in python-mne 0.7.3-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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| # Authors: Alexandre Gramfort <gramfort@nmr.mgh.harvard.edu>
# Matti Hamalainen <msh@nmr.mgh.harvard.edu>
# Denis A. Engemann <d.engemann@fz-juelich.de>
#
# License: BSD (3-clause)
import os
from os import path as op
import sys
from struct import pack
import numpy as np
from scipy.spatial.distance import cdist
from scipy import sparse
from .fiff.constants import FIFF
from .fiff.open import fiff_open
from .fiff.tree import dir_tree_find
from .fiff.tag import find_tag
from .fiff.write import (write_int, write_float, write_float_matrix,
write_int_matrix, start_file, end_block,
start_block, end_file, write_string,
write_float_sparse_rcs)
from .utils import logger, verbose, get_subjects_dir
##############################################################################
# BEM
@verbose
def read_bem_surfaces(fname, add_geom=False, s_id=None, verbose=None):
"""Read the BEM surfaces from a FIF file
Parameters
----------
fname : string
The name of the file containing the surfaces.
add_geom : bool, optional (default False)
If True add geometry information to the surfaces.
s_id : int | None
If int, only read and return the surface with the given s_id.
An error will be raised if it doesn't exist. If None, all
surfaces are read and returned.
verbose : bool, str, int, or None
If not None, override default verbose level (see mne.verbose).
Returns
-------
surf: list | dict
A list of dictionaries that each contain a surface. If s_id
is not None, only the requested surface will be returned.
"""
#
# Default coordinate frame
#
coord_frame = FIFF.FIFFV_COORD_MRI
#
# Open the file, create directory
#
fid, tree, _ = fiff_open(fname)
#
# Find BEM
#
bem = dir_tree_find(tree, FIFF.FIFFB_BEM)
if bem is None:
fid.close()
raise ValueError('BEM data not found')
bem = bem[0]
#
# Locate all surfaces
#
bemsurf = dir_tree_find(bem, FIFF.FIFFB_BEM_SURF)
if bemsurf is None:
fid.close()
raise ValueError('BEM surface data not found')
logger.info(' %d BEM surfaces found' % len(bemsurf))
#
# Coordinate frame possibly at the top level
#
tag = find_tag(fid, bem, FIFF.FIFF_BEM_COORD_FRAME)
if tag is not None:
coord_frame = tag.data
#
# Read all surfaces
#
if s_id is not None:
surfs = [_read_bem_surface(fid, bsurf, coord_frame, s_id)
for bsurf in bemsurf]
surfs = [s for s in surfs if s is not None]
if not len(surfs) == 1:
raise ValueError('surface with id %d not found' % s_id)
fid.close()
return surfs[0]
surf = []
for bsurf in bemsurf:
logger.info(' Reading a surface...')
this = _read_bem_surface(fid, bsurf, coord_frame)
logger.info('[done]')
if add_geom:
_complete_surface_info(this)
surf.append(this)
logger.info(' %d BEM surfaces read' % len(surf))
fid.close()
return surf
def _read_bem_surface(fid, this, def_coord_frame, s_id=None):
"""Read one bem surface
"""
res = dict()
#
# Read all the interesting stuff
#
tag = find_tag(fid, this, FIFF.FIFF_BEM_SURF_ID)
if tag is None:
res['id'] = FIFF.FIFFV_BEM_SURF_ID_UNKNOWN
else:
res['id'] = int(tag.data)
if s_id is not None:
if res['id'] != s_id:
return None
tag = find_tag(fid, this, FIFF.FIFF_BEM_SIGMA)
if tag is None:
res['sigma'] = 1.0
else:
res['sigma'] = float(tag.data)
tag = find_tag(fid, this, FIFF.FIFF_BEM_SURF_NNODE)
if tag is None:
fid.close()
raise ValueError('Number of vertices not found')
res['np'] = int(tag.data)
tag = find_tag(fid, this, FIFF.FIFF_BEM_SURF_NTRI)
if tag is None:
fid.close()
raise ValueError('Number of triangles not found')
else:
res['ntri'] = int(tag.data)
tag = find_tag(fid, this, FIFF.FIFF_MNE_COORD_FRAME)
if tag is None:
tag = find_tag(fid, this, FIFF.FIFF_BEM_COORD_FRAME)
if tag is None:
res['coord_frame'] = def_coord_frame
else:
res['coord_frame'] = tag.data
else:
res['coord_frame'] = tag.data
#
# Vertices, normals, and triangles
#
tag = find_tag(fid, this, FIFF.FIFF_BEM_SURF_NODES)
if tag is None:
fid.close()
raise ValueError('Vertex data not found')
res['rr'] = tag.data.astype(np.float) # XXX : double because of mayavi bug
if res['rr'].shape[0] != res['np']:
fid.close()
raise ValueError('Vertex information is incorrect')
tag = find_tag(fid, this, FIFF.FIFF_MNE_SOURCE_SPACE_NORMALS)
if tag is None:
res['nn'] = []
else:
res['nn'] = tag.data
if res['nn'].shape[0] != res['np']:
fid.close()
raise ValueError('Vertex normal information is incorrect')
tag = find_tag(fid, this, FIFF.FIFF_BEM_SURF_TRIANGLES)
if tag is None:
fid.close()
raise ValueError('Triangulation not found')
res['tris'] = tag.data - 1 # index start at 0 in Python
if res['tris'].shape[0] != res['ntri']:
fid.close()
raise ValueError('Triangulation information is incorrect')
return res
@verbose
def read_bem_solution(fname, verbose=None):
"""Read the BEM solution from a file
Parameters
----------
fname : string
The file containing the BEM solution.
verbose : bool, str, int, or None
If not None, override default verbose level (see mne.verbose).
Returns
-------
bem : dict
The BEM solution.
"""
logger.info('Loading surfaces...')
bem_surfs = read_bem_surfaces(fname, add_geom=True, verbose=False)
if len(bem_surfs) == 3:
logger.info('Three-layer model surfaces loaded.')
needed = np.array([FIFF.FIFFV_BEM_SURF_ID_HEAD,
FIFF.FIFFV_BEM_SURF_ID_SKULL,
FIFF.FIFFV_BEM_SURF_ID_BRAIN])
if not all([x['id'] in needed for x in bem_surfs]):
raise RuntimeError('Could not find necessary BEM surfaces')
# reorder surfaces as necessary (shouldn't need to?)
reorder = [None] * 3
for x in bem_surfs:
reorder[np.where(x['id'] == needed)[0][0]] = x
bem_surfs = reorder
elif len(bem_surfs) == 1:
if not bem_surfs[0]['id'] == FIFF.FIFFV_BEM_SURF_ID_BRAIN:
raise RuntimeError('BEM Surfaces not found')
logger.info('Homogeneous model surface loaded.')
# convert from surfaces to solution
bem = dict(surfs=bem_surfs)
logger.info('\nLoading the solution matrix...\n')
f, tree, _ = fiff_open(fname)
with f as fid:
# Find the BEM data
nodes = dir_tree_find(tree, FIFF.FIFFB_BEM)
if len(nodes) == 0:
raise RuntimeError('No BEM data in %s' % fname)
bem_node = nodes[0]
# Approximation method
tag = find_tag(f, bem_node, FIFF.FIFF_BEM_APPROX)
method = tag.data[0]
if method == FIFF.FIFFV_BEM_APPROX_CONST:
method = 'constant collocation'
elif method == FIFF.FIFFV_BEM_APPROX_LINEAR:
method = 'linear collocation'
else:
raise RuntimeError('Cannot handle BEM approximation method : %d'
% method)
tag = find_tag(fid, bem_node, FIFF.FIFF_BEM_POT_SOLUTION)
dims = tag.data.shape
if len(dims) != 2:
raise RuntimeError('Expected a two-dimensional solution matrix '
'instead of a %d dimensional one' % dims[0])
dim = 0
for surf in bem['surfs']:
if method == 'linear collocation':
dim += surf['np']
else:
dim += surf['ntri']
if dims[0] != dim or dims[1] != dim:
raise RuntimeError('Expected a %d x %d solution matrix instead of '
'a %d x %d one' % (dim, dim, dims[1], dims[0]))
sol = tag.data
nsol = dims[0]
# Gamma factors and multipliers
bem['sigma'] = np.array([surf['sigma'] for surf in bem['surfs']])
# Dirty trick for the zero conductivity outside
sigma = np.r_[0.0, bem['sigma']]
bem['source_mult'] = 2.0 / (sigma[1:] + sigma[:-1])
bem['field_mult'] = sigma[1:] - sigma[:-1]
# make sure subsequent "zip"s work correctly
assert len(bem['surfs']) == len(bem['field_mult'])
bem['gamma'] = ((sigma[1:] - sigma[:-1])[np.newaxis, :] /
(sigma[1:] + sigma[:-1])[:, np.newaxis])
bem['sol_name'] = fname
bem['solution'] = sol
bem['nsol'] = nsol
bem['bem_method'] = method
logger.info('Loaded %s BEM solution from %s', bem['bem_method'], fname)
return bem
###############################################################################
# EFFICIENCY UTILITIES
def fast_cross_3d(x, y):
"""Compute cross product between list of 3D vectors
Much faster than np.cross() when the number of cross products
becomes large (>500). This is because np.cross() methods become
less memory efficient at this stage.
Parameters
----------
x : array
Input array 1.
y : array
Input array 2.
Returns
-------
z : array
Cross product of x and y.
Notes
-----
x and y must both be 2D row vectors. One must have length 1, or both
lengths must match.
"""
assert x.ndim == 2
assert y.ndim == 2
assert x.shape[1] == 3
assert y.shape[1] == 3
assert (x.shape[0] == 1 or y.shape[0] == 1) or x.shape[0] == y.shape[0]
if max([x.shape[0], y.shape[0]]) >= 500:
return np.c_[x[:, 1] * y[:, 2] - x[:, 2] * y[:, 1],
x[:, 2] * y[:, 0] - x[:, 0] * y[:, 2],
x[:, 0] * y[:, 1] - x[:, 1] * y[:, 0]]
else:
return np.cross(x, y)
def _accumulate_normals(tris, tri_nn, npts):
"""Efficiently accumulate triangle normals"""
# this code replaces the following, but is faster (vectorized):
#
# this['nn'] = np.zeros((this['np'], 3))
# for p in xrange(this['ntri']):
# verts = this['tris'][p]
# this['nn'][verts, :] += this['tri_nn'][p, :]
#
nn = np.zeros((npts, 3))
for verts in tris.T: # note this only loops 3x (number of verts per tri)
counts = np.bincount(verts, minlength=npts)
reord = np.argsort(verts)
vals = np.r_[np.zeros((1, 3)), np.cumsum(tri_nn[reord, :], 0)]
idx = np.cumsum(np.r_[0, counts])
nn += vals[idx[1:], :] - vals[idx[:-1], :]
return nn
def _triangle_neighbors(tris, npts):
"""Efficiently compute vertex neighboring triangles"""
# this code replaces the following, but is faster (vectorized):
#
# this['neighbor_tri'] = [list() for _ in xrange(this['np'])]
# for p in xrange(this['ntri']):
# verts = this['tris'][p]
# this['neighbor_tri'][verts[0]].append(p)
# this['neighbor_tri'][verts[1]].append(p)
# this['neighbor_tri'][verts[2]].append(p)
# this['neighbor_tri'] = [np.array(nb, int) for nb in this['neighbor_tri']]
#
verts = tris.ravel()
counts = np.bincount(verts, minlength=npts)
reord = np.argsort(verts)
tri_idx = np.unravel_index(reord, (len(tris), 3))[0]
idx = np.cumsum(np.r_[0, counts])
# the sort below slows it down a bit, but is needed for equivalence
neighbor_tri = [np.sort(tri_idx[v1:v2])
for v1, v2 in zip(idx[:-1], idx[1:])]
return neighbor_tri
def _triangle_coords(r, geom, best):
"""Get coordinates of a vertex projected to a triangle"""
r1 = geom['r1'][best]
tri_nn = geom['nn'][best]
r12 = geom['r12'][best]
r13 = geom['r13'][best]
a = geom['a'][best]
b = geom['b'][best]
c = geom['c'][best]
rr = r - r1
z = np.sum(rr * tri_nn)
v1 = np.sum(rr * r12)
v2 = np.sum(rr * r13)
det = a * b - c * c
x = (b * v1 - c * v2) / det
y = (a * v2 - c * v1) / det
return x, y, z
def _complete_surface_info(this, do_neighbor_vert=False):
"""Complete surface info"""
# based on mne_source_space_add_geometry_info() in mne_add_geometry_info.c
# Main triangulation [mne_add_triangle_data()]
this['tri_area'] = np.zeros(this['ntri'])
r1 = this['rr'][this['tris'][:, 0], :]
r2 = this['rr'][this['tris'][:, 1], :]
r3 = this['rr'][this['tris'][:, 2], :]
this['tri_cent'] = (r1 + r2 + r3) / 3.0
this['tri_nn'] = fast_cross_3d((r2 - r1), (r3 - r1))
# Triangle normals and areas
size = np.sqrt(np.sum(this['tri_nn'] ** 2, axis=1))
this['tri_area'] = size / 2.0
zidx = np.where(size == 0)[0]
for idx in zidx:
logger.info(' Warning: zero size triangle # %s' % idx)
size[zidx] = 1.0 # prevent ugly divide-by-zero
this['tri_nn'] /= size[:, None]
# Find neighboring triangles, accumulate vertex normals, normalize
logger.info(' Triangle neighbors and vertex normals...')
this['neighbor_tri'] = _triangle_neighbors(this['tris'], this['np'])
this['nn'] = _accumulate_normals(this['tris'], this['tri_nn'], this['np'])
_normalize_vectors(this['nn'])
# Check for topological defects
idx = np.where([len(n) == 0 for n in this['neighbor_tri']])[0]
if len(idx) > 0:
logger.info(' Vertices [%s] do not have any neighboring'
'triangles!' % ','.join([str(ii) for ii in idx]))
idx = np.where([len(n) < 3 for n in this['neighbor_tri']])[0]
if len(idx) > 0:
logger.info(' Vertices [%s] have fewer than three neighboring '
'tris, omitted' % ','.join([str(ii) for ii in idx]))
for k in idx:
this['neighbor_tri'] = np.array([], int)
# Determine the neighboring vertices and fix errors
if do_neighbor_vert is True:
this['neighbor_vert'] = [_get_surf_neighbors(this, k)
for k in xrange(this['np'])]
return this
def _get_surf_neighbors(surf, k):
"""Calculate the surface neighbors based on triangulation"""
verts = np.concatenate([surf['tris'][nt]
for nt in surf['neighbor_tri'][k]])
verts = np.setdiff1d(verts, [k], assume_unique=False)
if np.any(verts >= surf['np']):
raise RuntimeError
nneighbors = len(verts)
nneigh_max = len(surf['neighbor_tri'][k])
if nneighbors > nneigh_max:
raise RuntimeError('Too many neighbors for vertex %d' % k)
elif nneighbors != nneigh_max:
logger.info(' Incorrect number of distinct neighbors for vertex'
' %d (%d instead of %d) [fixed].' % (k, nneighbors,
nneigh_max))
return verts
def _normalize_vectors(rr):
"""Normalize surface vertices"""
size = np.sqrt(np.sum(rr * rr, axis=1))
size[size == 0] = 1.0 # avoid divide-by-zero
rr /= size[:, np.newaxis] # operate in-place
def _compute_nearest(xhs, rr, use_balltree=True, return_dists=False):
"""Find nearest neighbors
Note: The rows in xhs and rr must all be unit-length vectors, otherwise
the result will be incorrect.
Parameters
----------
xhs : array, shape=(n_samples, n_dim)
Points of data set.
rr : array, shape=(n_query, n_dim)
Points to find nearest neighbors for.
use_balltree : bool
Use fast BallTree based search from scikit-learn. If scikit-learn
is not installed it will fall back to the slow brute force search.
Returns
-------
nearest : array, shape=(n_query,)
Index of nearest neighbor in xhs for every point in rr.
"""
if use_balltree:
try:
from sklearn.neighbors import BallTree
except ImportError:
logger.info('Nearest-neighbor searches will be significantly '
'faster if scikit-learn is installed.')
use_balltree = False
if use_balltree is True:
ball_tree = BallTree(xhs)
if return_dists:
out = ball_tree.query(rr, k=1, return_distance=True)
return out[1][:, 0], out[0][:, 0]
else:
nearest = ball_tree.query(rr, k=1, return_distance=False)[:, 0]
return nearest
else:
if return_dists:
nearest = list()
dists = list()
for r in rr:
d = cdist(r[np.newaxis, :], xhs)
idx = np.argmin(d)
nearest.append(idx)
dists.append(d[0, idx])
return (np.array(nearest), np.array(dists))
else:
nearest = np.array([np.argmin(cdist(r[np.newaxis, :], xhs))
for r in rr])
return nearest
###############################################################################
# Handle freesurfer
def _fread3(fobj):
"""Docstring"""
b1, b2, b3 = np.fromfile(fobj, ">u1", 3)
return (b1 << 16) + (b2 << 8) + b3
def _fread3_many(fobj, n):
"""Read 3-byte ints from an open binary file object."""
b1, b2, b3 = np.fromfile(fobj, ">u1",
3 * n).reshape(-1, 3).astype(np.int).T
return (b1 << 16) + (b2 << 8) + b3
def read_curvature(filepath):
"""Load in curavature values from the ?h.curv file."""
with open(filepath, "rb") as fobj:
magic = _fread3(fobj)
if magic == 16777215:
vnum = np.fromfile(fobj, ">i4", 3)[0]
curv = np.fromfile(fobj, ">f4", vnum)
else:
vnum = magic
_fread3(fobj)
curv = np.fromfile(fobj, ">i2", vnum) / 100
bin_curv = 1 - np.array(curv != 0, np.int)
return bin_curv
@verbose
def read_surface(fname, verbose=None):
"""Load a Freesurfer surface mesh in triangular format
Parameters
----------
fname : str
The name of the file containing the surface.
verbose : bool, str, int, or None
If not None, override default verbose level (see mne.verbose).
Returns
-------
rr : array, shape=(n_vertices, 3)
Coordinate points.
tris : int array, shape=(n_faces, 3)
Triangulation (each line contains indexes for three points which
together form a face).
"""
with open(fname, "rb") as fobj:
magic = _fread3(fobj)
if (magic == 16777215) or (magic == 16777213): # Quad file or new quad
nvert = _fread3(fobj)
nquad = _fread3(fobj)
coords = np.fromfile(fobj, ">i2", nvert * 3).astype(np.float)
coords = coords.reshape(-1, 3) / 100.0
quads = _fread3_many(fobj, nquad * 4)
quads = quads.reshape(nquad, 4)
#
# Face splitting follows
#
faces = np.zeros((2 * nquad, 3), dtype=np.int)
nface = 0
for quad in quads:
if (quad[0] % 2) == 0:
faces[nface] = quad[0], quad[1], quad[3]
nface += 1
faces[nface] = quad[2], quad[3], quad[1]
nface += 1
else:
faces[nface] = quad[0], quad[1], quad[2]
nface += 1
faces[nface] = quad[0], quad[2], quad[3]
nface += 1
elif magic == 16777214: # Triangle file
create_stamp = fobj.readline()
_ = fobj.readline()
vnum = np.fromfile(fobj, ">i4", 1)[0]
fnum = np.fromfile(fobj, ">i4", 1)[0]
coords = np.fromfile(fobj, ">f4", vnum * 3).reshape(vnum, 3)
faces = np.fromfile(fobj, ">i4", fnum * 3).reshape(fnum, 3)
else:
raise ValueError("%s does not appear to be a Freesurfer surface"
% fname)
logger.info('Triangle file: %s nvert = %s ntri = %s'
% (create_stamp.strip(), len(coords), len(faces)))
coords = coords.astype(np.float) # XXX: due to mayavi bug on mac 32bits
return coords, faces
@verbose
def _read_surface_geom(fname, add_geom=True, norm_rr=False, verbose=None):
"""Load the surface as dict, optionally add the geometry information"""
# based on mne_load_surface_geom() in mne_surface_io.c
if isinstance(fname, basestring):
rr, tris = read_surface(fname) # mne_read_triangle_file()
nvert = len(rr)
ntri = len(tris)
s = dict(rr=rr, tris=tris, use_tris=tris, ntri=ntri,
np=nvert)
elif isinstance(fname, dict):
s = fname
else:
raise RuntimeError('fname cannot be understood as str or dict')
if add_geom is True:
s = _complete_surface_info(s)
if norm_rr is True:
_normalize_vectors(s['rr'])
return s
##############################################################################
# SURFACE CREATION
def _get_ico_surface(grade):
"""Return an icosahedral surface of the desired grade"""
# always use verbose=False since users don't need to know we're pulling
# these from a file
ico_file_name = op.join(op.dirname(__file__), 'data',
'icos.fif.gz')
ico = read_bem_surfaces(ico_file_name, s_id=9000 + grade, verbose=False)
return ico
def _tessellate_sphere_surf(level, rad=1.0):
"""Return a surface structure instead of the details"""
rr, tris = _tessellate_sphere(level)
npt = len(rr) # called "npt" instead of "np" because of numpy...
ntri = len(tris)
nn = rr.copy()
rr *= rad
s = dict(rr=rr, np=npt, tris=tris, use_tris=tris, ntri=ntri, nuse=np,
nn=nn, inuse=np.ones(npt, int))
return s
def _norm_midpt(ai, bi, rr):
a = np.array([rr[aii] for aii in ai])
b = np.array([rr[bii] for bii in bi])
c = (a + b) / 2.
return c / np.sqrt(np.sum(c ** 2, 1))[:, np.newaxis]
def _tessellate_sphere(mylevel):
"""Create a tessellation of a unit sphere"""
# Vertices of a unit octahedron
rr = np.array([[1, 0, 0], [-1, 0, 0], # xplus, xminus
[0, 1, 0], [0, -1, 0], # yplus, yminus
[0, 0, 1], [0, 0, -1]], float) # zplus, zminus
tris = np.array([[0, 4, 2], [2, 4, 1], [1, 4, 3], [3, 4, 0],
[0, 2, 5], [2, 1, 5], [1, 3, 5], [3, 0, 5]], int)
# A unit octahedron
if mylevel < 1:
raise ValueError('# of levels must be >= 1')
# Reverse order of points in each triangle
# for counter-clockwise ordering
tris = tris[:, [2, 1, 0]]
# Subdivide each starting triangle (mylevel - 1) times
for _ in range(1, mylevel):
"""
Subdivide each triangle in the old approximation and normalize
the new points thus generated to lie on the surface of the unit
sphere.
Each input triangle with vertices labelled [0,1,2] as shown
below will be turned into four new triangles:
Make new points
a = (0+2)/2
b = (0+1)/2
c = (1+2)/2
1
/\ Normalize a, b, c
/ \
b/____\c Construct new triangles
/\ /\ [0,b,a]
/ \ / \ [b,1,c]
/____\/____\ [a,b,c]
0 a 2 [a,c,2]
"""
# use new method: first make new points (rr)
a = _norm_midpt(tris[:, 0], tris[:, 2], rr)
b = _norm_midpt(tris[:, 0], tris[:, 1], rr)
c = _norm_midpt(tris[:, 1], tris[:, 2], rr)
lims = np.cumsum([len(rr), len(a), len(b), len(c)])
aidx = np.arange(lims[0], lims[1])
bidx = np.arange(lims[1], lims[2])
cidx = np.arange(lims[2], lims[3])
rr = np.concatenate((rr, a, b, c))
# now that we have our points, make new triangle definitions
tris = np.array((np.c_[tris[:, 0], bidx, aidx],
np.c_[bidx, tris[:, 1], cidx],
np.c_[aidx, bidx, cidx],
np.c_[aidx, cidx, tris[:, 2]]), int).swapaxes(0, 1)
tris = np.reshape(tris, (np.prod(tris.shape[:2]), 3))
# Copy the resulting approximation into standard table
rr_orig = rr
rr = np.empty_like(rr)
nnode = 0
for k, tri in enumerate(tris):
for j in range(3):
coord = rr_orig[tri[j]]
# this is faster than cdist (no need for sqrt)
similarity = np.dot(rr[:nnode], coord)
idx = np.where(similarity > 0.99999)[0]
if len(idx) > 0:
tris[k, j] = idx[0]
else:
rr[nnode] = coord
tris[k, j] = nnode
nnode += 1
rr = rr[:nnode].copy()
return rr, tris
def _create_surf_spacing(surf, hemi, subject, stype, sval, ico_surf,
subjects_dir):
"""Load a surf and use the subdivided icosahedron to get points"""
# Based on load_source_space_surf_spacing() in load_source_space.c
surf = _read_surface_geom(surf)
if stype in ['ico', 'oct']:
### from mne_ico_downsample.c ###
surf_name = op.join(subjects_dir, subject, 'surf', hemi + '.sphere')
logger.info('Loading geometry from %s...' % surf_name)
from_surf = _read_surface_geom(surf_name, norm_rr=True, add_geom=False)
_normalize_vectors(ico_surf['rr'])
# Make the maps
logger.info('Mapping %s %s -> %s (%d) ...'
% (hemi, subject, stype, sval))
mmap = _compute_nearest(from_surf['rr'], ico_surf['rr'])
nmap = len(mmap)
surf['inuse'] = np.zeros(surf['np'], int)
for k in xrange(nmap):
if surf['inuse'][mmap[k]]:
# Try the nearest neighbors
neigh = _get_surf_neighbors(surf, mmap[k])
was = mmap[k]
inds = np.where(np.logical_not(surf['inuse'][neigh]))[0]
if len(inds) == 0:
raise RuntimeError('Could not find neighbor for vertex '
'%d / %d' % (k, nmap))
else:
mmap[k] = neigh[inds[-1]]
logger.info(' Source space vertex moved from %d to %d '
'because of double occupation', was, mmap[k])
elif mmap[k] < 0 or mmap[k] > surf['np']:
raise RuntimeError('Map number out of range (%d), this is '
'probably due to inconsistent surfaces. '
'Parts of the FreeSurfer reconstruction '
'need to be redone.' % mmap[k])
surf['inuse'][mmap[k]] = True
logger.info('Setting up the triangulation for the decimated '
'surface...')
surf['use_tris'] = np.array([mmap[ist] for ist in ico_surf['tris']],
np.int32)
else: # use_all is True
surf['inuse'] = np.ones(surf['np'], int)
surf['use_tris'] = None
if surf['use_tris'] is not None:
surf['nuse_tri'] = len(surf['use_tris'])
else:
surf['nuse_tri'] = 0
surf['nuse'] = np.sum(surf['inuse'])
surf['vertno'] = np.where(surf['inuse'])[0]
# set some final params
inds = np.arange(surf['np'])
sizes = np.sqrt(np.sum(surf['nn'] ** 2, axis=1))
surf['nn'][inds] = surf['nn'][inds] / sizes[:, np.newaxis]
surf['inuse'][sizes <= 0] = False
surf['nuse'] = np.sum(surf['inuse'])
surf['subject_his_id'] = subject
return surf
def write_surface(fname, coords, faces, create_stamp=''):
"""Write a triangular Freesurfer surface mesh
Accepts the same data format as is returned by read_surface().
Parameters
----------
fname : str
File to write.
coords : array, shape=(n_vertices, 3)
Coordinate points.
faces : int array, shape=(n_faces, 3)
Triangulation (each line contains indexes for three points which
together form a face).
create_stamp : str
Comment that is written to the beginning of the file. Can not contain
line breaks.
"""
if len(create_stamp.splitlines()) > 1:
raise ValueError("create_stamp can only contain one line")
with open(fname, 'w') as fid:
fid.write(pack('>3B', 255, 255, 254))
fid.writelines(('%s\n' % create_stamp, '\n'))
vnum = len(coords)
fnum = len(faces)
fid.write(pack('>2i', vnum, fnum))
fid.write(np.array(coords, dtype='>f4').tostring())
fid.write(np.array(faces, dtype='>i4').tostring())
###############################################################################
# Write
def write_bem_surface(fname, surf):
"""Write one bem surface
Parameters
----------
fname : string
File to write
surf : dict
A surface structured as obtained with read_bem_surfaces
"""
# Create the file and save the essentials
fid = start_file(fname)
start_block(fid, FIFF.FIFFB_BEM)
start_block(fid, FIFF.FIFFB_BEM_SURF)
write_int(fid, FIFF.FIFF_BEM_SURF_ID, surf['id'])
write_float(fid, FIFF.FIFF_BEM_SIGMA, surf['sigma'])
write_int(fid, FIFF.FIFF_BEM_SURF_NNODE, surf['np'])
write_int(fid, FIFF.FIFF_BEM_SURF_NTRI, surf['ntri'])
write_int(fid, FIFF.FIFF_BEM_COORD_FRAME, surf['coord_frame'])
write_float_matrix(fid, FIFF.FIFF_BEM_SURF_NODES, surf['rr'])
if 'nn' in surf and surf['nn'] is not None and len(surf['nn']) > 0:
write_float_matrix(fid, FIFF.FIFF_MNE_SOURCE_SPACE_NORMALS, surf['nn'])
# index start at 0 in Python
write_int_matrix(fid, FIFF.FIFF_BEM_SURF_TRIANGLES, surf['tris'] + 1)
end_block(fid, FIFF.FIFFB_BEM_SURF)
end_block(fid, FIFF.FIFFB_BEM)
end_file(fid)
def _decimate_surface(points, triangles, reduction):
"""Aux function"""
if 'DISPLAY' not in os.environ and sys.platform != 'win32':
os.environ['ETS_TOOLKIT'] = 'null'
try:
from tvtk.api import tvtk
except ImportError:
raise ValueError('This function requires the TVTK package to be '
'installed')
if triangles.max() > len(points) - 1:
raise ValueError('The triangles refer to undefined points. '
'Please check your mesh.')
src = tvtk.PolyData(points=points, polys=triangles)
decimate = tvtk.QuadricDecimation(input=src, target_reduction=reduction)
decimate.update()
out = decimate.output
tris = out.polys.to_array()
# n-tuples + interleaved n-next -- reshape trick
return out.points.to_array(), tris.reshape(tris.size / 4, 4)[:, 1:]
def decimate_surface(points, triangles, n_triangles):
""" Decimate surface data
Note. Requires TVTK to be installed for this to function.
Note. If an if an odd target number was requested,
the ``quadric decimation`` algorithm used results in the
next even number of triangles. For example a reduction request to 30001
triangles will result in 30000 triangles.
Parameters
----------
points : ndarray
The surface to be decimated, a 3 x number of points array.
triangles : ndarray
The surface to be decimated, a 3 x number of triangles array.
n_triangles : int
The desired number of triangles.
Returns
-------
points : ndarray
The decimated points.
triangles : ndarray
The decimated triangles.
"""
reduction = 1 - (float(n_triangles) / len(triangles))
return _decimate_surface(points, triangles, reduction)
###############################################################################
# Morph maps
@verbose
def read_morph_map(subject_from, subject_to, subjects_dir=None,
verbose=None):
"""Read morph map
Morph maps can be generated with mne_make_morph_maps. If one isn't
available, it will be generated automatically and saved to the
``subjects_dir/morph_maps`` directory.
Parameters
----------
subject_from : string
Name of the original subject as named in the SUBJECTS_DIR.
subject_to : string
Name of the subject on which to morph as named in the SUBJECTS_DIR.
subjects_dir : string
Path to SUBJECTS_DIR is not set in the environment.
verbose : bool, str, int, or None
If not None, override default verbose level (see mne.verbose).
Returns
-------
left_map, right_map : sparse matrix
The morph maps for the 2 hemispheres.
"""
subjects_dir = get_subjects_dir(subjects_dir)
# First check for morph-map dir existence
mmap_dir = op.join(subjects_dir, 'morph-maps')
if not op.isdir(mmap_dir):
try:
os.mkdir(mmap_dir)
except:
logger.warn('Could not find or make morph map directory "%s"'
% mmap_dir)
# Does the file exist
fname = op.join(mmap_dir, '%s-%s-morph.fif' % (subject_from, subject_to))
if not op.exists(fname):
fname = op.join(mmap_dir, '%s-%s-morph.fif'
% (subject_to, subject_from))
if not op.exists(fname):
logger.warning('Morph map "%s" does not exist, '
'creating it and saving it to disk (this may take '
'a few minutes)' % fname)
logger.info('Creating morph map %s -> %s'
% (subject_from, subject_to))
mmap_1 = _make_morph_map(subject_from, subject_to, subjects_dir)
logger.info('Creating morph map %s -> %s'
% (subject_to, subject_from))
mmap_2 = _make_morph_map(subject_to, subject_from, subjects_dir)
try:
_write_morph_map(fname, subject_from, subject_to,
mmap_1, mmap_2)
except Exception as exp:
logger.warn('Could not write morph-map file "%s" (error: %s)'
% (fname, exp))
return mmap_1
f, tree, _ = fiff_open(fname)
with f as fid:
# Locate all maps
maps = dir_tree_find(tree, FIFF.FIFFB_MNE_MORPH_MAP)
if len(maps) == 0:
raise ValueError('Morphing map data not found')
# Find the correct ones
left_map = None
right_map = None
for m in maps:
tag = find_tag(fid, m, FIFF.FIFF_MNE_MORPH_MAP_FROM)
if tag.data == subject_from:
tag = find_tag(fid, m, FIFF.FIFF_MNE_MORPH_MAP_TO)
if tag.data == subject_to:
# Names match: which hemishere is this?
tag = find_tag(fid, m, FIFF.FIFF_MNE_HEMI)
if tag.data == FIFF.FIFFV_MNE_SURF_LEFT_HEMI:
tag = find_tag(fid, m, FIFF.FIFF_MNE_MORPH_MAP)
left_map = tag.data
logger.info(' Left-hemisphere map read.')
elif tag.data == FIFF.FIFFV_MNE_SURF_RIGHT_HEMI:
tag = find_tag(fid, m, FIFF.FIFF_MNE_MORPH_MAP)
right_map = tag.data
logger.info(' Right-hemisphere map read.')
if left_map is None:
raise ValueError('Left hemisphere map not found in %s' % fname)
if right_map is None:
raise ValueError('Left hemisphere map not found in %s' % fname)
return left_map, right_map
def _write_morph_map(fname, subject_from, subject_to, mmap_1, mmap_2):
"""Write a morph map to disk"""
fid = start_file(fname)
assert len(mmap_1) == 2
assert len(mmap_2) == 2
hemis = [FIFF.FIFFV_MNE_SURF_LEFT_HEMI, FIFF.FIFFV_MNE_SURF_RIGHT_HEMI]
for m, hemi in zip(mmap_1, hemis):
start_block(fid, FIFF.FIFFB_MNE_MORPH_MAP)
write_string(fid, FIFF.FIFF_MNE_MORPH_MAP_FROM, subject_from)
write_string(fid, FIFF.FIFF_MNE_MORPH_MAP_TO, subject_to)
write_int(fid, FIFF.FIFF_MNE_HEMI, hemi)
write_float_sparse_rcs(fid, FIFF.FIFF_MNE_MORPH_MAP, m)
end_block(fid, FIFF.FIFFB_MNE_MORPH_MAP)
for m, hemi in zip(mmap_2, hemis):
start_block(fid, FIFF.FIFFB_MNE_MORPH_MAP)
write_string(fid, FIFF.FIFF_MNE_MORPH_MAP_FROM, subject_to)
write_string(fid, FIFF.FIFF_MNE_MORPH_MAP_TO, subject_from)
write_int(fid, FIFF.FIFF_MNE_HEMI, hemi)
write_float_sparse_rcs(fid, FIFF.FIFF_MNE_MORPH_MAP, m)
end_block(fid, FIFF.FIFFB_MNE_MORPH_MAP)
end_file(fid)
def _get_tri_dist(p, q, p0, q0, a, b, c, dist):
"""Auxiliary function for getting the distance to a triangle edge"""
return np.sqrt((p - p0) * (p - p0) * a +
(q - q0) * (q - q0) * b +
(p - p0) * (q - q0) * c +
dist * dist)
def _get_tri_supp_geom(tris, rr):
"""Create supplementary geometry information using tris and rrs"""
r1 = rr[tris[:, 0], :]
r12 = rr[tris[:, 1], :] - r1
r13 = rr[tris[:, 2], :] - r1
r1213 = np.array([r12, r13]).swapaxes(0, 1)
a = np.sum(r12 * r12, axis=1)
b = np.sum(r13 * r13, axis=1)
c = np.sum(r12 * r13, axis=1)
mat = np.rollaxis(np.array([[b, -c], [-c, a]]), 2)
mat /= (a * b - c * c)[:, np.newaxis, np.newaxis]
nn = fast_cross_3d(r12, r13)
_normalize_vectors(nn)
return dict(r1=r1, r12=r12, r13=r13, r1213=r1213,
a=a, b=b, c=c, mat=mat, nn=nn)
@verbose
def _make_morph_map(subject_from, subject_to, subjects_dir=None):
"""Construct morph map from one subject to another
Note that this is close, but not exactly like the C version.
For example, parts are more accurate due to double precision,
so expect some small morph-map differences!
Note: This seems easily parallelizable, but the overhead
of pickling all the data structures makes it less efficient
than just running on a single core :(
"""
subjects_dir = get_subjects_dir(subjects_dir)
morph_maps = list()
# add speedy short-circuit for self-maps
if subject_from == subject_to:
for hemi in ['lh', 'rh']:
fname = op.join(subjects_dir, subject_from, 'surf',
'%s.sphere.reg' % hemi)
from_pts = read_surface(fname, verbose=False)[0]
n_pts = len(from_pts)
morph_maps.append(sparse.eye(n_pts, n_pts, format='csr'))
return morph_maps
for hemi in ['lh', 'rh']:
# load surfaces and normalize points to be on unit sphere
fname = op.join(subjects_dir, subject_from, 'surf',
'%s.sphere.reg' % hemi)
from_pts, from_tris = read_surface(fname, verbose=False)
n_from_pts = len(from_pts)
_normalize_vectors(from_pts)
tri_geom = _get_tri_supp_geom(from_tris, from_pts)
fname = op.join(subjects_dir, subject_to, 'surf',
'%s.sphere.reg' % hemi)
to_pts = read_surface(fname, verbose=False)[0]
n_to_pts = len(to_pts)
_normalize_vectors(to_pts)
# from surface: get nearest neighbors, find triangles for each vertex
nn_pts_idx = _compute_nearest(from_pts, to_pts)
from_pt_tris = _triangle_neighbors(from_tris, len(from_pts))
from_pt_tris = [from_pt_tris[pt_idx] for pt_idx in nn_pts_idx]
# find triangle in which point lies and assoc. weights
nn_tri_inds = []
nn_tris_weights = []
for pt_tris, to_pt in zip(from_pt_tris, to_pts):
p, q, idx, dist = _find_nearest_tri_pt(pt_tris, to_pt, tri_geom)
nn_tri_inds.append(idx)
nn_tris_weights.extend([1. - (p + q), p, q])
nn_tris = from_tris[nn_tri_inds]
row_ind = np.repeat(np.arange(n_to_pts), 3)
this_map = sparse.csr_matrix((nn_tris_weights,
(row_ind, nn_tris.ravel())),
shape=(n_to_pts, n_from_pts))
morph_maps.append(this_map)
return morph_maps
def _find_nearest_tri_pt(pt_tris, to_pt, tri_geom, run_all=False):
"""Find nearest point mapping to a set of triangles
If run_all is False, if the point lies within a triangle, it stops.
If run_all is True, edges of other triangles are checked in case
those (somehow) are closer.
"""
# The following dense code is equivalent to the following:
# rr = r1[pt_tris] - to_pts[ii]
# v1s = np.sum(rr * r12[pt_tris], axis=1)
# v2s = np.sum(rr * r13[pt_tris], axis=1)
# aas = a[pt_tris]
# bbs = b[pt_tris]
# ccs = c[pt_tris]
# dets = aas * bbs - ccs * ccs
# pp = (bbs * v1s - ccs * v2s) / dets
# qq = (aas * v2s - ccs * v1s) / dets
# pqs = np.array(pp, qq)
# This einsum is equivalent to doing:
# pqs = np.array([np.dot(x, y) for x, y in zip(r1213, r1-to_pt)])
r1 = tri_geom['r1'][pt_tris]
rrs = to_pt - r1
tri_nn = tri_geom['nn'][pt_tris]
vect = np.einsum('ijk,ik->ij', tri_geom['r1213'][pt_tris], rrs)
mats = tri_geom['mat'][pt_tris]
# This einsum is equivalent to doing:
# pqs = np.array([np.dot(m, v) for m, v in zip(mats, vect)]).T
pqs = np.einsum('ijk,ik->ji', mats, vect)
found = False
dists = np.sum(rrs * tri_nn, axis=1)
# There can be multiple (sadness), find closest
idx = np.where(np.all(pqs >= 0., axis=0))[0]
idx = idx[np.where(np.all(pqs[:, idx] <= 1., axis=0))[0]]
idx = idx[np.where(np.sum(pqs[:, idx], axis=0) < 1.)[0]]
dist = np.inf
if len(idx) > 0:
found = True
pt = idx[np.argmin(np.abs(dists[idx]))]
p, q = pqs[:, pt]
dist = dists[pt]
# re-reference back to original numbers
pt = pt_tris[pt]
if found is False or run_all is True:
# don't include ones that we might have found before
s = np.setdiff1d(np.arange(len(pt_tris)), idx) # ones to check sides
# Tough: must investigate the sides
pp, qq, ptt, distt = _nearest_tri_edge(pt_tris[s], to_pt, pqs[:, s],
dists[s], tri_geom)
if np.abs(distt) < np.abs(dist):
p, q, pt, dist = pp, qq, ptt, distt
return p, q, pt, dist
def _nearest_tri_edge(pt_tris, to_pt, pqs, dist, tri_geom):
"""Get nearest location from a point to the edge of a set of triangles"""
# We might do something intelligent here. However, for now
# it is ok to do it in the hard way
aa = tri_geom['a'][pt_tris]
bb = tri_geom['b'][pt_tris]
cc = tri_geom['c'][pt_tris]
pp = pqs[0]
qq = pqs[1]
# Find the nearest point from a triangle:
# Side 1 -> 2
p0 = np.minimum(np.maximum(pp + 0.5 * (qq * cc) / aa,
0.0), 1.0)
q0 = np.zeros_like(p0)
# Side 2 -> 3
t1 = (0.5 * ((2.0 * aa - cc) * (1.0 - pp)
+ (2.0 * bb - cc) * qq) / (aa + bb - cc))
t1 = np.minimum(np.maximum(t1, 0.0), 1.0)
p1 = 1.0 - t1
q1 = t1
# Side 1 -> 3
q2 = np.minimum(np.maximum(qq + 0.5 * (pp * cc)
/ bb, 0.0), 1.0)
p2 = np.zeros_like(q2)
# figure out which one had the lowest distance
dist0 = _get_tri_dist(pp, qq, p0, q0, aa, bb, cc, dist)
dist1 = _get_tri_dist(pp, qq, p1, q1, aa, bb, cc, dist)
dist2 = _get_tri_dist(pp, qq, p2, q2, aa, bb, cc, dist)
pp = np.r_[p0, p1, p2]
qq = np.r_[q0, q1, q2]
dists = np.r_[dist0, dist1, dist2]
ii = np.argmin(np.abs(dists))
p, q, pt, dist = pp[ii], qq[ii], pt_tris[ii % len(pt_tris)], dists[ii]
return p, q, pt, dist
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