# Authors: The MNE-Python contributors.
# License: BSD-3-Clause
# Copyright the MNE-Python contributors.
# Many of the computations in this code were derived from Matti Hämäläinen's
# C code.
import json
import time
import warnings
from collections import OrderedDict
from copy import deepcopy
from functools import lru_cache, partial
from glob import glob
from os import path as op
from pathlib import Path
import numpy as np
from scipy.ndimage import binary_dilation
from scipy.sparse import coo_array, csr_array
from scipy.spatial import ConvexHull, Delaunay
from scipy.spatial.distance import cdist
from ._fiff.constants import FIFF
from ._fiff.pick import pick_types
from .fixes import bincount, jit, prange
from .parallel import parallel_func
from .transforms import (
Transform,
_angle_between_quats,
_cart_to_sph,
_fit_matched_points,
_get_trans,
_MatchedDisplacementFieldInterpolator,
_pol_to_cart,
apply_trans,
transform_surface_to,
)
from .utils import (
_check_fname,
_check_freesurfer_home,
_check_option,
_ensure_int,
_hashable_ndarray,
_import_nibabel,
_pl,
_soft_import,
_TempDir,
_validate_type,
fill_doc,
get_subjects_dir,
logger,
run_subprocess,
verbose,
warn,
)
_helmet_path = Path(__file__).parent / "data" / "helmets"
###############################################################################
# AUTOMATED SURFACE FINDING
@verbose
def get_head_surf(
subject, source=("bem", "head"), subjects_dir=None, on_defects="raise", verbose=None
):
"""Load the subject head surface.
Parameters
----------
subject : str
Subject name.
source : str | list of str
Type to load. Common choices would be ``'bem'`` or ``'head'``. We first
try loading ``'$SUBJECTS_DIR/$SUBJECT/bem/$SUBJECT-$SOURCE.fif'``, and
then look for ``'$SUBJECT*$SOURCE.fif'`` in the same directory by going
through all files matching the pattern. The head surface will be read
from the first file containing a head surface. Can also be a list
to try multiple strings.
subjects_dir : path-like | None
Path to the ``SUBJECTS_DIR``. If None, the path is obtained by using
the environment variable ``SUBJECTS_DIR``.
%(on_defects)s
.. versionadded:: 1.0
%(verbose)s
Returns
-------
surf : dict
The head surface.
"""
return _get_head_surface(
subject=subject, source=source, subjects_dir=subjects_dir, on_defects=on_defects
)
# TODO this should be refactored with mne._freesurfer._get_head_surface
def _get_head_surface(subject, source, subjects_dir, on_defects, raise_error=True):
"""Load the subject head surface."""
from .bem import read_bem_surfaces
# Load the head surface from the BEM
subjects_dir = str(get_subjects_dir(subjects_dir, raise_error=True))
_validate_type(subject, str, "subject")
# use realpath to allow for linked surfaces (c.f. MNE manual 196-197)
if isinstance(source, str):
source = [source]
surf = None
for this_source in source:
this_head = op.realpath(
op.join(subjects_dir, subject, "bem", f"{subject}-{this_source}.fif")
)
if op.exists(this_head):
surf = read_bem_surfaces(
this_head,
True,
FIFF.FIFFV_BEM_SURF_ID_HEAD,
on_defects=on_defects,
verbose=False,
)
else:
# let's do a more sophisticated search
path = op.join(subjects_dir, subject, "bem")
if not op.isdir(path):
raise OSError(f'Subject bem directory "{path}" does not exist.')
files = sorted(glob(op.join(path, f"{subject}*{this_source}.fif")))
for this_head in files:
try:
surf = read_bem_surfaces(
this_head,
True,
FIFF.FIFFV_BEM_SURF_ID_HEAD,
on_defects=on_defects,
verbose=False,
)
except ValueError:
pass
else:
break
if surf is not None:
break
if surf is None:
if raise_error:
raise OSError(
f'No file matching "{subject}*{this_source}" and containing a head '
"surface found."
)
else:
return surf
logger.info(f"Using surface from {this_head}.")
return surf
# New helmets can be written for example with:
#
# import os.path as op
# import mne
# from mne.io.constants import FIFF
# surf = mne.read_surface('kernel.obj', return_dict=True)[-1]
# surf['rr'] *= 1000 # needs to be in mm
# mne.surface.complete_surface_info(surf, copy=False, do_neighbor_tri=False)
# surf['coord_frame'] = FIFF.FIFFV_COORD_DEVICE
# surfs = mne.bem._surfaces_to_bem(
# [surf], ids=[FIFF.FIFFV_MNE_SURF_MEG_HELMET], sigmas=[1.],
# incomplete='ignore')
# del surfs[0]['sigma']
# bem_fname = op.join(op.dirname(mne.__file__), 'data', 'helmets',
# 'kernel.fif.gz')
# mne.write_bem_surfaces(bem_fname, surfs, overwrite=True)
@verbose
def get_meg_helmet_surf(info, trans=None, *, upsampling=1, verbose=None):
"""Load the MEG helmet associated with the MEG sensors.
Parameters
----------
%(info_not_none)s
trans : dict
The head<->MRI transformation, usually obtained using
read_trans(). Can be None, in which case the surface will
be in head coordinates instead of MRI coordinates.
%(helmet_upsampling)s
%(verbose)s
Returns
-------
surf : dict
The MEG helmet as a surface.
Notes
-----
A built-in helmet is loaded if possible. If not, a helmet surface
will be approximated based on the sensor locations.
"""
from .bem import _fit_sphere, read_bem_surfaces
from .channels.channels import _get_meg_system
_validate_type(upsampling, "int", "upsampling")
system, have_helmet = _get_meg_system(info)
incomplete = False
if have_helmet:
logger.info(f"Getting helmet for system {system}")
fname = _helmet_path / f"{system}.fif.gz"
surf = read_bem_surfaces(
fname, False, FIFF.FIFFV_MNE_SURF_MEG_HELMET, verbose=False
)
surf = _scale_helmet_to_sensors(system, surf, info)
else:
rr = np.array(
[
info["chs"][pick]["loc"][:3]
for pick in pick_types(info, meg=True, ref_meg=False, exclude=())
]
)
logger.info(
"Getting helmet for system %s (derived from %d MEG channel locations)",
system,
len(rr),
)
hull = ConvexHull(rr)
rr = rr[np.unique(hull.simplices)]
R, center = _fit_sphere(rr)
sph = _cart_to_sph(rr - center)[:, 1:]
# add a point at the front of the helmet (where the face should be):
# 90 deg az and maximal el (down from Z/up axis)
front_sph = [[np.pi / 2.0, sph[:, 1].max()]]
sph = np.concatenate((sph, front_sph))
xy = _pol_to_cart(sph[:, ::-1])
tris = Delaunay(xy).simplices
# remove the frontal point we added from the simplices
tris = tris[(tris != len(sph) - 1).all(-1)]
tris = _reorder_ccw(rr, tris)
surf = dict(rr=rr, tris=tris)
incomplete = True
if upsampling > 1:
# Use VTK (could also use Butterfly but Loop is smoother)
pv = _soft_import("pyvista", "upsample a mesh")
factor = 4 ** (upsampling - 1)
rr, tris = surf["rr"], surf["tris"]
logger.info(
f"Upsampling from {len(rr)} to {len(rr) * factor} vertices ({upsampling=})"
)
tris = np.c_[np.full(len(tris), 3), tris]
mesh = pv.PolyData(rr, tris)
mesh = mesh.subdivide(upsampling - 1, subfilter="linear")
rr, tris = mesh.points, mesh.faces.reshape(-1, 4)[:, 1:]
tris = _reorder_ccw(rr, tris)
surf = dict(rr=rr, tris=tris)
incomplete = True
if incomplete:
complete_surface_info(surf, copy=False, verbose=False)
# Ignore what the file says, it's in device coords and we want MRI coords
surf["coord_frame"] = FIFF.FIFFV_COORD_DEVICE
dev_head_t = info["dev_head_t"]
if dev_head_t is None:
dev_head_t = Transform("meg", "head")
transform_surface_to(surf, "head", dev_head_t)
if trans is not None:
transform_surface_to(surf, "mri", trans)
return surf
def _scale_helmet_to_sensors(system, surf, info):
fname = _helmet_path / f"{system}_ch_pos.txt"
if not fname.is_file():
return surf
with open(fname) as fid:
ch_pos_from = json.load(fid)
# find correspondence
fro, to = list(), list()
for key, f_ in ch_pos_from.items():
t_ = [ch["loc"][:3] for ch in info["chs"] if ch["ch_name"].startswith(key)]
if not len(t_):
continue
fro.append(f_)
to.append(np.mean(t_, axis=0))
if len(fro) < 4:
logger.info(
"Using untransformed helmet, not enough sensors found to deform to match "
f"acquisition based on sensor positions (got {len(fro)}, need at least 4)"
)
return surf
fro = np.array(fro, float)
to = np.array(to, float)
delta = np.ptp(surf["rr"], axis=0) * 0.1 # 10% beyond bounds
extrema = np.array([surf["rr"].min(0) - delta, surf["rr"].max(0) + delta])
interp = _MatchedDisplacementFieldInterpolator(fro, to, extrema=extrema)
new_rr = interp(surf["rr"])
try:
quat, sc = _fit_matched_points(surf["rr"], new_rr)
except np.linalg.LinAlgError as exc:
logger.info(
f"Using untransformed helmet, deformation using {len(fro)} points "
f"failed ({exc})"
)
return surf
rot = np.rad2deg(_angle_between_quats(quat[:3]))
tr = 1000 * np.linalg.norm(quat[3:])
logger.info(
f" Deforming CAD helmet to match {len(fro)} acquisition sensor positions:"
)
logger.info(f" 1. Affine: {rot:0.1f}°, {tr:0.1f} mm, {sc:0.2f}× scale")
deltas = interp._last_deltas * 1000
mu, mx = np.mean(deltas), np.max(deltas)
logger.info(f" 2. Nonlinear displacement: mean={mu:0.1f}, max={mx:0.1f} mm")
surf["rr"] = new_rr
complete_surface_info(surf, copy=False, verbose=False)
return surf
def _reorder_ccw(rrs, tris):
"""Reorder tris of a convex hull to be wound counter-clockwise."""
# This ensures that rendering with front-/back-face culling works properly
com = np.mean(rrs, axis=0)
rr_tris = rrs[tris]
dirs = np.sign(
(
np.cross(rr_tris[:, 1] - rr_tris[:, 0], rr_tris[:, 2] - rr_tris[:, 0])
* (rr_tris[:, 0] - com)
).sum(-1)
).astype(int)
return np.array([t[::d] for d, t in zip(dirs, tris)])
###############################################################################
# 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, shape (..., 3).
y : array
Input array 2, shape (..., 3).
Returns
-------
z : array, shape (..., 3)
Cross product of x and y along the last dimension.
Notes
-----
x and y must broadcast against each other.
"""
assert x.ndim >= 1
assert y.ndim >= 1
assert x.shape[-1] == 3
assert y.shape[-1] == 3
if max(x.size, y.size) >= 500:
out = np.empty(np.broadcast(x, y).shape)
_jit_cross(out, x, y)
return out
else:
return np.cross(x, y)
@jit()
def _jit_cross(out, x, y):
out[..., 0] = x[..., 1] * y[..., 2]
out[..., 0] -= x[..., 2] * y[..., 1]
out[..., 1] = x[..., 2] * y[..., 0]
out[..., 1] -= x[..., 0] * y[..., 2]
out[..., 2] = x[..., 0] * y[..., 1]
out[..., 2] -= x[..., 1] * y[..., 0]
@jit()
def _fast_cross_nd_sum(a, b, c):
"""Fast cross and sum."""
return (
(a[..., 1] * b[..., 2] - a[..., 2] * b[..., 1]) * c[..., 0]
+ (a[..., 2] * b[..., 0] - a[..., 0] * b[..., 2]) * c[..., 1]
+ (a[..., 0] * b[..., 1] - a[..., 1] * b[..., 0]) * c[..., 2]
)
@jit()
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 vi in range(3):
verts = tris[:, vi]
for idx in range(3): # x, y, z
nn[:, idx] += bincount(verts, weights=tri_nn[:, idx], minlength=npts)
return nn
def _triangle_neighbors(tris, npts):
"""Efficiently compute vertex neighboring triangles."""
# this code replaces the following, but is faster (vectorized):
# neighbor_tri = [list() for _ in range(npts)]
# for ti, tri in enumerate(tris):
# for t in tri:
# neighbor_tri[t].append(ti)
rows = tris.ravel()
cols = np.repeat(np.arange(len(tris)), 3)
data = np.ones(len(cols))
csr = coo_array((data, (rows, cols)), shape=(npts, len(tris))).tocsr()
neighbor_tri = [
csr.indices[start:stop] for start, stop in zip(csr.indptr[:-1], csr.indptr[1:])
]
assert len(neighbor_tri) == npts
return neighbor_tri
@jit()
def _triangle_coords(r, best, r1, nn, r12, r13, a, b, c): # pragma: no cover
"""Get coordinates of a vertex projected to a triangle."""
r1 = r1[best]
tri_nn = nn[best]
r12 = r12[best]
r13 = r13[best]
a = a[best]
b = b[best]
c = 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 _project_onto_surface(
rrs, surf, project_rrs=False, return_nn=False, method="accurate"
):
"""Project points onto (scalp) surface."""
if method == "accurate":
surf_geom = _get_tri_supp_geom(surf)
pt_tris = np.empty((0,), int)
pt_lens = np.zeros(len(rrs) + 1, int)
out = _find_nearest_tri_pts(rrs, pt_tris, pt_lens, reproject=True, **surf_geom)
if project_rrs: #
out += (np.einsum("ij,ijk->ik", out[0], surf["rr"][surf["tris"][out[1]]]),)
if return_nn:
out += (surf_geom["nn"][out[1]],)
else: # nearest neighbor
assert project_rrs
idx = _compute_nearest(surf["rr"], rrs)
out = (None, None, surf["rr"][idx])
if return_nn:
surf_geom = _get_tri_supp_geom(surf)
nn = _accumulate_normals(
surf["tris"].astype(int), surf_geom["nn"], len(surf["rr"])
)
nn = nn[idx]
_normalize_vectors(nn)
out += (nn,)
return out
def _normal_orth(nn):
"""Compute orthogonal basis given a normal."""
assert nn.shape[-1:] == (3,)
prod = np.einsum("...i,...j->...ij", nn, nn)
_, u = np.linalg.eigh(np.eye(3) - prod)
u = u[..., ::-1]
# Make sure that ez is in the direction of nn
signs = np.sign(np.matmul(nn[..., np.newaxis, :], u[..., -1:]))
signs[signs == 0] = 1
u *= signs
return u.swapaxes(-1, -2)
@verbose
def complete_surface_info(
surf, do_neighbor_vert=False, copy=True, do_neighbor_tri=True, *, verbose=None
):
"""Complete surface information.
Parameters
----------
surf : dict
The surface.
do_neighbor_vert : bool
If True (default False), add neighbor vertex information.
copy : bool
If True (default), make a copy. If False, operate in-place.
do_neighbor_tri : bool
If True (default), compute triangle neighbors.
%(verbose)s
Returns
-------
surf : dict
The transformed surface.
"""
if copy:
surf = deepcopy(surf)
# based on mne_source_space_add_geometry_info() in mne_add_geometry_info.c
# Main triangulation [mne_add_triangle_data()]
surf["ntri"] = surf.get("ntri", len(surf["tris"]))
surf["np"] = surf.get("np", len(surf["rr"]))
surf["tri_area"] = np.zeros(surf["ntri"])
r1 = surf["rr"][surf["tris"][:, 0], :]
r2 = surf["rr"][surf["tris"][:, 1], :]
r3 = surf["rr"][surf["tris"][:, 2], :]
surf["tri_cent"] = (r1 + r2 + r3) / 3.0
surf["tri_nn"] = fast_cross_3d((r2 - r1), (r3 - r1))
# Triangle normals and areas
surf["tri_area"] = _normalize_vectors(surf["tri_nn"]) / 2.0
zidx = np.where(surf["tri_area"] == 0)[0]
if len(zidx) > 0:
logger.info(f" Warning: zero size triangles: {zidx}")
# Find neighboring triangles, accumulate vertex normals, normalize
logger.info(" Triangle neighbors and vertex normals...")
surf["nn"] = _accumulate_normals(
surf["tris"].astype(int), surf["tri_nn"], surf["np"]
)
_normalize_vectors(surf["nn"])
# Check for topological defects
if do_neighbor_tri:
surf["neighbor_tri"] = _triangle_neighbors(surf["tris"], surf["np"])
zero, fewer = list(), list()
for ni, n in enumerate(surf["neighbor_tri"]):
if len(n) < 3:
if len(n) == 0:
zero.append(ni)
else:
fewer.append(ni)
surf["neighbor_tri"][ni] = np.array([], int)
if len(zero) > 0:
logger.info(
" Vertices do not have any neighboring triangles: "
f"[{', '.join(str(z) for z in zero)}]"
)
if len(fewer) > 0:
fewer = ", ".join(str(f) for f in fewer)
logger.info(
" Vertices have fewer than three neighboring triangles, removing "
f"neighbors: [{fewer}]"
)
# Determine the neighboring vertices and fix errors
if do_neighbor_vert is True:
logger.info(" Vertex neighbors...")
surf["neighbor_vert"] = [
_get_surf_neighbors(surf, k) for k in range(surf["np"])
]
return surf
def _get_surf_neighbors(surf, k):
"""Calculate the surface neighbors based on triangulation."""
verts = set()
for v in surf["tris"][surf["neighbor_tri"][k]].flat:
verts.add(v)
verts.remove(k)
verts = np.array(sorted(verts))
assert np.all(verts < surf["np"])
nneighbors = len(verts)
nneigh_max = len(surf["neighbor_tri"][k])
if nneighbors > nneigh_max:
raise RuntimeError(f"Too many neighbors for vertex {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.linalg.norm(rr, axis=1)
mask = size > 0
rr[mask] /= size[mask, np.newaxis] # operate in-place
return size
class _CDist:
"""Wrapper for cdist that uses a Tree-like pattern."""
def __init__(self, xhs):
self._xhs = xhs
def query(self, rr):
nearest = list()
dists = list()
for r in rr:
d = cdist(r[np.newaxis, :], self._xhs)
idx = np.argmin(d)
nearest.append(idx)
dists.append(d[0, idx])
return np.array(dists), np.array(nearest)
def _compute_nearest(xhs, rr, method="BallTree", return_dists=False):
"""Find nearest neighbors.
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.
method : str
The query method. If scikit-learn and scipy<1.0 are installed,
it will fall back to the slow brute-force search.
return_dists : bool
If True, return associated distances.
Returns
-------
nearest : array, shape=(n_query,)
Index of nearest neighbor in xhs for every point in rr.
distances : array, shape=(n_query,)
The distances. Only returned if return_dists is True.
"""
if xhs.size == 0 or rr.size == 0:
if return_dists:
return np.array([], int), np.array([])
return np.array([], int)
tree = _DistanceQuery(xhs, method=method)
out = tree.query(rr)
return out[::-1] if return_dists else out[1]
def _safe_query(rr, func, reduce=False, **kwargs):
if len(rr) == 0:
return np.array([]), np.array([], int)
out = func(rr)
out = [out[0][:, 0], out[1][:, 0]] if reduce else out
return out
class _DistanceQuery:
"""Wrapper for fast distance queries."""
def __init__(self, xhs, method="BallTree"):
assert method in ("BallTree", "KDTree", "cdist")
# Fastest for our problems: balltree
if method == "BallTree":
try:
from sklearn.neighbors import BallTree
except ImportError:
logger.info(
"Nearest-neighbor searches will be significantly "
"faster if scikit-learn is installed."
)
method = "KDTree"
else:
self.query = partial(
_safe_query,
func=BallTree(xhs).query,
reduce=True,
return_distance=True,
)
# Then KDTree
if method == "KDTree":
from scipy.spatial import KDTree
self.query = KDTree(xhs).query
# Then the worst: cdist
if method == "cdist":
self.query = _CDist(xhs).query
self.data = xhs
@verbose
def _points_outside_surface(rr, surf, n_jobs=None, verbose=None):
"""Check whether points are outside a surface.
Parameters
----------
rr : ndarray
Nx3 array of points to check.
surf : dict
Surface with entries "rr" and "tris".
Returns
-------
outside : ndarray
1D logical array of size N for which points are outside the surface.
"""
rr = np.atleast_2d(rr)
assert rr.shape[1] == 3
parallel, p_fun, n_jobs = parallel_func(_get_solids, n_jobs)
tot_angles = parallel(
p_fun(surf["rr"][tris], rr) for tris in np.array_split(surf["tris"], n_jobs)
)
return np.abs(np.sum(tot_angles, axis=0) / (2 * np.pi) - 1.0) > 1e-5
def _surface_to_polydata(surf):
import pyvista as pv
vertices = np.array(surf["rr"])
if "tris" not in surf:
return pv.PolyData(vertices)
else:
triangles = np.array(surf["tris"])
triangles = np.c_[np.full(len(triangles), 3), triangles]
return pv.PolyData(vertices, triangles)
def _polydata_to_surface(pd, normals=True):
from pyvista import PolyData
if not isinstance(pd, PolyData):
pd = PolyData(pd)
out = dict(rr=pd.points, tris=pd.faces.reshape(-1, 4)[:, 1:])
if normals:
out["nn"] = pd.point_normals
return out
class _CheckInside:
"""Efficiently check if points are inside a surface."""
@verbose
def __init__(self, surf, *, mode="old", verbose=None):
assert mode in ("pyvista", "old")
self.mode = mode
t0 = time.time()
self.surf = surf
if self.mode == "pyvista":
self._init_pyvista()
else:
self._init_old()
logger.debug(
f"Setting up {mode} interior check for {len(self.surf['rr'])} "
f"points took {(time.time() - t0) * 1000:0.1f} ms"
)
def _init_old(self):
self.inner_r = None
self.cm = self.surf["rr"].mean(0)
# We could use Delaunay or ConvexHull here, Delaunay is slightly slower
# to construct but faster to evaluate
# See https://stackoverflow.com/questions/16750618/whats-an-efficient-way-to-find-if-a-point-lies-in-the-convex-hull-of-a-point-cl # noqa
self.del_tri = Delaunay(self.surf["rr"])
if self.del_tri.find_simplex(self.cm) >= 0:
# Immediately cull some points from the checks
dists = np.linalg.norm(self.surf["rr"] - self.cm, axis=-1)
self.inner_r = dists.min()
self.outer_r = dists.max()
def _init_pyvista(self):
if not isinstance(self.surf, dict):
self.pdata = self.surf
self.surf = _polydata_to_surface(self.pdata)
else:
self.pdata = _surface_to_polydata(self.surf).clean()
@verbose
def __call__(self, rr, n_jobs=None, verbose=None):
n_orig = len(rr)
logger.info(
f"Checking surface interior status for {n_orig} point{_pl(n_orig, ' ')}..."
)
t0 = time.time()
if self.mode == "pyvista":
inside = self._call_pyvista(rr)
else:
inside = self._call_old(rr, n_jobs)
n = inside.sum()
logger.info(f" Total {n}/{n_orig} point{_pl(n, ' ')} inside the surface")
logger.info(f"Interior check completed in {(time.time() - t0) * 1000:0.1f} ms")
return inside
def _call_pyvista(self, rr):
pdata = _surface_to_polydata(dict(rr=rr))
out = pdata.select_enclosed_points(self.pdata, check_surface=False)
return out["SelectedPoints"].astype(bool)
def _call_old(self, rr, n_jobs):
n_orig = len(rr)
prec = int(np.ceil(np.log10(max(n_orig, 10))))
inside = np.ones(n_orig, bool) # innocent until proven guilty
idx = np.arange(n_orig)
# Limit to indices that can plausibly be outside the surf
# but are not definitely outside it
if self.inner_r is not None:
dists = np.linalg.norm(rr - self.cm, axis=-1)
in_mask = dists < self.inner_r
n = (in_mask).sum()
n_pad = str(n).rjust(prec)
logger.info(
f" Found {n_pad}/{n_orig} point{_pl(n, ' ')} "
f"inside an interior sphere of radius "
f"{1000 * self.inner_r:6.1f} mm"
)
out_mask = dists > self.outer_r
inside[out_mask] = False
n = (out_mask).sum()
n_pad = str(n).rjust(prec)
logger.info(
f" Found {n_pad}/{n_orig} point{_pl(n, ' ')} "
f"outside an exterior sphere of radius "
f"{1000 * self.outer_r:6.1f} mm"
)
mask = (~in_mask) & (~out_mask) # not definitely inside or outside
idx = idx[mask]
rr = rr[mask]
# Use qhull as our first pass (*much* faster than our check)
del_outside = self.del_tri.find_simplex(rr) < 0
n = sum(del_outside)
inside[idx[del_outside]] = False
idx = idx[~del_outside]
rr = rr[~del_outside]
n_pad = str(n).rjust(prec)
check_pad = str(len(del_outside)).rjust(prec)
logger.info(
f" Found {n_pad}/{check_pad} point{_pl(n, ' ')} outside using "
"surface Qhull"
)
# use our more accurate check
solid_outside = _points_outside_surface(rr, self.surf, n_jobs)
n = np.sum(solid_outside)
n_pad = str(n).rjust(prec)
check_pad = str(len(solid_outside)).rjust(prec)
logger.info(
f" Found {n_pad}/{check_pad} point{_pl(n, ' ')} outside using "
"solid angles"
)
inside[idx[solid_outside]] = False
return inside
###############################################################################
# Handle freesurfer
def _fread3(fobj):
"""Read 3 bytes and adjust."""
b1, b2, b3 = np.fromfile(fobj, ">u1", 3).astype(np.int64)
return (b1 << 16) + (b2 << 8) + b3
def read_curvature(filepath, binary=True):
"""Load in curvature values from the ?h.curv file.
Parameters
----------
filepath : path-like
Input path to the ``.curv`` file.
binary : bool
Specify if the output array is to hold binary values. Defaults to True.
Returns
-------
curv : array of shape (n_vertices,)
The curvature values loaded from the user given 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
if binary:
return 1 - np.array(curv != 0, np.int64)
else:
return curv
@verbose
def read_surface(
fname, read_metadata=False, return_dict=False, file_format="auto", verbose=None
):
"""Load a Freesurfer surface mesh in triangular format.
Parameters
----------
fname : path-like
The name of the file containing the surface.
read_metadata : bool
Read metadata as key-value pairs. Only works when reading a FreeSurfer
surface file. For .obj files this dictionary will be empty.
Valid keys:
* 'head' : array of int
* 'valid' : str
* 'filename' : str
* 'volume' : array of int, shape (3,)
* 'voxelsize' : array of float, shape (3,)
* 'xras' : array of float, shape (3,)
* 'yras' : array of float, shape (3,)
* 'zras' : array of float, shape (3,)
* 'cras' : array of float, shape (3,)
.. versionadded:: 0.13.0
return_dict : bool
If True, a dictionary with surface parameters is returned.
file_format : 'auto' | 'freesurfer' | 'obj'
File format to use. Can be 'freesurfer' to read a FreeSurfer surface
file, or 'obj' to read a Wavefront .obj file (common format for
importing in other software), or 'auto' to attempt to infer from the
file name. Defaults to 'auto'.
.. versionadded:: 0.21.0
%(verbose)s
Returns
-------
rr : array, shape=(n_vertices, 3)
Coordinate points.
tris : int array, shape=(n_faces, 3)
Triangulation (each line contains indices for three points which
together form a face).
volume_info : dict-like
If read_metadata is true, key-value pairs found in the geometry file.
surf : dict
The surface parameters. Only returned if ``return_dict`` is True.
See Also
--------
write_surface
read_tri
"""
fname = _check_fname(fname, "read", True)
_check_option("file_format", file_format, ["auto", "freesurfer", "obj"])
if file_format == "auto":
if fname.suffix.lower() == ".obj":
file_format = "obj"
else:
file_format = "freesurfer"
if file_format == "freesurfer":
_import_nibabel("read surface geometry")
from nibabel.freesurfer import read_geometry
ret = read_geometry(fname, read_metadata=read_metadata)
elif file_format == "obj":
ret = _read_wavefront_obj(fname)
if read_metadata:
ret += (dict(),)
if return_dict:
ret += (_rr_tris_dict(ret[0], ret[1]),)
return ret
def _rr_tris_dict(rr, tris):
return dict(rr=rr, tris=tris, ntri=len(tris), use_tris=tris, np=len(rr))
def _read_mri_surface(fname):
surf = read_surface(fname, return_dict=True)[2]
surf["rr"] /= 1000.0
surf.update(coord_frame=FIFF.FIFFV_COORD_MRI)
return surf
def _read_wavefront_obj(fname):
"""Read a surface form a Wavefront .obj file.
Parameters
----------
fname : str
Name of the .obj file to read.
Returns
-------
coords : ndarray, shape (n_points, 3)
The XYZ coordinates of each vertex.
faces : ndarray, shape (n_faces, 3)
For each face of the mesh, the integer indices of the vertices that
make up the face.
"""
coords = []
faces = []
with open(fname) as f:
for line in f:
line = line.strip()
if len(line) == 0 or line[0] == "#":
continue
split = line.split()
if split[0] == "v": # vertex
coords.append([float(item) for item in split[1:]])
elif split[0] == "f": # face
dat = [int(item.split("/")[0]) for item in split[1:]]
if len(dat) != 3:
raise RuntimeError("Only triangle faces allowed.")
# In .obj files, indexing starts at 1
faces.append([d - 1 for d in dat])
return np.array(coords), np.array(faces)
def _read_patch(fname):
"""Load a FreeSurfer binary patch file.
Parameters
----------
fname : str
The filename.
Returns
-------
rrs : ndarray, shape (n_vertices, 3)
The points.
tris : ndarray, shape (n_tris, 3)
The patches. Not all vertices will be present.
"""
# This is adapted from PySurfer PR #269, Bruce Fischl's read_patch.m,
# and PyCortex (BSD)
patch = dict()
with open(fname) as fid:
ver = np.fromfile(fid, dtype=">i4", count=1).item()
if ver != -1:
raise RuntimeError(f"incorrect version # {ver} (not -1) found")
npts = np.fromfile(fid, dtype=">i4", count=1).item()
dtype = np.dtype([("vertno", ">i4"), ("x", ">f"), ("y", ">f"), ("z", ">f")])
recs = np.fromfile(fid, dtype=dtype, count=npts)
# numpy to dict
patch = {key: recs[key] for key in dtype.fields.keys()}
patch["vertno"] -= 1
# read surrogate surface
rrs, tris = read_surface(
op.join(op.dirname(fname), op.basename(fname)[:3] + "sphere")
)
orig_tris = tris
is_vert = patch["vertno"] > 0 # negative are edges, ignored for now
verts = patch["vertno"][is_vert]
# eliminate invalid tris and zero out unused rrs
mask = np.zeros((len(rrs),), dtype=bool)
mask[verts] = True
rrs[~mask] = 0.0
tris = tris[mask[tris].all(1)]
for ii, key in enumerate(["x", "y", "z"]):
rrs[verts, ii] = patch[key][is_vert]
return rrs, tris, orig_tris
##############################################################################
# SURFACE CREATION
def _get_ico_surface(grade, patch_stats=False):
"""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
from .bem import read_bem_surfaces
ico_file_name = op.join(op.dirname(__file__), "data", "icos.fif.gz")
ico = read_bem_surfaces(
ico_file_name, patch_stats, 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=npt,
nn=nn,
inuse=np.ones(npt, int),
)
return s
def _norm_midpt(ai, bi, rr):
"""Get normalized midpoint."""
c = rr[ai]
c += rr[bi]
_normalize_vectors(c)
return c
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("oct subdivision 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):
r"""
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, 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(surf, return_dict=True)[-1]
do_neighbor_vert = stype == "spacing"
complete_surface_info(surf, do_neighbor_vert, copy=False)
if stype == "all":
surf["inuse"] = np.ones(surf["np"], int)
surf["use_tris"] = None
elif stype == "spacing":
_decimate_surface_spacing(surf, ico_surf)
surf["use_tris"] = None
del surf["neighbor_vert"]
else: # ico or oct
# ## from mne_ico_downsample.c ## #
surf_name = subjects_dir / subject / "surf" / f"{hemi}.sphere"
logger.info(f"Loading geometry from {surf_name}...")
from_surf = read_surface(surf_name, return_dict=True)[-1]
_normalize_vectors(from_surf["rr"])
if from_surf["np"] != surf["np"]:
raise RuntimeError(
"Mismatch between number of surface vertices, "
"possible parcellation error?"
)
_normalize_vectors(ico_surf["rr"])
# Make the maps
mmap = _compute_nearest(from_surf["rr"], ico_surf["rr"])
nmap = len(mmap)
surf["inuse"] = np.zeros(surf["np"], int)
for k in range(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(
f"Could not find neighbor for vertex {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(
f"Map number out of range ({mmap[k]}), this is probably due to "
"inconsistent surfaces. Parts of the FreeSurfer reconstruction "
"need to be redone."
)
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)
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
sizes = _normalize_vectors(surf["nn"])
surf["inuse"][sizes <= 0] = False
surf["nuse"] = np.sum(surf["inuse"])
surf["subject_his_id"] = subject
return surf
def _decimate_surface_spacing(surf, spacing):
assert isinstance(spacing, int)
assert spacing > 0
logger.info(" Decimating...")
d = np.full(surf["np"], 10000, int)
# A mysterious algorithm follows
for k in range(surf["np"]):
neigh = surf["neighbor_vert"][k]
d[k] = min(np.min(d[neigh]) + 1, d[k])
if d[k] >= spacing:
d[k] = 0
d[neigh] = np.minimum(d[neigh], d[k] + 1)
if spacing == 2.0:
for k in range(surf["np"] - 1, -1, -1):
for n in surf["neighbor_vert"][k]:
d[k] = min(d[k], d[n] + 1)
d[n] = min(d[n], d[k] + 1)
for k in range(surf["np"]):
if d[k] > 0:
neigh = surf["neighbor_vert"][k]
n = np.sum(d[neigh] == 0)
if n <= 2:
d[k] = 0
d[neigh] = np.minimum(d[neigh], d[k] + 1)
surf["inuse"] = np.zeros(surf["np"], int)
surf["inuse"][d == 0] = 1
return surf
@verbose
def write_surface(
fname,
coords,
faces,
create_stamp="",
volume_info=None,
file_format="auto",
overwrite=False,
*,
verbose=None,
):
"""Write a triangular Freesurfer surface mesh.
Accepts the same data format as is returned by read_surface().
Parameters
----------
fname : path-like
File to write.
coords : array, shape=(n_vertices, 3)
Coordinate points.
faces : int array, shape=(n_faces, 3)
Triangulation (each line contains indices 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.
volume_info : dict-like or None
Key-value pairs to encode at the end of the file.
Valid keys:
* 'head' : array of int
* 'valid' : str
* 'filename' : str
* 'volume' : array of int, shape (3,)
* 'voxelsize' : array of float, shape (3,)
* 'xras' : array of float, shape (3,)
* 'yras' : array of float, shape (3,)
* 'zras' : array of float, shape (3,)
* 'cras' : array of float, shape (3,)
.. versionadded:: 0.13.0
file_format : 'auto' | 'freesurfer' | 'obj'
File format to use. Can be 'freesurfer' to write a FreeSurfer surface
file, or 'obj' to write a Wavefront .obj file (common format for
importing in other software), or 'auto' to attempt to infer from the
file name. Defaults to 'auto'.
.. versionadded:: 0.21.0
%(overwrite)s
%(verbose)s
See Also
--------
read_surface
read_tri
"""
fname = _check_fname(fname, overwrite=overwrite)
_check_option("file_format", file_format, ["auto", "freesurfer", "obj"])
if file_format == "auto":
if fname.suffix.lower() == ".obj":
file_format = "obj"
else:
file_format = "freesurfer"
if file_format == "freesurfer":
_import_nibabel("write surface geometry")
from nibabel.freesurfer import write_geometry
write_geometry(
fname, coords, faces, create_stamp=create_stamp, volume_info=volume_info
)
else:
assert file_format == "obj"
with open(fname, "w") as fid:
for line in create_stamp.splitlines():
fid.write(f"# {line}\n")
for v in coords:
fid.write(f"v {v[0]} {v[1]} {v[2]}\n")
for f in faces:
fid.write(f"f {f[0] + 1} {f[1] + 1} {f[2] + 1}\n")
###############################################################################
# Decimation
def _decimate_surface_vtk(points, triangles, n_triangles):
"""Aux function."""
try:
from vtkmodules.util.numpy_support import numpy_to_vtk, numpy_to_vtkIdTypeArray
from vtkmodules.vtkCommonCore import vtkPoints
from vtkmodules.vtkCommonDataModel import vtkCellArray, vtkPolyData
from vtkmodules.vtkFiltersCore import vtkQuadricDecimation
except ImportError:
raise ValueError("This function requires the VTK package to be installed")
if triangles.max() > len(points) - 1:
raise ValueError(
"The triangles refer to undefined points. Please check your mesh."
)
src = vtkPolyData()
vtkpoints = vtkPoints()
with warnings.catch_warnings(record=True):
warnings.simplefilter("ignore")
vtkpoints.SetData(numpy_to_vtk(points.astype(np.float64)))
src.SetPoints(vtkpoints)
vtkcells = vtkCellArray()
triangles_ = np.pad(triangles, ((0, 0), (1, 0)), "constant", constant_values=3)
with warnings.catch_warnings(record=True):
warnings.simplefilter("ignore")
idarr = numpy_to_vtkIdTypeArray(triangles_.ravel().astype(np.int64))
vtkcells.SetCells(triangles.shape[0], idarr)
src.SetPolys(vtkcells)
# vtkDecimatePro was not very good, even with SplittingOff and
# PreserveTopologyOn
decimate = vtkQuadricDecimation()
decimate.VolumePreservationOn()
decimate.SetInputData(src)
reduction = 1 - (float(n_triangles) / len(triangles))
decimate.SetTargetReduction(reduction)
decimate.Update()
out = _polydata_to_surface(decimate.GetOutput(), normals=False)
return out["rr"], out["tris"]
def _decimate_surface_sphere(rr, tris, n_triangles):
_check_freesurfer_home()
map_ = {}
ico_levels = [20, 80, 320, 1280, 5120, 20480]
map_.update({n_tri: ("ico", ii) for ii, n_tri in enumerate(ico_levels)})
oct_levels = 2 ** (2 * np.arange(7) + 3)
map_.update({n_tri: ("oct", ii) for ii, n_tri in enumerate(oct_levels, 1)})
_check_option(
"n_triangles", n_triangles, sorted(map_), extra=' when method="sphere"'
)
func_map = dict(ico=_get_ico_surface, oct=_tessellate_sphere_surf)
kind, level = map_[n_triangles]
logger.info(f"Decimating using Freesurfer spherical {kind}{level} downsampling")
ico_surf = func_map[kind](level)
assert len(ico_surf["tris"]) == n_triangles
tempdir = _TempDir()
orig = op.join(tempdir, "lh.temp")
write_surface(orig, rr, tris)
logger.info(" Extracting main mesh component ...")
run_subprocess(["mris_extract_main_component", orig, orig], verbose="error")
logger.info(" Smoothing ...")
smooth = orig + ".smooth"
run_subprocess(["mris_smooth", "-nw", orig, smooth], verbose="error")
logger.info(" Inflating ...")
inflated = orig + ".inflated"
run_subprocess(["mris_inflate", "-no-save-sulc", smooth, inflated], verbose="error")
logger.info(" Sphere ...")
qsphere = orig + ".qsphere"
run_subprocess(["mris_sphere", "-q", inflated, qsphere], verbose="error")
sphere_rr, _ = read_surface(qsphere)
norms = np.linalg.norm(sphere_rr, axis=1, keepdims=True)
sphere_rr /= norms
idx = _compute_nearest(sphere_rr, ico_surf["rr"], method="KDTree")
n_dup = len(idx) - len(np.unique(idx))
if n_dup:
raise RuntimeError(
f"Could not reduce to {n_triangles} triangles using ico, "
f"{n_dup}/{len(idx)} vertices were duplicates."
)
logger.info("[done]")
return rr[idx], ico_surf["tris"]
@verbose
def decimate_surface(points, triangles, n_triangles, method="quadric", *, verbose=None):
"""Decimate surface data.
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.
method : str
Can be "quadric" or "sphere". "sphere" will inflate the surface to a
sphere using Freesurfer and downsample to an icosahedral or
octahedral mesh.
.. versionadded:: 0.20
%(verbose)s
Returns
-------
points : ndarray
The decimated points.
triangles : ndarray
The decimated triangles.
Notes
-----
**"quadric" mode**
This requires VTK. If an odd target number was requested,
the ``'decimation'`` algorithm used results in the
next even number of triangles. For example a reduction request
to 30001 triangles may result in 30000 triangles.
**"sphere" mode**
This requires Freesurfer to be installed and available in the
environment. The destination number of triangles must be one of
``[20, 80, 320, 1280, 5120, 20480]`` for ico (0-5) downsampling or one of
``[8, 32, 128, 512, 2048, 8192, 32768]`` for oct (1-7) downsampling.
This mode is slower, but could be more suitable for decimating meshes for
BEM creation (recommended ``n_triangles=5120``) due to better topological
property preservation.
"""
n_triangles = _ensure_int(n_triangles)
method_map = dict(quadric=_decimate_surface_vtk, sphere=_decimate_surface_sphere)
_check_option("method", method, sorted(method_map))
if n_triangles > len(triangles):
raise ValueError(
f"Requested n_triangles ({n_triangles}) exceeds number of "
f"original triangles ({len(triangles)})"
)
return method_map[method](points, triangles, n_triangles)
###############################################################################
# Geometry
@jit()
def _get_tri_dist(p, q, p0, q0, a, b, c, dist): # pragma: no cover
"""Get the distance to a triangle edge."""
p1 = p - p0
q1 = q - q0
out = p1 * p1 * a
out += q1 * q1 * b
out += p1 * q1 * c
out += dist * dist
return np.sqrt(out)
def _get_tri_supp_geom(surf):
"""Create supplementary geometry information using tris and rrs."""
r1 = surf["rr"][surf["tris"][:, 0], :]
r12 = surf["rr"][surf["tris"][:, 1], :] - r1
r13 = surf["rr"][surf["tris"][:, 2], :] - r1
r1213 = np.ascontiguousarray(np.array([r12, r13]).swapaxes(0, 1))
a = np.einsum("ij,ij->i", r12, r12)
b = np.einsum("ij,ij->i", r13, r13)
c = np.einsum("ij,ij->i", r12, r13)
mat = np.ascontiguousarray(np.rollaxis(np.array([[b, -c], [-c, a]]), 2))
norm = a * b - c * c
norm[norm == 0] = 1.0 # avoid divide by zero
mat /= norm[:, 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)
@jit(parallel=True)
def _find_nearest_tri_pts(
rrs,
pt_triss,
pt_lens,
a,
b,
c,
nn,
r1,
r12,
r13,
r1213,
mat,
run_all=True,
reproject=False,
): # pragma: no cover
"""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)
weights = np.empty((len(rrs), 3))
tri_idx = np.empty(len(rrs), np.int64)
for ri in prange(len(rrs)):
rr = np.reshape(rrs[ri], (1, 3))
start, stop = pt_lens[ri : ri + 2]
if start == stop == 0: # use all
drs = rr - r1
tri_nn = nn
mats = mat
r1213s = r1213
reindex = False
else:
pt_tris = pt_triss[start:stop]
drs = rr - r1[pt_tris]
tri_nn = nn[pt_tris]
mats = mat[pt_tris]
r1213s = r1213[pt_tris]
reindex = True
use = np.ones(len(drs), np.int64)
pqs = np.empty((len(drs), 2))
dists = np.empty(len(drs))
dist = np.inf
# make life easier for numba var typing
p, q, pt = np.float64(0.0), np.float64(1.0), np.int64(0)
found = False
for ii in range(len(drs)):
pqs[ii] = np.dot(mats[ii], np.dot(r1213s[ii], drs[ii]))
dists[ii] = np.dot(drs[ii], tri_nn[ii])
pp, qq = pqs[ii]
if pp >= 0 and qq >= 0 and pp <= 1 and qq <= 1 and pp + qq < 1:
found = True
use[ii] = False
if np.abs(dists[ii]) < np.abs(dist):
p, q, pt, dist = pp, qq, ii, dists[ii]
# re-reference back to original numbers
if found and reindex:
pt = pt_tris[pt]
if not found or run_all:
# don't include ones that we might have found before
# these are the ones that we want to check the sides of
s = np.where(use)[0]
# Tough: must investigate the sides
if reindex:
use_pt_tris = pt_tris[s].astype(np.int64)
else:
use_pt_tris = s.astype(np.int64)
pp, qq, ptt, distt = _nearest_tri_edge(
use_pt_tris, pqs[s], dists[s], a, b, c
)
if np.abs(distt) < np.abs(dist):
p, q, pt, dist = pp, qq, ptt, distt
w = (1 - p - q, p, q)
if reproject:
# Calculate a linear interpolation between the vertex values to
# get coords of pt projected onto closest triangle
coords = _triangle_coords(rr[0], pt, r1, nn, r12, r13, a, b, c)
w = (1.0 - coords[0] - coords[1], coords[0], coords[1])
weights[ri] = w
tri_idx[ri] = pt
return weights, tri_idx
@jit()
def _nearest_tri_edge(pt_tris, pqs, dist, a, b, c): # pragma: no cover
"""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 = a[pt_tris]
bb = b[pt_tris]
cc = 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.concatenate((p0, p1, p2))
qq = np.concatenate((q0, q1, q2))
dists = np.concatenate((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
def mesh_edges(tris):
"""Return sparse matrix with edges as an adjacency matrix.
Parameters
----------
tris : array of shape [n_triangles x 3]
The triangles.
Returns
-------
edges : scipy.sparse.spmatrix
The adjacency matrix.
"""
tris = _hashable_ndarray(tris)
return _mesh_edges(tris=tris)
@lru_cache(maxsize=10)
def _mesh_edges(tris=None):
if np.max(tris) > len(np.unique(tris)):
raise ValueError("Cannot compute adjacency on a selection of triangles.")
npoints = np.max(tris) + 1
ones_ntris = np.ones(3 * len(tris))
a, b, c = tris.T
x = np.concatenate((a, b, c))
y = np.concatenate((b, c, a))
edges = coo_array((ones_ntris, (x, y)), shape=(npoints, npoints))
edges = edges.tocsr()
edges = edges + edges.T
return edges
def mesh_dist(tris, vert):
"""Compute adjacency matrix weighted by distances.
It generates an adjacency matrix where the entries are the distances
between neighboring vertices.
Parameters
----------
tris : array (n_tris x 3)
Mesh triangulation.
vert : array (n_vert x 3)
Vertex locations.
Returns
-------
dist_matrix : scipy.sparse.csr_array
Sparse matrix with distances between adjacent vertices.
"""
edges = mesh_edges(tris).tocoo()
# Euclidean distances between neighboring vertices
dist = np.linalg.norm(vert[edges.row, :] - vert[edges.col, :], axis=1)
dist_matrix = csr_array((dist, (edges.row, edges.col)), shape=edges.shape)
return dist_matrix
@verbose
def read_tri(fname_in, swap=False, verbose=None):
"""Read triangle definitions from an ascii file.
Parameters
----------
fname_in : path-like
Path to surface ASCII file (ending with ``'.tri'``).
swap : bool
Assume the ASCII file vertex ordering is clockwise instead of
counterclockwise.
%(verbose)s
Returns
-------
rr : array, shape=(n_vertices, 3)
Coordinate points.
tris : int array, shape=(n_faces, 3)
Triangulation (each line contains indices for three points which
together form a face).
See Also
--------
read_surface
write_surface
Notes
-----
.. versionadded:: 0.13.0
"""
with open(fname_in) as fid:
lines = fid.readlines()
n_nodes = int(lines[0])
n_tris = int(lines[n_nodes + 1])
n_items = len(lines[1].split())
if n_items in [3, 6, 14, 17]:
inds = range(3)
elif n_items in [4, 7]:
inds = range(1, 4)
else:
raise OSError("Unrecognized format of data.")
rr = np.array(
[
np.array([float(v) for v in line.split()])[inds]
for line in lines[1 : n_nodes + 1]
]
)
tris = np.array(
[
np.array([int(v) for v in line.split()])[inds]
for line in lines[n_nodes + 2 : n_nodes + 2 + n_tris]
]
)
if swap:
tris[:, [2, 1]] = tris[:, [1, 2]]
tris -= 1
logger.info(
f"Loaded surface from {fname_in} with {n_nodes} nodes and {n_tris} triangles."
)
if n_items in [3, 4]:
logger.info("Node normals were not included in the source file.")
else:
warn("Node normals were not read.")
return (rr, tris)
@jit()
def _get_solids(tri_rrs, fros):
"""Compute _sum_solids_div total angle in chunks."""
# NOTE: This incorporates the division by 4PI that used to be separate
tot_angle = np.zeros(len(fros))
for ti in range(len(tri_rrs)):
tri_rr = tri_rrs[ti]
v1 = fros - tri_rr[0]
v2 = fros - tri_rr[1]
v3 = fros - tri_rr[2]
v4 = np.empty((v1.shape[0], 3))
_jit_cross(v4, v1, v2)
triple = np.sum(v4 * v3, axis=1)
l1 = np.sqrt(np.sum(v1 * v1, axis=1))
l2 = np.sqrt(np.sum(v2 * v2, axis=1))
l3 = np.sqrt(np.sum(v3 * v3, axis=1))
s = (
l1 * l2 * l3
+ np.sum(v1 * v2, axis=1) * l3
+ np.sum(v1 * v3, axis=1) * l2
+ np.sum(v2 * v3, axis=1) * l1
)
tot_angle -= np.arctan2(triple, s)
return tot_angle
def _complete_sphere_surf(sphere, idx, level, complete=True):
"""Convert sphere conductor model to surface."""
rad = sphere["layers"][idx]["rad"]
r0 = sphere["r0"]
surf = _tessellate_sphere_surf(level, rad=rad)
surf["rr"] += r0
if complete:
complete_surface_info(surf, copy=False)
surf["coord_frame"] = sphere["coord_frame"]
return surf
@verbose
def dig_mri_distances(
info,
trans,
subject,
subjects_dir=None,
dig_kinds="auto",
exclude_frontal=False,
on_defects="raise",
verbose=None,
):
"""Compute distances between head shape points and the scalp surface.
This function is useful to check that coregistration is correct.
Unless outliers are present in the head shape points,
one can assume an average distance around 2-3 mm.
Parameters
----------
%(info_not_none)s Must contain the head shape points in ``info['dig']``.
trans : str | instance of Transform
The head<->MRI transform. If str is passed it is the
path to file on disk.
subject : str
The name of the subject.
subjects_dir : str | None
Directory containing subjects data. If None use
the Freesurfer SUBJECTS_DIR environment variable.
%(dig_kinds)s
%(exclude_frontal)s
Default is False.
%(on_defects)s
.. versionadded:: 1.0
%(verbose)s
Returns
-------
dists : array, shape (n_points,)
The distances.
See Also
--------
mne.bem.get_fitting_dig
Notes
-----
.. versionadded:: 0.19
"""
from .bem import get_fitting_dig
pts = get_head_surf(
subject,
("head-dense", "head", "bem"),
subjects_dir=subjects_dir,
on_defects=on_defects,
)["rr"]
trans = _get_trans(trans, fro="mri", to="head")[0]
pts = apply_trans(trans, pts)
info_dig = get_fitting_dig(info, dig_kinds, exclude_frontal=exclude_frontal)
dists = _compute_nearest(pts, info_dig, return_dists=True)[1]
return dists
def _mesh_borders(tris, mask):
assert isinstance(mask, np.ndarray) and mask.ndim == 1
edges = mesh_edges(tris)
edges = edges.tocoo()
border_edges = mask[edges.row] != mask[edges.col]
return np.unique(edges.row[border_edges])
def _marching_cubes(image, level, smooth=0, fill_hole_size=None, use_flying_edges=True):
"""Compute marching cubes on a 3D image."""
# vtkDiscreteMarchingCubes would be another option, but it merges
# values at boundaries which is not what we want
# https://kitware.github.io/vtk-examples/site/Cxx/Medical/GenerateModelsFromLabels/ # noqa: E501
# Also vtkDiscreteFlyingEdges3D should be faster.
# If we ever want not-discrete (continuous/float) marching cubes,
# we should probably use vtkFlyingEdges3D rather than vtkMarchingCubes.
from vtkmodules.util.numpy_support import numpy_to_vtk, vtk_to_numpy
from vtkmodules.vtkCommonDataModel import vtkDataSetAttributes, vtkImageData
from vtkmodules.vtkFiltersCore import vtkThreshold
from vtkmodules.vtkFiltersGeneral import (
vtkDiscreteFlyingEdges3D,
vtkDiscreteMarchingCubes,
)
from vtkmodules.vtkFiltersGeometry import vtkGeometryFilter
if image.ndim != 3:
raise ValueError(f"3D data must be supplied, got {image.shape}")
level = np.array(level)
if level.ndim != 1 or level.size == 0 or level.dtype.kind not in "ui":
raise TypeError(
"level must be non-empty numeric or 1D array-like of int, "
f"got {level.ndim}D array-like of {level.dtype} with "
f"{level.size} elements"
)
# vtkImageData indexes as slice, row, col (Z, Y, X):
# https://discourse.vtk.org/t/very-confused-about-imdata-matrix-index-order/6608/2
# We can accomplish this by raveling with order='F' later, so we might as
# well make a copy with Fortran order now.
# We also use double as passing integer types directly can be problematic!
image = np.array(image, dtype=float, order="F")
image_shape = image.shape
# fill holes
if fill_hole_size is not None:
for val in level:
bin_image = image == val
mask = image == 0 # don't go into other areas
bin_image = binary_dilation(bin_image, iterations=fill_hole_size, mask=mask)
image[bin_image] = val
data_vtk = numpy_to_vtk(image.ravel(order="F"), deep=False)
mc = vtkDiscreteFlyingEdges3D() if use_flying_edges else vtkDiscreteMarchingCubes()
# create image
imdata = vtkImageData()
imdata.SetDimensions(image_shape)
imdata.SetSpacing([1, 1, 1])
imdata.SetOrigin([0, 0, 0])
imdata.GetPointData().SetScalars(data_vtk)
# compute marching cubes on smoothed data
mc.SetNumberOfContours(len(level))
for li, lev in enumerate(level):
mc.SetValue(li, lev)
mc.SetInputData(imdata)
mc.Update()
mc = _vtk_smooth(mc.GetOutput(), smooth)
# get verts and triangles
selector = vtkThreshold()
selector.SetInputData(mc)
dsa = vtkDataSetAttributes()
selector.SetInputArrayToProcess(
0,
0,
0,
imdata.FIELD_ASSOCIATION_POINTS
if use_flying_edges
else imdata.FIELD_ASSOCIATION_CELLS,
dsa.SCALARS,
)
geometry = vtkGeometryFilter()
geometry.SetInputConnection(selector.GetOutputPort())
out = list()
for val in level:
try:
selector.SetLowerThreshold
except AttributeError:
selector.ThresholdBetween(val, val)
else:
# default SetThresholdFunction is between, so:
selector.SetLowerThreshold(val)
selector.SetUpperThreshold(val)
geometry.Update()
polydata = geometry.GetOutput()
rr = vtk_to_numpy(polydata.GetPoints().GetData())
tris = vtk_to_numpy(polydata.GetPolys().GetConnectivityArray()).reshape(-1, 3)
rr = np.ascontiguousarray(rr)
tris = np.ascontiguousarray(tris)
out.append((rr, tris))
return out
def _vtk_smooth(pd, smooth):
_validate_type(smooth, "numeric", smooth)
smooth = float(smooth)
if not 0 <= smooth < 1:
raise ValueError(
"smoothing factor must be between 0 (inclusive) and "
f"1 (exclusive), got {smooth}"
)
if smooth == 0:
return pd
from vtkmodules.vtkFiltersCore import vtkWindowedSincPolyDataFilter
logger.info(f" Smoothing by a factor of {smooth}")
return_ndarray = False
if isinstance(pd, dict):
pd = _surface_to_polydata(pd)
return_ndarray = True
smoother = vtkWindowedSincPolyDataFilter()
smoother.SetInputData(pd)
smoother.SetNumberOfIterations(100)
smoother.BoundarySmoothingOff()
smoother.FeatureEdgeSmoothingOff()
smoother.SetFeatureAngle(120.0)
smoother.SetPassBand(1 - smooth)
smoother.NonManifoldSmoothingOn()
smoother.NormalizeCoordinatesOff()
smoother.Update()
out = smoother.GetOutput()
if return_ndarray:
out = _polydata_to_surface(out, normals=False)
return out
_VOXELS_MAX = 1000 # define constant to avoid runtime issues
@fill_doc
def get_montage_volume_labels(montage, subject, subjects_dir=None, aseg="auto", dist=2):
"""Get regions of interest near channels from a Freesurfer parcellation.
.. note:: This is applicable for channels inside the brain
(intracranial electrodes).
Parameters
----------
%(montage)s
%(subject)s
%(subjects_dir)s
%(aseg)s
dist : float
The distance in mm to use for identifying regions of interest.
Returns
-------
labels : dict
The regions of interest labels within ``dist`` of each channel.
colors : dict
The Freesurfer lookup table colors for the labels.
"""
from ._freesurfer import _get_aseg, read_freesurfer_lut
from .channels import DigMontage
_validate_type(montage, DigMontage, "montage")
_validate_type(dist, (int, float), "dist")
if dist < 0 or dist > 10:
raise ValueError("`dist` must be between 0 and 10")
aseg, aseg_data = _get_aseg(aseg, subject, subjects_dir)
# read freesurfer lookup table
lut, fs_colors = read_freesurfer_lut()
label_lut = {v: k for k, v in lut.items()}
# assert that all the values in the aseg are in the labels
assert all([idx in label_lut for idx in np.unique(aseg_data)])
# get transform to surface RAS for distance units instead of voxels
vox2ras_tkr = aseg.header.get_vox2ras_tkr()
ch_dict = montage.get_positions()
if ch_dict["coord_frame"] != "mri":
raise RuntimeError(
"Coordinate frame not supported, expected "
'"mri", got ' + str(ch_dict["coord_frame"])
)
ch_coords = np.array(list(ch_dict["ch_pos"].values()))
# convert to freesurfer voxel space
ch_coords = apply_trans(
np.linalg.inv(aseg.header.get_vox2ras_tkr()), ch_coords * 1000
)
labels = OrderedDict()
for ch_name, ch_coord in zip(montage.ch_names, ch_coords):
if np.isnan(ch_coord).any():
labels[ch_name] = list()
else:
voxels = _voxel_neighbors(
ch_coord,
aseg_data,
dist=dist,
vox2ras_tkr=vox2ras_tkr,
voxels_max=_VOXELS_MAX,
)
label_idxs = set([aseg_data[tuple(voxel)].astype(int) for voxel in voxels])
labels[ch_name] = [label_lut[idx] for idx in label_idxs]
all_labels = set([label for val in labels.values() for label in val])
colors = {label: tuple(fs_colors[label][:3] / 255) + (1.0,) for label in all_labels}
return labels, colors
def _get_neighbors(loc, image, voxels, thresh, dist_params):
"""Find all the neighbors above a threshold near a voxel."""
neighbors = set()
for axis in range(len(loc)):
for i in (-1, 1):
next_loc = np.array(loc)
next_loc[axis] += i
if thresh is not None:
assert dist_params is None
# must be above thresh, monotonically decreasing from
# the peak and not already found
next_loc = tuple(next_loc)
if (
image[next_loc] > thresh
and image[next_loc] <= image[loc]
and next_loc not in voxels
):
neighbors.add(next_loc)
else:
assert thresh is None
dist, seed_fs_ras, vox2ras_tkr = dist_params
next_loc_fs_ras = apply_trans(vox2ras_tkr, next_loc + 0.5)
if np.linalg.norm(seed_fs_ras - next_loc_fs_ras) <= dist:
neighbors.add(tuple(next_loc))
return neighbors
def _voxel_neighbors(
seed,
image,
thresh=None,
max_peak_dist=1,
use_relative=True,
dist=None,
vox2ras_tkr=None,
voxels_max=100,
):
"""Find voxels above a threshold contiguous with a seed location.
Parameters
----------
seed : tuple | ndarray
The location in image coordinated to seed the algorithm.
image : ndarray
The image to search.
thresh : float
The threshold to use as a cutoff for what qualifies as a neighbor.
Will be relative to the peak if ``use_relative`` or absolute if not.
max_peak_dist : int
The maximum number of voxels to search for the peak near
the seed location.
use_relative : bool
If ``True``, the threshold will be relative to the peak, if
``False``, the threshold will be absolute.
dist : float
The distance in mm to include surrounding voxels.
vox2ras_tkr : ndarray
The voxel to surface RAS affine. Must not be None if ``dist``
if not None.
voxels_max : int
The maximum size of the output ``voxels``.
Returns
-------
voxels : set
The set of locations including the ``seed`` voxel and
surrounding that meet the criteria.
.. note:: Either ``dist`` or ``thesh`` may be used but not both.
When ``thresh`` is used, first a peak nearby the seed
location is found and then voxels are only included if they
decrease monotonically from the peak. When ``dist`` is used,
only voxels within ``dist`` mm of the seed are included.
"""
seed = np.array(seed).round().astype(int)
assert ((dist is not None) + (thresh is not None)) == 1
if thresh is not None:
dist_params = None
check_grid = image[
tuple([slice(idx - max_peak_dist, idx + max_peak_dist + 1) for idx in seed])
]
peak = (
np.array(np.unravel_index(np.argmax(check_grid), check_grid.shape))
- max_peak_dist
+ seed
)
voxels = neighbors = set([tuple(peak)])
if use_relative:
thresh *= image[tuple(peak)]
else:
assert vox2ras_tkr is not None
seed_fs_ras = apply_trans(vox2ras_tkr, seed + 0.5) # center of voxel
dist_params = (dist, seed_fs_ras, vox2ras_tkr)
voxels = neighbors = set([tuple(seed)])
while neighbors and len(voxels) <= voxels_max:
next_neighbors = set()
for next_loc in neighbors:
voxel_neighbors = _get_neighbors(
next_loc, image, voxels, thresh, dist_params
)
# prevent looping back to already visited voxels
voxel_neighbors = voxel_neighbors.difference(voxels)
# add voxels not already visited to search next
next_neighbors = next_neighbors.union(voxel_neighbors)
# add new voxels that match the criteria to the overall set
voxels = voxels.union(voxel_neighbors)
if len(voxels) > voxels_max:
break
neighbors = next_neighbors # start again checking all new neighbors
return voxels
Datasets
Models
