coreg.py

# -*- coding: utf-8 -*-
"""Coregistration between different coordinate frames."""

# Authors: Christian Brodbeck <christianbrodbeck@nyu.edu>
#
# License: BSD-3-Clause

import configparser
import fnmatch
from glob import glob, iglob
import os
import os.path as op
import stat
import sys
import re
import shutil
from functools import reduce

import numpy as np

from .io import read_fiducials, write_fiducials, read_info
from .io.constants import FIFF
from .io.meas_info import Info
from .io._digitization import _get_data_as_dict_from_dig
# keep get_mni_fiducials for backward compat (no burden to keep in this
# namespace, too)
from ._freesurfer import (_read_mri_info, get_mni_fiducials,  # noqa: F401
                          estimate_head_mri_t)  # noqa: F401
from .label import read_label, Label
from .source_space import (add_source_space_distances, read_source_spaces,  # noqa: E501,F401
                           write_source_spaces)
from .surface import (read_surface, write_surface, _normalize_vectors,
                      complete_surface_info, decimate_surface,
                      _DistanceQuery)
from .bem import read_bem_surfaces, write_bem_surfaces
from .transforms import (rotation, rotation3d, scaling, translation, Transform,
                         _read_fs_xfm, _write_fs_xfm, invert_transform,
                         combine_transforms, _quat_to_euler,
                         _fit_matched_points, apply_trans,
                         rot_to_quat, _angle_between_quats)
from .channels import make_dig_montage
from .utils import (get_config, get_subjects_dir, logger, pformat, verbose,
                    warn, has_nibabel, fill_doc, _validate_type,
                    _check_subject, _check_option)
from .viz._3d import _fiducial_coords

# some path templates
trans_fname = os.path.join('{raw_dir}', '{subject}-trans.fif')
subject_dirname = os.path.join('{subjects_dir}', '{subject}')
bem_dirname = os.path.join(subject_dirname, 'bem')
mri_dirname = os.path.join(subject_dirname, 'mri')
mri_transforms_dirname = os.path.join(subject_dirname, 'mri', 'transforms')
surf_dirname = os.path.join(subject_dirname, 'surf')
bem_fname = os.path.join(bem_dirname, "{subject}-{name}.fif")
head_bem_fname = pformat(bem_fname, name='head')
head_sparse_fname = pformat(bem_fname, name='head-sparse')
fid_fname = pformat(bem_fname, name='fiducials')
fid_fname_general = os.path.join(bem_dirname, "{head}-fiducials.fif")
src_fname = os.path.join(bem_dirname, '{subject}-{spacing}-src.fif')
_head_fnames = (os.path.join(bem_dirname, 'outer_skin.surf'),
                head_sparse_fname,
                head_bem_fname)
_high_res_head_fnames = (os.path.join(bem_dirname, '{subject}-head-dense.fif'),
                         os.path.join(surf_dirname, 'lh.seghead'),
                         os.path.join(surf_dirname, 'lh.smseghead'))


def _map_fid_name_to_idx(name: str) -> int:
    """Map a fiducial name to its index in the DigMontage."""
    name = name.lower()

    if name == 'lpa':
        return 0
    elif name == 'nasion':
        return 1
    else:
        assert name == 'rpa'
        return 2


def _make_writable(fname):
    """Make a file writable."""
    os.chmod(fname, stat.S_IMODE(os.lstat(fname)[stat.ST_MODE]) | 128)  # write


def _make_writable_recursive(path):
    """Recursively set writable."""
    if sys.platform.startswith('win'):
        return  # can't safely set perms
    for root, dirs, files in os.walk(path, topdown=False):
        for f in dirs + files:
            _make_writable(os.path.join(root, f))


def _find_head_bem(subject, subjects_dir, high_res=False):
    """Find a high resolution head."""
    # XXX this should be refactored with mne.surface.get_head_surf ...
    fnames = _high_res_head_fnames if high_res else _head_fnames
    for fname in fnames:
        path = fname.format(subjects_dir=subjects_dir, subject=subject)
        if os.path.exists(path):
            return path


@fill_doc
def coregister_fiducials(info, fiducials, tol=0.01):
    """Create a head-MRI transform by aligning 3 fiducial points.

    Parameters
    ----------
    %(info_not_none)s
    fiducials : str | list of dict
        Fiducials in MRI coordinate space (either path to a ``*-fiducials.fif``
        file or list of fiducials as returned by :func:`read_fiducials`.

    Returns
    -------
    trans : Transform
        The device-MRI transform.

    .. note:: The :class:`mne.Info` object fiducials must be in the
              head coordinate space.
    """
    if isinstance(info, str):
        info = read_info(info)
    if isinstance(fiducials, str):
        fiducials, coord_frame_to = read_fiducials(fiducials)
    else:
        coord_frame_to = FIFF.FIFFV_COORD_MRI
    frames_from = {d['coord_frame'] for d in info['dig']}
    if len(frames_from) > 1:
        raise ValueError("info contains fiducials from different coordinate "
                         "frames")
    else:
        coord_frame_from = frames_from.pop()
    coords_from = _fiducial_coords(info['dig'])
    coords_to = _fiducial_coords(fiducials, coord_frame_to)
    trans = fit_matched_points(coords_from, coords_to, tol=tol)
    return Transform(coord_frame_from, coord_frame_to, trans)


@verbose
def create_default_subject(fs_home=None, update=False, subjects_dir=None,
                           verbose=None):
    """Create an average brain subject for subjects without structural MRI.

    Create a copy of fsaverage from the Freesurfer directory in subjects_dir
    and add auxiliary files from the mne package.

    Parameters
    ----------
    fs_home : None | str
        The freesurfer home directory (only needed if FREESURFER_HOME is not
        specified as environment variable).
    update : bool
        In cases where a copy of the fsaverage brain already exists in the
        subjects_dir, this option allows to only copy files that don't already
        exist in the fsaverage directory.
    subjects_dir : None | str
        Override the SUBJECTS_DIR environment variable
        (os.environ['SUBJECTS_DIR']) as destination for the new subject.
    %(verbose)s

    Notes
    -----
    When no structural MRI is available for a subject, an average brain can be
    substituted. Freesurfer comes with such an average brain model, and MNE
    comes with some auxiliary files which make coregistration easier.
    :py:func:`create_default_subject` copies the relevant
    files from Freesurfer into the current subjects_dir, and also adds the
    auxiliary files provided by MNE.
    """
    subjects_dir = get_subjects_dir(subjects_dir, raise_error=True)
    if fs_home is None:
        fs_home = get_config('FREESURFER_HOME', fs_home)
        if fs_home is None:
            raise ValueError(
                "FREESURFER_HOME environment variable not found. Please "
                "specify the fs_home parameter in your call to "
                "create_default_subject().")

    # make sure freesurfer files exist
    fs_src = os.path.join(fs_home, 'subjects', 'fsaverage')
    if not os.path.exists(fs_src):
        raise IOError('fsaverage not found at %r. Is fs_home specified '
                      'correctly?' % fs_src)
    for name in ('label', 'mri', 'surf'):
        dirname = os.path.join(fs_src, name)
        if not os.path.isdir(dirname):
            raise IOError("Freesurfer fsaverage seems to be incomplete: No "
                          "directory named %s found in %s" % (name, fs_src))

    # make sure destination does not already exist
    dest = os.path.join(subjects_dir, 'fsaverage')
    if dest == fs_src:
        raise IOError(
            "Your subjects_dir points to the freesurfer subjects_dir (%r). "
            "The default subject can not be created in the freesurfer "
            "installation directory; please specify a different "
            "subjects_dir." % subjects_dir)
    elif (not update) and os.path.exists(dest):
        raise IOError(
            "Can not create fsaverage because %r already exists in "
            "subjects_dir %r. Delete or rename the existing fsaverage "
            "subject folder." % ('fsaverage', subjects_dir))

    # copy fsaverage from freesurfer
    logger.info("Copying fsaverage subject from freesurfer directory...")
    if (not update) or not os.path.exists(dest):
        shutil.copytree(fs_src, dest)
        _make_writable_recursive(dest)

    # copy files from mne
    source_fname = os.path.join(os.path.dirname(__file__), 'data', 'fsaverage',
                                'fsaverage-%s.fif')
    dest_bem = os.path.join(dest, 'bem')
    if not os.path.exists(dest_bem):
        os.mkdir(dest_bem)
    logger.info("Copying auxiliary fsaverage files from mne...")
    dest_fname = os.path.join(dest_bem, 'fsaverage-%s.fif')
    _make_writable_recursive(dest_bem)
    for name in ('fiducials', 'head', 'inner_skull-bem', 'trans'):
        if not os.path.exists(dest_fname % name):
            shutil.copy(source_fname % name, dest_bem)


def _decimate_points(pts, res=10):
    """Decimate the number of points using a voxel grid.

    Create a voxel grid with a specified resolution and retain at most one
    point per voxel. For each voxel, the point closest to its center is
    retained.

    Parameters
    ----------
    pts : array, shape (n_points, 3)
        The points making up the head shape.
    res : scalar
        The resolution of the voxel space (side length of each voxel).

    Returns
    -------
    pts : array, shape = (n_points, 3)
        The decimated points.
    """
    from scipy.spatial.distance import cdist
    pts = np.asarray(pts)

    # find the bin edges for the voxel space
    xmin, ymin, zmin = pts.min(0) - res / 2.
    xmax, ymax, zmax = pts.max(0) + res
    xax = np.arange(xmin, xmax, res)
    yax = np.arange(ymin, ymax, res)
    zax = np.arange(zmin, zmax, res)

    # find voxels containing one or more point
    H, _ = np.histogramdd(pts, bins=(xax, yax, zax), density=False)
    xbins, ybins, zbins = np.nonzero(H)
    x = xax[xbins]
    y = yax[ybins]
    z = zax[zbins]
    mids = np.c_[x, y, z] + res / 2.

    # each point belongs to at most one voxel center, so figure those out
    # (cKDTree faster than BallTree for these small problems)
    tree = _DistanceQuery(mids, method='cKDTree')
    _, mid_idx = tree.query(pts)

    # then figure out which to actually use based on proximity
    # (take advantage of sorting the mid_idx to get our mapping of
    # pts to nearest voxel midpoint)
    sort_idx = np.argsort(mid_idx)
    bounds = np.cumsum(
        np.concatenate([[0], np.bincount(mid_idx, minlength=len(mids))]))
    assert len(bounds) == len(mids) + 1
    out = list()
    for mi, mid in enumerate(mids):
        # Now we do this:
        #
        #     use_pts = pts[mid_idx == mi]
        #
        # But it's faster for many points than making a big boolean indexer
        # over and over (esp. since each point can only belong to a single
        # voxel).
        use_pts = pts[sort_idx[bounds[mi]:bounds[mi + 1]]]
        if not len(use_pts):
            out.append([np.inf] * 3)
        else:
            out.append(
                use_pts[np.argmin(cdist(use_pts, mid[np.newaxis])[:, 0])])
    out = np.array(out, float).reshape(-1, 3)
    out = out[np.abs(out - mids).max(axis=1) < res / 2.]
    # """

    return out


def _trans_from_params(param_info, params):
    """Convert transformation parameters into a transformation matrix."""
    do_rotate, do_translate, do_scale = param_info
    i = 0
    trans = []

    if do_rotate:
        x, y, z = params[:3]
        trans.append(rotation(x, y, z))
        i += 3

    if do_translate:
        x, y, z = params[i:i + 3]
        trans.insert(0, translation(x, y, z))
        i += 3

    if do_scale == 1:
        s = params[i]
        trans.append(scaling(s, s, s))
    elif do_scale == 3:
        x, y, z = params[i:i + 3]
        trans.append(scaling(x, y, z))

    trans = reduce(np.dot, trans)
    return trans


_ALLOW_ANALITICAL = True


# XXX this function should be moved out of coreg as used elsewhere
def fit_matched_points(src_pts, tgt_pts, rotate=True, translate=True,
                       scale=False, tol=None, x0=None, out='trans',
                       weights=None):
    """Find a transform between matched sets of points.

    This minimizes the squared distance between two matching sets of points.

    Uses :func:`scipy.optimize.leastsq` to find a transformation involving
    a combination of rotation, translation, and scaling (in that order).

    Parameters
    ----------
    src_pts : array, shape = (n, 3)
        Points to which the transform should be applied.
    tgt_pts : array, shape = (n, 3)
        Points to which src_pts should be fitted. Each point in tgt_pts should
        correspond to the point in src_pts with the same index.
    rotate : bool
        Allow rotation of the ``src_pts``.
    translate : bool
        Allow translation of the ``src_pts``.
    scale : bool
        Number of scaling parameters. With False, points are not scaled. With
        True, points are scaled by the same factor along all axes.
    tol : scalar | None
        The error tolerance. If the distance between any of the matched points
        exceeds this value in the solution, a RuntimeError is raised. With
        None, no error check is performed.
    x0 : None | tuple
        Initial values for the fit parameters.
    out : 'params' | 'trans'
        In what format to return the estimate: 'params' returns a tuple with
        the fit parameters; 'trans' returns a transformation matrix of shape
        (4, 4).

    Returns
    -------
    trans : array, shape (4, 4)
        Transformation that, if applied to src_pts, minimizes the squared
        distance to tgt_pts. Only returned if out=='trans'.
    params : array, shape (n_params, )
        A single tuple containing the rotation, translation, and scaling
        parameters in that order (as applicable).
    """
    src_pts = np.atleast_2d(src_pts)
    tgt_pts = np.atleast_2d(tgt_pts)
    if src_pts.shape != tgt_pts.shape:
        raise ValueError("src_pts and tgt_pts must have same shape (got "
                         "{}, {})".format(src_pts.shape, tgt_pts.shape))
    if weights is not None:
        weights = np.asarray(weights, src_pts.dtype)
        if weights.ndim != 1 or weights.size not in (src_pts.shape[0], 1):
            raise ValueError("weights (shape=%s) must be None or have shape "
                             "(%s,)" % (weights.shape, src_pts.shape[0],))
        weights = weights[:, np.newaxis]

    param_info = (bool(rotate), bool(translate), int(scale))
    del rotate, translate, scale

    # very common use case, rigid transformation (maybe with one scale factor,
    # with or without weighted errors)
    if param_info in ((True, True, 0), (True, True, 1)) and _ALLOW_ANALITICAL:
        src_pts = np.asarray(src_pts, float)
        tgt_pts = np.asarray(tgt_pts, float)
        if weights is not None:
            weights = np.asarray(weights, float)
        x, s = _fit_matched_points(
            src_pts, tgt_pts, weights, bool(param_info[2]))
        x[:3] = _quat_to_euler(x[:3])
        x = np.concatenate((x, [s])) if param_info[2] else x
    else:
        x = _generic_fit(src_pts, tgt_pts, param_info, weights, x0)

    # re-create the final transformation matrix
    if (tol is not None) or (out == 'trans'):
        trans = _trans_from_params(param_info, x)

    # assess the error of the solution
    if tol is not None:
        src_pts = np.hstack((src_pts, np.ones((len(src_pts), 1))))
        est_pts = np.dot(src_pts, trans.T)[:, :3]
        err = np.sqrt(np.sum((est_pts - tgt_pts) ** 2, axis=1))
        if np.any(err > tol):
            raise RuntimeError("Error exceeds tolerance. Error = %r" % err)

    if out == 'params':
        return x
    elif out == 'trans':
        return trans
    else:
        raise ValueError("Invalid out parameter: %r. Needs to be 'params' or "
                         "'trans'." % out)


def _generic_fit(src_pts, tgt_pts, param_info, weights, x0):
    from scipy.optimize import leastsq
    if param_info[1]:  # translate
        src_pts = np.hstack((src_pts, np.ones((len(src_pts), 1))))

    if param_info == (True, False, 0):
        def error(x):
            rx, ry, rz = x
            trans = rotation3d(rx, ry, rz)
            est = np.dot(src_pts, trans.T)
            d = tgt_pts - est
            if weights is not None:
                d *= weights
            return d.ravel()
        if x0 is None:
            x0 = (0, 0, 0)
    elif param_info == (True, True, 0):
        def error(x):
            rx, ry, rz, tx, ty, tz = x
            trans = np.dot(translation(tx, ty, tz), rotation(rx, ry, rz))
            est = np.dot(src_pts, trans.T)[:, :3]
            d = tgt_pts - est
            if weights is not None:
                d *= weights
            return d.ravel()
        if x0 is None:
            x0 = (0, 0, 0, 0, 0, 0)
    elif param_info == (True, True, 1):
        def error(x):
            rx, ry, rz, tx, ty, tz, s = x
            trans = reduce(np.dot, (translation(tx, ty, tz),
                                    rotation(rx, ry, rz),
                                    scaling(s, s, s)))
            est = np.dot(src_pts, trans.T)[:, :3]
            d = tgt_pts - est
            if weights is not None:
                d *= weights
            return d.ravel()
        if x0 is None:
            x0 = (0, 0, 0, 0, 0, 0, 1)
    elif param_info == (True, True, 3):
        def error(x):
            rx, ry, rz, tx, ty, tz, sx, sy, sz = x
            trans = reduce(np.dot, (translation(tx, ty, tz),
                                    rotation(rx, ry, rz),
                                    scaling(sx, sy, sz)))
            est = np.dot(src_pts, trans.T)[:, :3]
            d = tgt_pts - est
            if weights is not None:
                d *= weights
            return d.ravel()
        if x0 is None:
            x0 = (0, 0, 0, 0, 0, 0, 1, 1, 1)
    else:
        raise NotImplementedError(
            "The specified parameter combination is not implemented: "
            "rotate=%r, translate=%r, scale=%r" % param_info)

    x, _, _, _, _ = leastsq(error, x0, full_output=True)
    return x


def _find_label_paths(subject='fsaverage', pattern=None, subjects_dir=None):
    """Find paths to label files in a subject's label directory.

    Parameters
    ----------
    subject : str
        Name of the mri subject.
    pattern : str | None
        Pattern for finding the labels relative to the label directory in the
        MRI subject directory (e.g., "aparc/*.label" will find all labels
        in the "subject/label/aparc" directory). With None, find all labels.
    subjects_dir : None | str
        Override the SUBJECTS_DIR environment variable
        (sys.environ['SUBJECTS_DIR'])

    Returns
    -------
    paths : list
        List of paths relative to the subject's label directory
    """
    subjects_dir = get_subjects_dir(subjects_dir, raise_error=True)
    subject_dir = os.path.join(subjects_dir, subject)
    lbl_dir = os.path.join(subject_dir, 'label')

    if pattern is None:
        paths = []
        for dirpath, _, filenames in os.walk(lbl_dir):
            rel_dir = os.path.relpath(dirpath, lbl_dir)
            for filename in fnmatch.filter(filenames, '*.label'):
                path = os.path.join(rel_dir, filename)
                paths.append(path)
    else:
        paths = [os.path.relpath(path, lbl_dir) for path in iglob(pattern)]

    return paths


def _find_mri_paths(subject, skip_fiducials, subjects_dir):
    """Find all files of an mri relevant for source transformation.

    Parameters
    ----------
    subject : str
        Name of the mri subject.
    skip_fiducials : bool
        Do not scale the MRI fiducials. If False, an IOError will be raised
        if no fiducials file can be found.
    subjects_dir : None | str
        Override the SUBJECTS_DIR environment variable
        (sys.environ['SUBJECTS_DIR'])

    Returns
    -------
    paths : dict
        Dictionary whose keys are relevant file type names (str), and whose
        values are lists of paths.
    """
    subjects_dir = get_subjects_dir(subjects_dir, raise_error=True)
    paths = {}

    # directories to create
    paths['dirs'] = [bem_dirname, surf_dirname]

    # surf/ files
    paths['surf'] = []
    surf_fname = os.path.join(surf_dirname, '{name}')
    surf_names = ('inflated', 'white', 'orig', 'orig_avg', 'inflated_avg',
                  'inflated_pre', 'pial', 'pial_avg', 'smoothwm', 'white_avg',
                  'seghead', 'smseghead')
    if os.getenv('_MNE_FEW_SURFACES', '') == 'true':  # for testing
        surf_names = surf_names[:4]
    for surf_name in surf_names:
        for hemi in ('lh.', 'rh.'):
            name = hemi + surf_name
            path = surf_fname.format(subjects_dir=subjects_dir,
                                     subject=subject, name=name)
            if os.path.exists(path):
                paths['surf'].append(pformat(surf_fname, name=name))
    surf_fname = os.path.join(bem_dirname, '{name}')
    surf_names = ('inner_skull.surf', 'outer_skull.surf', 'outer_skin.surf')
    for surf_name in surf_names:
        path = surf_fname.format(subjects_dir=subjects_dir,
                                 subject=subject, name=surf_name)
        if os.path.exists(path):
            paths['surf'].append(pformat(surf_fname, name=surf_name))
    del surf_names, surf_name, path, hemi

    # BEM files
    paths['bem'] = bem = []
    path = head_bem_fname.format(subjects_dir=subjects_dir, subject=subject)
    if os.path.exists(path):
        bem.append('head')
    bem_pattern = pformat(bem_fname, subjects_dir=subjects_dir,
                          subject=subject, name='*-bem')
    re_pattern = pformat(bem_fname, subjects_dir=subjects_dir, subject=subject,
                         name='(.+)').replace('\\', '\\\\')
    for path in iglob(bem_pattern):
        match = re.match(re_pattern, path)
        name = match.group(1)
        bem.append(name)
    del bem, path, bem_pattern, re_pattern

    # fiducials
    if skip_fiducials:
        paths['fid'] = []
    else:
        paths['fid'] = _find_fiducials_files(subject, subjects_dir)
        # check that we found at least one
        if len(paths['fid']) == 0:
            raise IOError("No fiducials file found for %s. The fiducials "
                          "file should be named "
                          "{subject}/bem/{subject}-fiducials.fif. In "
                          "order to scale an MRI without fiducials set "
                          "skip_fiducials=True." % subject)

    # duplicate files (curvature and some surfaces)
    paths['duplicate'] = []
    path = os.path.join(surf_dirname, '{name}')
    surf_fname = os.path.join(surf_dirname, '{name}')
    surf_dup_names = ('curv', 'sphere', 'sphere.reg', 'sphere.reg.avg')
    for surf_dup_name in surf_dup_names:
        for hemi in ('lh.', 'rh.'):
            name = hemi + surf_dup_name
            path = surf_fname.format(subjects_dir=subjects_dir,
                                     subject=subject, name=name)
            if os.path.exists(path):
                paths['duplicate'].append(pformat(surf_fname, name=name))
    del surf_dup_name, name, path, hemi

    # transform files (talairach)
    paths['transforms'] = []
    transform_fname = os.path.join(mri_transforms_dirname, 'talairach.xfm')
    path = transform_fname.format(subjects_dir=subjects_dir, subject=subject)
    if os.path.exists(path):
        paths['transforms'].append(transform_fname)
    del transform_fname, path

    # find source space files
    paths['src'] = src = []
    bem_dir = bem_dirname.format(subjects_dir=subjects_dir, subject=subject)
    fnames = fnmatch.filter(os.listdir(bem_dir), '*-src.fif')
    prefix = subject + '-'
    for fname in fnames:
        if fname.startswith(prefix):
            fname = "{subject}-%s" % fname[len(prefix):]
        path = os.path.join(bem_dirname, fname)
        src.append(path)

    # find MRIs
    mri_dir = mri_dirname.format(subjects_dir=subjects_dir, subject=subject)
    fnames = fnmatch.filter(os.listdir(mri_dir), '*.mgz')
    paths['mri'] = [os.path.join(mri_dir, f) for f in fnames]

    return paths


def _find_fiducials_files(subject, subjects_dir):
    """Find fiducial files."""
    fid = []
    # standard fiducials
    if os.path.exists(fid_fname.format(subjects_dir=subjects_dir,
                                       subject=subject)):
        fid.append(fid_fname)
    # fiducials with subject name
    pattern = pformat(fid_fname_general, subjects_dir=subjects_dir,
                      subject=subject, head='*')
    regex = pformat(fid_fname_general, subjects_dir=subjects_dir,
                    subject=subject, head='(.+)').replace('\\', '\\\\')
    for path in iglob(pattern):
        match = re.match(regex, path)
        head = match.group(1).replace(subject, '{subject}')
        fid.append(pformat(fid_fname_general, head=head))
    return fid


def _is_mri_subject(subject, subjects_dir=None):
    """Check whether a directory in subjects_dir is an mri subject directory.

    Parameters
    ----------
    subject : str
        Name of the potential subject/directory.
    subjects_dir : None | str
        Override the SUBJECTS_DIR environment variable.

    Returns
    -------
    is_mri_subject : bool
        Whether ``subject`` is an mri subject.
    """
    subjects_dir = get_subjects_dir(subjects_dir, raise_error=True)
    return bool(_find_head_bem(subject, subjects_dir) or
                _find_head_bem(subject, subjects_dir, high_res=True))


def _is_scaled_mri_subject(subject, subjects_dir=None):
    """Check whether a directory in subjects_dir is a scaled mri subject.

    Parameters
    ----------
    subject : str
        Name of the potential subject/directory.
    subjects_dir : None | str
        Override the SUBJECTS_DIR environment variable.

    Returns
    -------
    is_scaled_mri_subject : bool
        Whether ``subject`` is a scaled mri subject.
    """
    subjects_dir = get_subjects_dir(subjects_dir, raise_error=True)
    if not _is_mri_subject(subject, subjects_dir):
        return False
    fname = os.path.join(subjects_dir, subject, 'MRI scaling parameters.cfg')
    return os.path.exists(fname)


def _mri_subject_has_bem(subject, subjects_dir=None):
    """Check whether an mri subject has a file matching the bem pattern.

    Parameters
    ----------
    subject : str
        Name of the subject.
    subjects_dir : None | str
        Override the SUBJECTS_DIR environment variable.

    Returns
    -------
    has_bem_file : bool
        Whether ``subject`` has a bem file.
    """
    subjects_dir = get_subjects_dir(subjects_dir, raise_error=True)
    pattern = bem_fname.format(subjects_dir=subjects_dir, subject=subject,
                               name='*-bem')
    fnames = glob(pattern)
    return bool(len(fnames))


def read_mri_cfg(subject, subjects_dir=None):
    """Read information from the cfg file of a scaled MRI brain.

    Parameters
    ----------
    subject : str
        Name of the scaled MRI subject.
    subjects_dir : None | str
        Override the SUBJECTS_DIR environment variable.

    Returns
    -------
    cfg : dict
        Dictionary with entries from the MRI's cfg file.
    """
    subjects_dir = get_subjects_dir(subjects_dir, raise_error=True)
    fname = os.path.join(subjects_dir, subject, 'MRI scaling parameters.cfg')

    if not os.path.exists(fname):
        raise IOError("%r does not seem to be a scaled mri subject: %r does "
                      "not exist." % (subject, fname))

    logger.info("Reading MRI cfg file %s" % fname)
    config = configparser.RawConfigParser()
    config.read(fname)
    n_params = config.getint("MRI Scaling", 'n_params')
    if n_params == 1:
        scale = config.getfloat("MRI Scaling", 'scale')
    elif n_params == 3:
        scale_str = config.get("MRI Scaling", 'scale')
        scale = np.array([float(s) for s in scale_str.split()])
    else:
        raise ValueError("Invalid n_params value in MRI cfg: %i" % n_params)

    out = {'subject_from': config.get("MRI Scaling", 'subject_from'),
           'n_params': n_params, 'scale': scale}
    return out


def _write_mri_config(fname, subject_from, subject_to, scale):
    """Write the cfg file describing a scaled MRI subject.

    Parameters
    ----------
    fname : str
        Target file.
    subject_from : str
        Name of the source MRI subject.
    subject_to : str
        Name of the scaled MRI subject.
    scale : float | array_like, shape = (3,)
        The scaling parameter.
    """
    scale = np.asarray(scale)
    if np.isscalar(scale) or scale.shape == ():
        n_params = 1
    else:
        n_params = 3

    config = configparser.RawConfigParser()
    config.add_section("MRI Scaling")
    config.set("MRI Scaling", 'subject_from', subject_from)
    config.set("MRI Scaling", 'subject_to', subject_to)
    config.set("MRI Scaling", 'n_params', str(n_params))
    if n_params == 1:
        config.set("MRI Scaling", 'scale', str(scale))
    else:
        config.set("MRI Scaling", 'scale', ' '.join([str(s) for s in scale]))
    config.set("MRI Scaling", 'version', '1')
    with open(fname, 'w') as fid:
        config.write(fid)


def _scale_params(subject_to, subject_from, scale, subjects_dir):
    """Assemble parameters for scaling.

    Returns
    -------
    subjects_dir : str
        Subjects directory.
    subject_from : str
        Name of the source subject.
    scale : array
        Scaling factor, either shape=() for uniform scaling or shape=(3,) for
        non-uniform scaling.
    uniform : bool
        Whether scaling is uniform.
    """
    subjects_dir = get_subjects_dir(subjects_dir, raise_error=True)
    if (subject_from is None) != (scale is None):
        raise TypeError("Need to provide either both subject_from and scale "
                        "parameters, or neither.")

    if subject_from is None:
        cfg = read_mri_cfg(subject_to, subjects_dir)
        subject_from = cfg['subject_from']
        n_params = cfg['n_params']
        assert n_params in (1, 3)
        scale = cfg['scale']
    scale = np.atleast_1d(scale)
    if scale.ndim != 1 or scale.shape[0] not in (1, 3):
        raise ValueError("Invalid shape for scale parameer. Need scalar "
                         "or array of length 3. Got shape %s."
                         % (scale.shape,))
    n_params = len(scale)
    return subjects_dir, subject_from, scale, n_params == 1


@verbose
def scale_bem(subject_to, bem_name, subject_from=None, scale=None,
              subjects_dir=None, *, on_defects='raise', verbose=None):
    """Scale a bem file.

    Parameters
    ----------
    subject_to : str
        Name of the scaled MRI subject (the destination mri subject).
    bem_name : str
        Name of the bem file. For example, to scale
        ``fsaverage-inner_skull-bem.fif``, the bem_name would be
        "inner_skull-bem".
    subject_from : None | str
        The subject from which to read the source space. If None, subject_from
        is read from subject_to's config file.
    scale : None | float | array, shape = (3,)
        Scaling factor. Has to be specified if subjects_from is specified,
        otherwise it is read from subject_to's config file.
    subjects_dir : None | str
        Override the SUBJECTS_DIR environment variable.
    %(on_defects)s

        .. versionadded:: 1.0
    %(verbose)s
    """
    subjects_dir, subject_from, scale, uniform = \
        _scale_params(subject_to, subject_from, scale, subjects_dir)

    src = bem_fname.format(subjects_dir=subjects_dir, subject=subject_from,
                           name=bem_name)
    dst = bem_fname.format(subjects_dir=subjects_dir, subject=subject_to,
                           name=bem_name)

    if os.path.exists(dst):
        raise IOError("File already exists: %s" % dst)

    surfs = read_bem_surfaces(src, on_defects=on_defects)
    for surf in surfs:
        surf['rr'] *= scale
        if not uniform:
            assert len(surf['nn']) > 0
            surf['nn'] /= scale
            _normalize_vectors(surf['nn'])
    write_bem_surfaces(dst, surfs)


def scale_labels(subject_to, pattern=None, overwrite=False, subject_from=None,
                 scale=None, subjects_dir=None):
    r"""Scale labels to match a brain that was previously created by scaling.

    Parameters
    ----------
    subject_to : str
        Name of the scaled MRI subject (the destination brain).
    pattern : str | None
        Pattern for finding the labels relative to the label directory in the
        MRI subject directory (e.g., "lh.BA3a.label" will scale
        "fsaverage/label/lh.BA3a.label"; "aparc/\*.label" will find all labels
        in the "fsaverage/label/aparc" directory). With None, scale all labels.
    overwrite : bool
        Overwrite any label file that already exists for subject_to (otherwise
        existing labels are skipped).
    subject_from : None | str
        Name of the original MRI subject (the brain that was scaled to create
        subject_to). If None, the value is read from subject_to's cfg file.
    scale : None | float | array_like, shape = (3,)
        Scaling parameter. If None, the value is read from subject_to's cfg
        file.
    subjects_dir : None | str
        Override the SUBJECTS_DIR environment variable.
    """
    subjects_dir, subject_from, scale, _ = _scale_params(
        subject_to, subject_from, scale, subjects_dir)

    # find labels
    paths = _find_label_paths(subject_from, pattern, subjects_dir)
    if not paths:
        return

    subjects_dir = get_subjects_dir(subjects_dir, raise_error=True)
    src_root = os.path.join(subjects_dir, subject_from, 'label')
    dst_root = os.path.join(subjects_dir, subject_to, 'label')

    # scale labels
    for fname in paths:
        dst = os.path.join(dst_root, fname)
        if not overwrite and os.path.exists(dst):
            continue

        dirname = os.path.dirname(dst)
        if not os.path.exists(dirname):
            os.makedirs(dirname)

        src = os.path.join(src_root, fname)
        l_old = read_label(src)
        pos = l_old.pos * scale
        l_new = Label(l_old.vertices, pos, l_old.values, l_old.hemi,
                      l_old.comment, subject=subject_to)
        l_new.save(dst)


@verbose
def scale_mri(subject_from, subject_to, scale, overwrite=False,
              subjects_dir=None, skip_fiducials=False, labels=True,
              annot=False, *, on_defects='raise', verbose=None):
    """Create a scaled copy of an MRI subject.

    Parameters
    ----------
    subject_from : str
        Name of the subject providing the MRI.
    subject_to : str
        New subject name for which to save the scaled MRI.
    scale : float | array_like, shape = (3,)
        The scaling factor (one or 3 parameters).
    overwrite : bool
        If an MRI already exists for subject_to, overwrite it.
    subjects_dir : None | str
        Override the SUBJECTS_DIR environment variable.
    skip_fiducials : bool
        Do not scale the MRI fiducials. If False (default), an IOError will be
        raised if no fiducials file can be found.
    labels : bool
        Also scale all labels (default True).
    annot : bool
        Copy ``*.annot`` files to the new location (default False).
    %(on_defects)s

        .. versionadded:: 1.0
    %(verbose)s

    See Also
    --------
    scale_bem : Add a scaled BEM to a scaled MRI.
    scale_labels : Add labels to a scaled MRI.
    scale_source_space : Add a source space to a scaled MRI.

    Notes
    -----
    This function will automatically call :func:`scale_bem`,
    :func:`scale_labels`, and :func:`scale_source_space` based on expected
    filename patterns in the subject directory.
    """
    subjects_dir = get_subjects_dir(subjects_dir, raise_error=True)
    paths = _find_mri_paths(subject_from, skip_fiducials, subjects_dir)
    scale = np.atleast_1d(scale)
    if scale.shape == (3,):
        if np.isclose(scale[1], scale[0]) and np.isclose(scale[2], scale[0]):
            scale = scale[0]  # speed up scaling conditionals using a singleton
    elif scale.shape != (1,):
        raise ValueError('scale must have shape (3,) or (1,), got %s'
                         % (scale.shape,))

    # make sure we have an empty target directory
    dest = subject_dirname.format(subject=subject_to,
                                  subjects_dir=subjects_dir)
    if os.path.exists(dest):
        if not overwrite:
            raise IOError("Subject directory for %s already exists: %r"
                          % (subject_to, dest))
        shutil.rmtree(dest)

    logger.debug('create empty directory structure')
    for dirname in paths['dirs']:
        dir_ = dirname.format(subject=subject_to, subjects_dir=subjects_dir)
        os.makedirs(dir_)

    logger.debug('save MRI scaling parameters')
    fname = os.path.join(dest, 'MRI scaling parameters.cfg')
    _write_mri_config(fname, subject_from, subject_to, scale)

    logger.debug('surf files [in mm]')
    for fname in paths['surf']:
        src = fname.format(subject=subject_from, subjects_dir=subjects_dir)
        src = os.path.realpath(src)
        dest = fname.format(subject=subject_to, subjects_dir=subjects_dir)
        pts, tri = read_surface(src)
        write_surface(dest, pts * scale, tri)

    logger.debug('BEM files [in m]')
    for bem_name in paths['bem']:
        scale_bem(subject_to, bem_name, subject_from, scale, subjects_dir,
                  on_defects=on_defects, verbose=False)

    logger.debug('fiducials [in m]')
    for fname in paths['fid']:
        src = fname.format(subject=subject_from, subjects_dir=subjects_dir)
        src = os.path.realpath(src)
        pts, cframe = read_fiducials(src, verbose=False)
        for pt in pts:
            pt['r'] = pt['r'] * scale
        dest = fname.format(subject=subject_to, subjects_dir=subjects_dir)
        write_fiducials(dest, pts, cframe, overwrite=True, verbose=False)

    logger.debug('MRIs [nibabel]')
    os.mkdir(mri_dirname.format(subjects_dir=subjects_dir,
                                subject=subject_to))
    for fname in paths['mri']:
        mri_name = os.path.basename(fname)
        _scale_mri(subject_to, mri_name, subject_from, scale, subjects_dir)

    logger.debug('Transforms')
    for mri_name in paths['mri']:
        if mri_name.endswith('T1.mgz'):
            os.mkdir(mri_transforms_dirname.format(subjects_dir=subjects_dir,
                                                   subject=subject_to))
            for fname in paths['transforms']:
                xfm_name = os.path.basename(fname)
                _scale_xfm(subject_to, xfm_name, mri_name,
                           subject_from, scale, subjects_dir)
            break

    logger.debug('duplicate files')
    for fname in paths['duplicate']:
        src = fname.format(subject=subject_from, subjects_dir=subjects_dir)
        dest = fname.format(subject=subject_to, subjects_dir=subjects_dir)
        shutil.copyfile(src, dest)

    logger.debug('source spaces')
    for fname in paths['src']:
        src_name = os.path.basename(fname)
        scale_source_space(subject_to, src_name, subject_from, scale,
                           subjects_dir, verbose=False)

    logger.debug('labels [in m]')
    os.mkdir(os.path.join(subjects_dir, subject_to, 'label'))
    if labels:
        scale_labels(subject_to, subject_from=subject_from, scale=scale,
                     subjects_dir=subjects_dir)

    logger.debug('copy *.annot files')
    # they don't contain scale-dependent information
    if annot:
        src_pattern = os.path.join(subjects_dir, subject_from, 'label',
                                   '*.annot')
        dst_dir = os.path.join(subjects_dir, subject_to, 'label')
        for src_file in iglob(src_pattern):
            shutil.copy(src_file, dst_dir)


@verbose
def scale_source_space(subject_to, src_name, subject_from=None, scale=None,
                       subjects_dir=None, n_jobs=None, verbose=None):
    """Scale a source space for an mri created with scale_mri().

    Parameters
    ----------
    subject_to : str
        Name of the scaled MRI subject (the destination mri subject).
    src_name : str
        Source space name. Can be a spacing parameter (e.g., ``'7'``,
        ``'ico4'``, ``'oct6'``) or a file name of a source space file relative
        to the bem directory; if the file name contains the subject name, it
        should be indicated as "{subject}" in ``src_name`` (e.g.,
        ``"{subject}-my_source_space-src.fif"``).
    subject_from : None | str
        The subject from which to read the source space. If None, subject_from
        is read from subject_to's config file.
    scale : None | float | array, shape = (3,)
        Scaling factor. Has to be specified if subjects_from is specified,
        otherwise it is read from subject_to's config file.
    subjects_dir : None | str
        Override the SUBJECTS_DIR environment variable.
    n_jobs : int
        Number of jobs to run in parallel if recomputing distances (only
        applies if scale is an array of length 3, and will not use more cores
        than there are source spaces).
    %(verbose)s

    Notes
    -----
    When scaling volume source spaces, the source (vertex) locations are
    scaled, but the reference to the MRI volume is left unchanged. Transforms
    are updated so that source estimates can be plotted on the original MRI
    volume.
    """
    subjects_dir, subject_from, scale, uniform = \
        _scale_params(subject_to, subject_from, scale, subjects_dir)
    # if n_params==1 scale is a scalar; if n_params==3 scale is a (3,) array

    # find the source space file names
    if src_name.isdigit():
        spacing = src_name  # spacing in mm
        src_pattern = src_fname
    else:
        match = re.match(r"(oct|ico|vol)-?(\d+)$", src_name)
        if match:
            spacing = '-'.join(match.groups())
            src_pattern = src_fname
        else:
            spacing = None
            src_pattern = os.path.join(bem_dirname, src_name)

    src = src_pattern.format(subjects_dir=subjects_dir, subject=subject_from,
                             spacing=spacing)
    dst = src_pattern.format(subjects_dir=subjects_dir, subject=subject_to,
                             spacing=spacing)

    # read and scale the source space [in m]
    sss = read_source_spaces(src)
    logger.info("scaling source space %s:  %s -> %s", spacing, subject_from,
                subject_to)
    logger.info("Scale factor: %s", scale)
    add_dist = False
    for ss in sss:
        ss['subject_his_id'] = subject_to
        ss['rr'] *= scale
        # additional tags for volume source spaces
        for key in ('vox_mri_t', 'src_mri_t'):
            # maintain transform to original MRI volume ss['mri_volume_name']
            if key in ss:
                ss[key]['trans'][:3] *= scale[:, np.newaxis]
        # distances and patch info
        if uniform:
            if ss['dist'] is not None:
                ss['dist'] *= scale[0]
                # Sometimes this is read-only due to how it's read
                ss['nearest_dist'] = ss['nearest_dist'] * scale
                ss['dist_limit'] = ss['dist_limit'] * scale
        else:  # non-uniform scaling
            ss['nn'] /= scale
            _normalize_vectors(ss['nn'])
            if ss['dist'] is not None:
                add_dist = True
                dist_limit = float(np.abs(sss[0]['dist_limit']))
            elif ss['nearest'] is not None:
                add_dist = True
                dist_limit = 0

    if add_dist:
        logger.info("Recomputing distances, this might take a while")
        add_source_space_distances(sss, dist_limit, n_jobs)

    write_source_spaces(dst, sss)


def _scale_mri(subject_to, mri_fname, subject_from, scale, subjects_dir):
    """Scale an MRI by setting its affine."""
    subjects_dir, subject_from, scale, _ = _scale_params(
        subject_to, subject_from, scale, subjects_dir)

    if not has_nibabel():
        warn('Skipping MRI scaling for %s, please install nibabel')
        return

    import nibabel
    fname_from = op.join(mri_dirname.format(
        subjects_dir=subjects_dir, subject=subject_from), mri_fname)
    fname_to = op.join(mri_dirname.format(
        subjects_dir=subjects_dir, subject=subject_to), mri_fname)
    img = nibabel.load(fname_from)
    zooms = np.array(img.header.get_zooms())
    zooms[[0, 2, 1]] *= scale
    img.header.set_zooms(zooms)
    # Hack to fix nibabel problems, see
    # https://github.com/nipy/nibabel/issues/619
    img._affine = img.header.get_affine()  # or could use None
    nibabel.save(img, fname_to)


def _scale_xfm(subject_to, xfm_fname, mri_name, subject_from, scale,
               subjects_dir):
    """Scale a transform."""
    subjects_dir, subject_from, scale, _ = _scale_params(
        subject_to, subject_from, scale, subjects_dir)

    # The nibabel warning should already be there in MRI step, if applicable,
    # as we only get here if T1.mgz is present (and thus a scaling was
    # attempted) so we can silently return here.
    if not has_nibabel():
        return

    fname_from = os.path.join(
        mri_transforms_dirname.format(
            subjects_dir=subjects_dir, subject=subject_from), xfm_fname)
    fname_to = op.join(
        mri_transforms_dirname.format(
            subjects_dir=subjects_dir, subject=subject_to), xfm_fname)
    assert op.isfile(fname_from), fname_from
    assert op.isdir(op.dirname(fname_to)), op.dirname(fname_to)
    # The "talairach.xfm" file stores the ras_mni transform.
    #
    # For "from" subj F, "to" subj T, F->T scaling S, some equivalent vertex
    # positions F_x and T_x in MRI (Freesurfer RAS) coords, knowing that
    # we have T_x = S @ F_x, we want to have the same MNI coords computed
    # for these vertices:
    #
    #              T_mri_mni @ T_x = F_mri_mni @ F_x
    #
    # We need to find the correct T_ras_mni (talaraich.xfm file) that yields
    # this. So we derive (where † indicates inversion):
    #
    #          T_mri_mni @ S @ F_x = F_mri_mni @ F_x
    #                T_mri_mni @ S = F_mri_mni
    #    T_ras_mni @ T_mri_ras @ S = F_ras_mni @ F_mri_ras
    #        T_ras_mni @ T_mri_ras = F_ras_mni @ F_mri_ras @ S⁻¹
    #                    T_ras_mni = F_ras_mni @ F_mri_ras @ S⁻¹ @ T_ras_mri
    #

    # prepare the scale (S) transform
    scale = np.atleast_1d(scale)
    scale = np.tile(scale, 3) if len(scale) == 1 else scale
    S = Transform('mri', 'mri', scaling(*scale))  # F_mri->T_mri

    #
    # Get the necessary transforms of the "from" subject
    #
    xfm, kind = _read_fs_xfm(fname_from)
    assert kind == 'MNI Transform File', kind
    _, _, F_mri_ras, _, _ = _read_mri_info(mri_name, units='mm')
    F_ras_mni = Transform('ras', 'mni_tal', xfm)
    del xfm

    #
    # Get the necessary transforms of the "to" subject
    #
    mri_name = op.join(mri_dirname.format(
        subjects_dir=subjects_dir, subject=subject_to), op.basename(mri_name))
    _, _, T_mri_ras, _, _ = _read_mri_info(mri_name, units='mm')
    T_ras_mri = invert_transform(T_mri_ras)
    del mri_name, T_mri_ras

    # Finally we construct as above:
    #
    #    T_ras_mni = F_ras_mni @ F_mri_ras @ S⁻¹ @ T_ras_mri
    #
    # By moving right to left through the equation.
    T_ras_mni = \
        combine_transforms(
            combine_transforms(
                combine_transforms(
                    T_ras_mri, invert_transform(S), 'ras', 'mri'),
                F_mri_ras, 'ras', 'ras'),
            F_ras_mni, 'ras', 'mni_tal')
    _write_fs_xfm(fname_to, T_ras_mni['trans'], kind)


def _read_surface(filename, *, on_defects):
    bem = dict()
    if filename is not None and op.exists(filename):
        if filename.endswith('.fif'):
            bem = read_bem_surfaces(
                filename, on_defects=on_defects, verbose=False
            )[0]
        else:
            try:
                bem = read_surface(filename, return_dict=True)[2]
                bem['rr'] *= 1e-3
                complete_surface_info(bem, copy=False)
            except Exception:
                raise ValueError(
                    "Error loading surface from %s (see "
                    "Terminal for details)." % filename)
    return bem


@fill_doc
class Coregistration(object):
    """Class for MRI<->head coregistration.

    Parameters
    ----------
    info : instance of Info | None
        The measurement info.
    %(subject)s
    %(subjects_dir)s
    %(fiducials)s
    %(on_defects)s

        .. versionadded:: 1.0

    Attributes
    ----------
    fiducials : instance of DigMontage
        A montage containing the MRI fiducials.
    trans : instance of Transform
        MRI<->Head coordinate transformation.

    See Also
    --------
    mne.scale_mri

    Notes
    -----
    Internal computation quantities parameters are in the following units:

    - rotation are in radians
    - translation are in m
    - scale are in scale proportion

    If using a scale mode, the :func:`~mne.scale_mri` should be used
    to create a surrogate MRI subject with the proper scale factors.
    """

    def __init__(self, info, subject, subjects_dir=None, fiducials='auto', *,
                 on_defects='raise'):
        _validate_type(info, (Info, None), 'info')
        self._info = info
        self._subject = _check_subject(subject, subject)
        self._subjects_dir = get_subjects_dir(subjects_dir, raise_error=True)
        self._scale_mode = None
        self._on_defects = on_defects

        self._rot_trans = None
        self._default_parameters = \
            np.array([0., 0., 0., 0., 0., 0., 1., 1., 1.])

        self._rotation = self._default_parameters[:3]
        self._translation = self._default_parameters[3:6]
        self._scale = self._default_parameters[6:9]
        self._icp_iterations = 20
        self._icp_angle = 0.2
        self._icp_distance = 0.2
        self._icp_scale = 0.2
        self._icp_fid_matches = ('nearest', 'matched')
        self._icp_fid_match = self._icp_fid_matches[0]
        self._lpa_weight = 1.
        self._nasion_weight = 10.
        self._rpa_weight = 1.
        self._hsp_weight = 1.
        self._eeg_weight = 1.
        self._hpi_weight = 1.
        self._extra_points_filter = None

        self._setup_digs()
        self._setup_bem()

        self._fid_filename = None
        self._setup_fiducials(fiducials)
        self.reset()

    def _setup_digs(self):
        if self._info is None:
            self._dig_dict = dict(
                hpi=np.zeros((1, 3)),
                dig_ch_pos_location=np.zeros((1, 3)),
                hsp=np.zeros((1, 3)),
                rpa=np.zeros((1, 3)),
                nasion=np.zeros((1, 3)),
                lpa=np.zeros((1, 3)),
            )
        else:
            self._dig_dict = _get_data_as_dict_from_dig(
                dig=self._info['dig'],
                exclude_ref_channel=False
            )
            # adjustments:
            # set weights to 0 for None input
            # convert fids to float arrays
            for k, w_atr in zip(['nasion', 'lpa', 'rpa', 'hsp', 'hpi'],
                                ['_nasion_weight', '_lpa_weight',
                                 '_rpa_weight', '_hsp_weight', '_hpi_weight']):
                if self._dig_dict[k] is None:
                    self._dig_dict[k] = np.zeros((0, 3))
                    setattr(self, w_atr, 0)
                elif k in ['rpa', 'nasion', 'lpa']:
                    self._dig_dict[k] = np.array([self._dig_dict[k]], float)

    def _setup_bem(self):
        # find high-res head model (if possible)
        high_res_path = _find_head_bem(self._subject, self._subjects_dir,
                                       high_res=True)
        low_res_path = _find_head_bem(self._subject, self._subjects_dir,
                                      high_res=False)
        if high_res_path is None and low_res_path is None:
            raise RuntimeError("No standard head model was "
                               f"found for subject {self._subject}")
        if high_res_path is not None:
            self._bem_high_res = _read_surface(
                high_res_path, on_defects=self._on_defects
            )
            logger.info(f'Using high resolution head model in {high_res_path}')
        else:
            self._bem_high_res = _read_surface(
                low_res_path, on_defects=self._on_defects
            )
            logger.info(f'Using low resolution head model in {low_res_path}')
        if low_res_path is None:
            # This should be very rare!
            warn('No low-resolution head found, decimating high resolution '
                 'mesh (%d vertices): %s' % (len(self._bem_high_res['rr']),
                                             high_res_path,))
            # Create one from the high res one, which we know we have
            rr, tris = decimate_surface(self._bem_high_res['rr'],
                                        self._bem_high_res['tris'],
                                        n_triangles=5120)
            # directly set the attributes of bem_low_res
            self._bem_low_res = complete_surface_info(
                dict(rr=rr, tris=tris), copy=False, verbose=False)
        else:
            self._bem_low_res = _read_surface(
                low_res_path, on_defects=self._on_defects
            )

    def _setup_fiducials(self, fids):
        _validate_type(fids, (str, dict, list))
        # find fiducials file
        fid_accurate = None
        if fids == 'auto':
            fid_files = _find_fiducials_files(self._subject,
                                              self._subjects_dir)
            if len(fid_files) > 0:
                # Read fiducials from disk
                fid_filename = fid_files[0].format(
                    subjects_dir=self._subjects_dir, subject=self._subject)
                logger.info(f'Using fiducials from: {fid_filename}.')
                fids, _ = read_fiducials(fid_filename)
                fid_accurate = True
                self._fid_filename = fid_filename
            else:
                fids = 'estimated'

        if fids == 'estimated':
            logger.info('Estimating fiducials from fsaverage.')
            fid_accurate = False
            fids = get_mni_fiducials(self._subject, self._subjects_dir)

        fid_accurate = True if fid_accurate is None else fid_accurate
        if isinstance(fids, list):
            fid_coords = _fiducial_coords(fids)
        else:
            assert isinstance(fids, dict)
            fid_coords = np.array([fids['lpa'], fids['nasion'], fids['rpa']],
                                  dtype=float)

        self._fid_points = fid_coords
        self._fid_accurate = fid_accurate

        # does not seem to happen by itself ... so hard code it:
        self._reset_fiducials()

    def _reset_fiducials(self):
        dig_montage = make_dig_montage(
            lpa=self._fid_points[0],
            nasion=self._fid_points[1],
            rpa=self._fid_points[2],
            coord_frame='mri'
        )
        self.fiducials = dig_montage

    def _update_params(self, rot=None, tra=None, sca=None,
                       force_update=False):
        if force_update and tra is None:
            tra = self._translation
        rot_changed = False
        if rot is not None:
            rot_changed = True
            self._last_rotation = self._rotation.copy()
            self._rotation = rot
        tra_changed = False
        if rot_changed or tra is not None:
            if tra is None:
                tra = self._translation
            tra_changed = True
            self._last_translation = self._translation.copy()
            self._translation = tra
            self._head_mri_t = rotation(*self._rotation).T
            self._head_mri_t[:3, 3] = \
                -np.dot(self._head_mri_t[:3, :3], tra)
            self._transformed_dig_hpi = \
                apply_trans(self._head_mri_t, self._dig_dict['hpi'])
            self._transformed_dig_eeg = \
                apply_trans(
                    self._head_mri_t, self._dig_dict['dig_ch_pos_location'])
            self._transformed_dig_extra = \
                apply_trans(self._head_mri_t,
                            self._filtered_extra_points)
            self._transformed_orig_dig_extra = \
                apply_trans(self._head_mri_t, self._dig_dict['hsp'])
            self._mri_head_t = rotation(*self._rotation)
            self._mri_head_t[:3, 3] = np.array(tra)
        if tra_changed or sca is not None:
            if sca is None:
                sca = self._scale
            self._last_scale = self._scale.copy()
            self._scale = sca
            self._mri_trans = np.eye(4)
            self._mri_trans[:, :3] *= sca
            self._transformed_high_res_mri_points = \
                apply_trans(self._mri_trans,
                            self._processed_high_res_mri_points)
            self._update_nearest_calc()

        if tra_changed:
            self._nearest_transformed_high_res_mri_idx_orig_hsp = \
                self._nearest_calc.query(self._transformed_orig_dig_extra)[1]
            self._nearest_transformed_high_res_mri_idx_hpi = \
                self._nearest_calc.query(self._transformed_dig_hpi)[1]
            self._nearest_transformed_high_res_mri_idx_eeg = \
                self._nearest_calc.query(self._transformed_dig_eeg)[1]
            self._nearest_transformed_high_res_mri_idx_rpa = \
                self._nearest_calc.query(
                    apply_trans(self._head_mri_t, self._dig_dict['rpa']))[1]
            self._nearest_transformed_high_res_mri_idx_nasion = \
                self._nearest_calc.query(
                    apply_trans(self._head_mri_t, self._dig_dict['nasion']))[1]
            self._nearest_transformed_high_res_mri_idx_lpa = \
                self._nearest_calc.query(
                    apply_trans(self._head_mri_t, self._dig_dict['lpa']))[1]

    def set_scale_mode(self, scale_mode):
        """Select how to fit the scale parameters.

        Parameters
        ----------
        scale_mode : None | str
            The scale mode can be 'uniform', '3-axis' or disabled.
            Defaults to None.

            * 'uniform': 1 scale factor is recovered.
            * '3-axis': 3 scale factors are recovered.
            * None: do not scale the MRI.

        Returns
        -------
        self : Coregistration
            The modified Coregistration object.
        """
        self._scale_mode = scale_mode
        return self

    def set_grow_hair(self, value):
        """Compensate for hair on the digitizer head shape.

        Parameters
        ----------
        value : float
            Move the back of the MRI head outwards by ``value`` (mm).

        Returns
        -------
        self : Coregistration
            The modified Coregistration object.
        """
        self._grow_hair = value
        self._update_params(force_update=True)
        return self

    def set_rotation(self, rot):
        """Set the rotation parameter.

        Parameters
        ----------
        rot : array, shape (3,)
            The rotation parameter (in radians).

        Returns
        -------
        self : Coregistration
            The modified Coregistration object.
        """
        self._update_params(rot=np.array(rot))
        return self

    def set_translation(self, tra):
        """Set the translation parameter.

        Parameters
        ----------
        tra : array, shape (3,)
            The translation parameter (in m.).

        Returns
        -------
        self : Coregistration
            The modified Coregistration object.
        """
        self._update_params(tra=np.array(tra))
        return self

    def set_scale(self, sca):
        """Set the scale parameter.

        Parameters
        ----------
        sca : array, shape (3,)
            The scale parameter.

        Returns
        -------
        self : Coregistration
            The modified Coregistration object.
        """
        self._update_params(sca=np.array(sca))
        return self

    def _update_nearest_calc(self):
        self._nearest_calc = _DistanceQuery(
            self._processed_high_res_mri_points * self._scale)

    @property
    def _filtered_extra_points(self):
        if self._extra_points_filter is None:
            return self._dig_dict['hsp']
        else:
            return self._dig_dict['hsp'][self._extra_points_filter]

    @property
    def _parameters(self):
        return np.concatenate((self._rotation, self._translation, self._scale))

    @property
    def _last_parameters(self):
        return np.concatenate((self._last_rotation,
                               self._last_translation, self._last_scale))

    @property
    def _changes(self):
        move = np.linalg.norm(self._last_translation - self._translation) * 1e3
        angle = np.rad2deg(_angle_between_quats(
            rot_to_quat(rotation(*self._rotation)[:3, :3]),
            rot_to_quat(rotation(*self._last_rotation)[:3, :3])))
        percs = 100 * (self._scale - self._last_scale) / self._last_scale
        return move, angle, percs

    @property
    def _nearest_transformed_high_res_mri_idx_hsp(self):
        return self._nearest_calc.query(
            apply_trans(self._head_mri_t, self._filtered_extra_points))[1]

    @property
    def _has_hsp_data(self):
        return (self._has_mri_data and
                len(self._nearest_transformed_high_res_mri_idx_hsp) > 0)

    @property
    def _has_hpi_data(self):
        return (self._has_mri_data and
                len(self._nearest_transformed_high_res_mri_idx_hpi) > 0)

    @property
    def _has_eeg_data(self):
        return (self._has_mri_data and
                len(self._nearest_transformed_high_res_mri_idx_eeg) > 0)

    @property
    def _has_lpa_data(self):
        mri_point = self.fiducials.dig[_map_fid_name_to_idx('lpa')]
        assert mri_point['ident'] == FIFF.FIFFV_POINT_LPA
        has_mri_data = np.any(mri_point['r'])
        has_head_data = np.any(self._dig_dict['lpa'])
        return has_mri_data and has_head_data

    @property
    def _has_nasion_data(self):
        mri_point = self.fiducials.dig[_map_fid_name_to_idx('nasion')]
        assert mri_point['ident'] == FIFF.FIFFV_POINT_NASION
        has_mri_data = np.any(mri_point['r'])
        has_head_data = np.any(self._dig_dict['nasion'])
        return has_mri_data and has_head_data

    @property
    def _has_rpa_data(self):
        mri_point = self.fiducials.dig[_map_fid_name_to_idx('rpa')]
        assert mri_point['ident'] == FIFF.FIFFV_POINT_RPA
        has_mri_data = np.any(mri_point['r'])
        has_head_data = np.any(self._dig_dict['rpa'])
        return has_mri_data and has_head_data

    @property
    def _processed_high_res_mri_points(self):
        return self._get_processed_mri_points('high')

    @property
    def _processed_low_res_mri_points(self):
        return self._get_processed_mri_points('low')

    def _get_processed_mri_points(self, res):
        bem = self._bem_low_res if res == 'low' else self._bem_high_res
        points = bem['rr'].copy()
        if self._grow_hair:
            assert len(bem['nn'])  # should be guaranteed by _read_surface
            scaled_hair_dist = (1e-3 * self._grow_hair /
                                np.array(self._scale))
            hair = points[:, 2] > points[:, 1]
            points[hair] += bem['nn'][hair] * scaled_hair_dist
        return points

    @property
    def _has_mri_data(self):
        return len(self._transformed_high_res_mri_points) > 0

    @property
    def _has_dig_data(self):
        return (self._has_mri_data and
                len(self._nearest_transformed_high_res_mri_idx_hsp) > 0)

    @property
    def _orig_hsp_point_distance(self):
        mri_points = self._transformed_high_res_mri_points[
            self._nearest_transformed_high_res_mri_idx_orig_hsp]
        hsp_points = self._transformed_orig_dig_extra
        return np.linalg.norm(mri_points - hsp_points, axis=-1)

    def _log_dig_mri_distance(self, prefix):
        errs_nearest = self.compute_dig_mri_distances()
        logger.info(f'{prefix} median distance: '
                    f'{np.median(errs_nearest * 1000):6.2f} mm')

    @property
    def scale(self):
        """Get the current scale factor.

        Returns
        -------
        scale : ndarray, shape (3,)
            The scale factors.
        """
        return self._scale.copy()

    @verbose
    def fit_fiducials(self, lpa_weight=1., nasion_weight=10., rpa_weight=1.,
                      verbose=None):
        """Find rotation and translation to fit all 3 fiducials.

        Parameters
        ----------
        lpa_weight : float
            Relative weight for LPA. The default value is 1.
        nasion_weight : float
            Relative weight for nasion. The default value is 10.
        rpa_weight : float
            Relative weight for RPA. The default value is 1.
        %(verbose)s

        Returns
        -------
        self : Coregistration
            The modified Coregistration object.
        """
        logger.info('Aligning using fiducials')
        self._log_dig_mri_distance('Start')
        n_scale_params = self._n_scale_params
        if n_scale_params == 3:
            # enforce 1 even for 3-axis here (3 points is not enough)
            logger.info("Enforcing 1 scaling parameter for fit "
                        "with fiducials.")
            n_scale_params = 1
        self._lpa_weight = lpa_weight
        self._nasion_weight = nasion_weight
        self._rpa_weight = rpa_weight

        head_pts = np.vstack((self._dig_dict['lpa'],
                              self._dig_dict['nasion'],
                              self._dig_dict['rpa']))
        mri_pts = np.vstack(
            (self.fiducials.dig[0]['r'],  # LPA
             self.fiducials.dig[1]['r'],  # Nasion
             self.fiducials.dig[2]['r'])  # RPA
        )
        weights = [lpa_weight, nasion_weight, rpa_weight]

        if n_scale_params == 0:
            mri_pts *= self._scale  # not done in fit_matched_points
        x0 = self._parameters
        x0 = x0[:6 + n_scale_params]
        est = fit_matched_points(mri_pts, head_pts, x0=x0, out='params',
                                 scale=n_scale_params, weights=weights)
        if n_scale_params == 0:
            self._update_params(rot=est[:3], tra=est[3:6])
        else:
            assert est.size == 7
            est = np.concatenate([est, [est[-1]] * 2])
            assert est.size == 9
            self._update_params(rot=est[:3], tra=est[3:6], sca=est[6:9])
        self._log_dig_mri_distance('End  ')
        return self

    def _setup_icp(self, n_scale_params):
        head_pts = list()
        mri_pts = list()
        weights = list()
        if self._has_dig_data and self._hsp_weight > 0:  # should be true
            head_pts.append(self._filtered_extra_points)
            mri_pts.append(self._processed_high_res_mri_points[
                self._nearest_transformed_high_res_mri_idx_hsp])
            weights.append(np.full(len(head_pts[-1]), self._hsp_weight))
        for key in ('lpa', 'nasion', 'rpa'):
            if getattr(self, f'_has_{key}_data'):
                head_pts.append(self._dig_dict[key])
                if self._icp_fid_match == 'matched':
                    idx = _map_fid_name_to_idx(name=key)
                    p = self.fiducials.dig[idx]['r'].reshape(1, -1)
                    mri_pts.append(p)
                else:
                    assert self._icp_fid_match == 'nearest'
                    mri_pts.append(self._processed_high_res_mri_points[
                        getattr(
                            self,
                            '_nearest_transformed_high_res_mri_idx_%s'
                            % (key,))])
                weights.append(np.full(len(mri_pts[-1]),
                                       getattr(self, '_%s_weight' % key)))
        if self._has_eeg_data and self._eeg_weight > 0:
            head_pts.append(self._dig_dict['dig_ch_pos_location'])
            mri_pts.append(self._processed_high_res_mri_points[
                self._nearest_transformed_high_res_mri_idx_eeg])
            weights.append(np.full(len(mri_pts[-1]), self._eeg_weight))
        if self._has_hpi_data and self._hpi_weight > 0:
            head_pts.append(self._dig_dict['hpi'])
            mri_pts.append(self._processed_high_res_mri_points[
                self._nearest_transformed_high_res_mri_idx_hpi])
            weights.append(np.full(len(mri_pts[-1]), self._hpi_weight))
        head_pts = np.concatenate(head_pts)
        mri_pts = np.concatenate(mri_pts)
        weights = np.concatenate(weights)
        if n_scale_params == 0:
            mri_pts *= self._scale  # not done in fit_matched_points
        return head_pts, mri_pts, weights

    def set_fid_match(self, match):
        """Set the strategy for fitting anatomical landmark (fiducial) points.

        Parameters
        ----------
        match : 'nearest' | 'matched'
            Alignment strategy; ``'nearest'`` aligns anatomical landmarks to
            any point on the head surface; ``'matched'`` aligns to the fiducial
            points in the MRI.

        Returns
        -------
        self : Coregistration
            The modified Coregistration object.
        """
        _check_option('match', match, self._icp_fid_matches)
        self._icp_fid_match = match
        return self

    @verbose
    def fit_icp(self, n_iterations=20, lpa_weight=1., nasion_weight=10.,
                rpa_weight=1., hsp_weight=1., eeg_weight=1., hpi_weight=1.,
                callback=None, verbose=None):
        """Find MRI scaling, translation, and rotation to match HSP.

        Parameters
        ----------
        n_iterations : int
            Maximum number of iterations.
        lpa_weight : float
            Relative weight for LPA. The default value is 1.
        nasion_weight : float
            Relative weight for nasion. The default value is 10.
        rpa_weight : float
            Relative weight for RPA. The default value is 1.
        hsp_weight : float
            Relative weight for HSP. The default value is 1.
        eeg_weight : float
            Relative weight for EEG. The default value is 1.
        hpi_weight : float
            Relative weight for HPI. The default value is 1.
        callback : callable | None
            A function to call on each iteration. Useful for status message
            updates. It will be passed the keyword arguments ``iteration``
            and ``n_iterations``.
        %(verbose)s

        Returns
        -------
        self : Coregistration
            The modified Coregistration object.
        """
        logger.info('Aligning using ICP')
        self._log_dig_mri_distance('Start    ')
        n_scale_params = self._n_scale_params
        self._lpa_weight = lpa_weight
        self._nasion_weight = nasion_weight
        self._rpa_weight = rpa_weight
        self._hsp_weight = hsp_weight
        self._eeg_weight = eeg_weight
        self._hsp_weight = hpi_weight

        # Initial guess (current state)
        est = self._parameters
        est = est[:[6, 7, None, 9][n_scale_params]]

        # Do the fits, assigning and evaluating at each step
        for iteration in range(n_iterations):
            head_pts, mri_pts, weights = self._setup_icp(n_scale_params)
            est = fit_matched_points(mri_pts, head_pts, scale=n_scale_params,
                                     x0=est, out='params', weights=weights)
            if n_scale_params == 0:
                self._update_params(rot=est[:3], tra=est[3:6])
            elif n_scale_params == 1:
                est = np.array(list(est) + [est[-1]] * 2)
                self._update_params(rot=est[:3], tra=est[3:6], sca=est[6:9])
            else:
                self._update_params(rot=est[:3], tra=est[3:6], sca=est[6:9])
            angle, move, scale = self._changes
            self._log_dig_mri_distance(f'  ICP {iteration + 1:2d} ')
            if callback is not None:
                callback(iteration, n_iterations)
            if angle <= self._icp_angle and move <= self._icp_distance and \
                    all(scale <= self._icp_scale):
                break
        self._log_dig_mri_distance('End      ')
        return self

    @property
    def _n_scale_params(self):
        if self._scale_mode is None:
            n_scale_params = 0
        elif self._scale_mode == 'uniform':
            n_scale_params = 1
        else:
            n_scale_params = 3
        return n_scale_params

    def omit_head_shape_points(self, distance):
        """Exclude head shape points that are far away from the MRI head.

        Parameters
        ----------
        distance : float
            Exclude all points that are further away from the MRI head than
            this distance (in m.). A value of distance <= 0 excludes nothing.

        Returns
        -------
        self : Coregistration
            The modified Coregistration object.
        """
        distance = float(distance)
        if distance <= 0:
            return

        # find the new filter
        mask = self._orig_hsp_point_distance <= distance
        n_excluded = np.sum(~mask)
        logger.info("Coregistration: Excluding %i head shape points with "
                    "distance >= %.3f m.", n_excluded, distance)
        # set the filter
        self._extra_points_filter = mask
        self._update_params(force_update=True)
        return self

    def compute_dig_mri_distances(self):
        """Compute distance between head shape points and MRI skin surface.

        Returns
        -------
        dist : array, shape (n_points,)
            The distance of the head shape points to the MRI skin surface.

        See Also
        --------
        mne.dig_mri_distances
        """
        # we don't use `dig_mri_distances` here because it should be much
        # faster to use our already-determined nearest points
        hsp_points, mri_points, _ = self._setup_icp(0)
        hsp_points = apply_trans(self._head_mri_t, hsp_points)
        return np.linalg.norm(mri_points - hsp_points, axis=-1)

    @property
    def trans(self):
        """The head->mri :class:`~mne.transforms.Transform`."""
        return Transform('head', 'mri', self._head_mri_t)

    def reset(self):
        """Reset all the parameters affecting the coregistration.

        Returns
        -------
        self : Coregistration
            The modified Coregistration object.
        """
        self._grow_hair = 0.
        self.set_rotation(self._default_parameters[:3])
        self.set_translation(self._default_parameters[3:6])
        self.set_scale(self._default_parameters[6:9])
        self._extra_points_filter = None
        self._update_nearest_calc()
        return self

    def _get_fiducials_distance(self):
        distance = dict()
        for key in ('lpa', 'nasion', 'rpa'):
            idx = _map_fid_name_to_idx(name=key)
            fid = self.fiducials.dig[idx]['r'].reshape(1, -1)

            transformed_mri = apply_trans(self._mri_trans, fid)
            transformed_hsp = apply_trans(
                self._head_mri_t, self._dig_dict[key])
            distance[key] = np.linalg.norm(
                np.ravel(transformed_mri - transformed_hsp))
        return np.array(list(distance.values())) * 1e3

    def _get_fiducials_distance_str(self):
        dists = self._get_fiducials_distance()
        return f"Fiducials: {dists[0]:.1f}, {dists[1]:.1f}, {dists[2]:.1f} mm"

    def _get_point_distance(self):
        mri_points = list()
        hsp_points = list()
        if self._hsp_weight > 0 and self._has_hsp_data:
            mri_points.append(self._transformed_high_res_mri_points[
                self._nearest_transformed_high_res_mri_idx_hsp])
            hsp_points.append(self._transformed_dig_extra)
            assert len(mri_points[-1]) == len(hsp_points[-1])
        if self._eeg_weight > 0 and self._has_eeg_data:
            mri_points.append(self._transformed_high_res_mri_points[
                self._nearest_transformed_high_res_mri_idx_eeg])
            hsp_points.append(self._transformed_dig_eeg)
            assert len(mri_points[-1]) == len(hsp_points[-1])
        if self._hpi_weight > 0 and self._has_hpi_data:
            mri_points.append(self._transformed_high_res_mri_points[
                self._nearest_transformed_high_res_mri_idx_hpi])
            hsp_points.append(self._transformed_dig_hpi)
            assert len(mri_points[-1]) == len(hsp_points[-1])
        if all(len(h) == 0 for h in hsp_points):
            return None
        mri_points = np.concatenate(mri_points)
        hsp_points = np.concatenate(hsp_points)
        return np.linalg.norm(mri_points - hsp_points, axis=-1)

    def _get_point_distance_str(self):
        point_distance = self._get_point_distance()
        if point_distance is None:
            return ""
        dists = 1e3 * point_distance
        av_dist = np.mean(dists)
        std_dist = np.std(dists)
        kinds = [kind for kind, check in
                 (('HSP', self._hsp_weight > 0 and self._has_hsp_data),
                  ('EEG', self._eeg_weight > 0 and self._has_eeg_data),
                  ('HPI', self._hpi_weight > 0 and self._has_hpi_data))
                 if check]
        kinds = '+'.join(kinds)
        return f"{len(dists)} {kinds}: {av_dist:.1f} ± {std_dist:.1f} mm"