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Add: * resampling images to images / mapped voxels * resampling images to output space * smoothing over voxel axes * FWHM / sigma conversion
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# emacs: -*- mode: python-mode; py-indent-offset: 4; indent-tabs-mode: nil -*- | ||
# vi: set ft=python sts=4 ts=4 sw=4 et: | ||
### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ## | ||
# | ||
# See COPYING file distributed along with the NiBabel package for the | ||
# copyright and license terms. | ||
# | ||
### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ## | ||
""" Image processing functions for: | ||
* smoothing | ||
* resampling | ||
* converting sd to and from FWHM | ||
Smoothing and resampling routines need scipy | ||
""" | ||
from __future__ import print_function, division, absolute_import | ||
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import numpy as np | ||
import numpy.linalg as npl | ||
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from .optpkg import optional_package | ||
spnd, _, _ = optional_package('scipy.ndimage') | ||
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from .affines import AffineError, to_matvec, from_matvec, append_diag | ||
from .spaces import vox2out_vox | ||
from .nifti1 import Nifti1Image | ||
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SIGMA2FWHM = np.sqrt(8 * np.log(2)) | ||
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def fwhm2sigma(fwhm): | ||
""" Convert a FWHM value to sigma in a Gaussian kernel. | ||
Parameters | ||
---------- | ||
fwhm : array-like | ||
FWHM value or values | ||
Returns | ||
------- | ||
sigma : array or float | ||
sigma values corresponding to `fwhm` values | ||
Examples | ||
-------- | ||
>>> sigma = fwhm2sigma(6) | ||
>>> sigmae = fwhm2sigma([6, 7, 8]) | ||
>>> sigma == sigmae[0] | ||
True | ||
""" | ||
return np.asarray(fwhm) / SIGMA2FWHM | ||
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def sigma2fwhm(sigma): | ||
""" Convert a sigma in a Gaussian kernel to a FWHM value | ||
Parameters | ||
---------- | ||
sigma : array-like | ||
sigma value or values | ||
Returns | ||
------- | ||
fwhm : array or float | ||
fwhm values corresponding to `sigma` values | ||
Examples | ||
-------- | ||
>>> fwhm = sigma2fwhm(3) | ||
>>> fwhms = sigma2fwhm([3, 4, 5]) | ||
>>> fwhm == fwhms[0] | ||
True | ||
""" | ||
return np.asarray(sigma) * SIGMA2FWHM | ||
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def adapt_affine(affine, n_dim): | ||
""" Adapt input / output dimensions of spatial `affine` for `n_dims` | ||
Adapts a spatial (4, 4) affine that is being applied to an image with fewer | ||
than 3 spatial dimensions, or more than 3 dimensions. If there are more | ||
than three dimensions, assume an identity transformation for these | ||
dimensions. | ||
Parameters | ||
---------- | ||
affine : array-like | ||
affine transform. Usually shape (4, 4). For what follows ``N, M = | ||
affine.shape`` | ||
n_dims : int | ||
Number of dimensions of underlying array, and therefore number of input | ||
dimensions for affine. | ||
Returns | ||
------- | ||
adapted : shape (M, n_dims+1) array | ||
Affine array adapted to number of input dimensions. Columns of the | ||
affine corresponding to missing input dimensions have been dropped, | ||
columns corresponding to extra input dimensions have an extra identity | ||
column added | ||
""" | ||
affine = np.asarray(affine) | ||
rzs, trans = to_matvec(affine) | ||
# For missing input dimensions, drop columns in rzs | ||
rzs = rzs[:, :n_dim] | ||
adapted = from_matvec(rzs, trans) | ||
n_extra_columns = n_dim - adapted.shape[1] + 1 | ||
if n_extra_columns > 0: | ||
adapted = append_diag(adapted, np.ones((n_extra_columns,))) | ||
return adapted | ||
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def resample_from_to(from_img, | ||
to_vox_map, | ||
order=3, | ||
mode='constant', | ||
cval = 0., | ||
out_class=Nifti1Image): | ||
""" Resample image `from_img` to mapped voxel space `to_vox_map` | ||
Parameters | ||
---------- | ||
from_img : object | ||
Object having attributes ``dataobj``, ``affine``, ``header``. If | ||
`out_class` is not None, ``img.__class__`` should be able to construct | ||
an image from data, affine and header. | ||
to_vox_map : image object or length 2 sequence | ||
If object, has attributes ``shape`` giving input voxel shape, and | ||
``affine`` giving mapping of input voxels to output space. If length 2 | ||
sequence, elements are (shape, affine) with same meaning as above. The | ||
affine is a (4, 4) array-like. | ||
order : int, optional | ||
The order of the spline interpolation, default is 3. The order has to | ||
be in the range 0-5 (see ``scipy.ndimage.affine_transform``) | ||
mode : str, optional | ||
Points outside the boundaries of the input are filled according | ||
to the given mode ('constant', 'nearest', 'reflect' or 'wrap'). | ||
Default is 'constant' (see ``scipy.ndimage.affine_transform``) | ||
cval : scalar, optional | ||
Value used for points outside the boundaries of the input if | ||
``mode='constant'``. Default is 0.0 (see | ||
``scipy.ndimage.affine_transform``) | ||
out_class : None or SpatialImage class, optional | ||
Class of output image. If None, use ``from_img.__class__``. | ||
Returns | ||
------- | ||
out_img : object | ||
Image of instance specified by `out_class`, containing data output from | ||
resampling `from_img` into axes aligned to the output space of | ||
``from_img.affine`` | ||
""" | ||
try: | ||
to_shape, to_affine = to_vox_map.shape, to_vox_map.affine | ||
except AttributeError: | ||
to_shape, to_affine = to_vox_map | ||
a_to_affine = adapt_affine(to_affine, len(to_shape)) | ||
if out_class is None: | ||
out_class = from_img.__class__ | ||
from_n_dim = len(from_img.shape) | ||
if from_n_dim < 3: | ||
raise AffineError('from_img must be at least 3D') | ||
a_from_affine = adapt_affine(from_img.affine, from_n_dim) | ||
to_vox2from_vox = npl.inv(a_from_affine).dot(a_to_affine) | ||
rzs, trans = to_matvec(to_vox2from_vox) | ||
data = spnd.affine_transform(from_img.dataobj, | ||
rzs, | ||
trans, | ||
to_shape, | ||
order = order, | ||
mode = mode, | ||
cval = cval) | ||
return out_class(data, to_affine, from_img.header) | ||
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def resample_to_output(in_img, | ||
voxel_sizes = None, | ||
order=3, | ||
mode='constant', | ||
cval = 0., | ||
out_class=Nifti1Image): | ||
""" Resample image `in_img` to output voxel axes (world space) | ||
Parameters | ||
---------- | ||
in_img : object | ||
Object having attributes ``dataobj``, ``affine``, ``header``. If | ||
`out_class` is not None, ``img.__class__`` should be able to construct | ||
an image from data, affine and header. | ||
voxel_sizes : None or sequence | ||
Gives the diagonal entries of ``out_img.affine` (except the trailing 1 | ||
for the homogenous coordinates) (``out_img.affine == np.diag(voxel_sizes | ||
+ [1])``). If None, return identity `out_img.affine`. | ||
order : int, optional | ||
The order of the spline interpolation, default is 3. The order has to | ||
be in the range 0-5 (see ``scipy.ndimage.affine_transform``). | ||
mode : str, optional | ||
Points outside the boundaries of the input are filled according | ||
to the given mode ('constant', 'nearest', 'reflect' or 'wrap'). | ||
Default is 'constant' (see ``scipy.ndimage.affine_transform``). | ||
cval : scalar, optional | ||
Value used for points outside the boundaries of the input if | ||
``mode='constant'``. Default is 0.0 (see | ||
``scipy.ndimage.affine_transform``). | ||
out_class : None or SpatialImage class, optional | ||
Class of output image. If None, use ``in_img.__class__``. | ||
Returns | ||
------- | ||
out_img : object | ||
Image of instance specified by `out_class`, containing data output from | ||
resampling `in_img` into axes aligned to the output space of | ||
``in_img.affine`` | ||
""" | ||
if out_class is None: | ||
out_class = in_img.__class__ | ||
# Allow 2D images by promoting to 3D. We might want to see what a slice | ||
# looks like when resampled into world coordinates | ||
in_shape = in_img.shape | ||
n_dim = len(in_shape) | ||
if n_dim < 3: # Expand image to 3D, make voxel sizes match | ||
new_shape = in_shape + (1,) * (3 - n_dim) | ||
data = in_img.get_data().reshape(new_shape) # 2D data should be small | ||
in_img = out_class(data, in_img.affine, in_img.header) | ||
if not voxel_sizes is None and len(voxel_sizes) == n_dim: | ||
# Need to pad out voxel sizes to match new image dimensions | ||
voxel_sizes = tuple(voxel_sizes) + (1,) * (3 - n_dim) | ||
out_vox_map = vox2out_vox((in_img.shape, in_img.affine), voxel_sizes) | ||
return resample_from_to(in_img, out_vox_map, order, mode, cval, out_class) | ||
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def smooth_image(img, | ||
fwhm, | ||
mode = 'nearest', | ||
cval = 0., | ||
out_class=Nifti1Image): | ||
""" Smooth image `img` along voxel axes by FWHM `fwhm` millimeters | ||
Parameters | ||
---------- | ||
img : object | ||
Object having attributes ``dataobj``, ``affine``, ``header``. If | ||
`out_class` is not None, ``img.__class__`` should be able to construct | ||
an image from data, affine and header. | ||
fwhm : scalar or length 3 sequence | ||
FWHM *in mm* over which to smooth. The smoothing applies to the voxel | ||
axes, not to the output axes, but is in millimeters. The function | ||
adjusts the FWHM to voxels using the voxel sizes calculated from the | ||
affine. A scalar implies the same smoothing across the spatial | ||
dimensions of the image, but 0 smoothing over any further dimensions | ||
such as time. A vector should be the same length as the number of | ||
image dimensions. | ||
mode : str, optional | ||
Points outside the boundaries of the input are filled according | ||
to the given mode ('constant', 'nearest', 'reflect' or 'wrap'). | ||
Default is 'nearest'. This is different from the default for | ||
``scipy.ndimage.affine_transform``, which is 'constant'. 'nearest' | ||
might be a better choice when smoothing to the edge of an image where | ||
there is still strong brain signal, otherwise this signal will get | ||
blurred towards zero. | ||
cval : scalar, optional | ||
Value used for points outside the boundaries of the input if | ||
``mode='constant'``. Default is 0.0 (see | ||
``scipy.ndimage.affine_transform``). | ||
out_class : None or SpatialImage class, optional | ||
Class of output image. If None, use ``img.__class__``. | ||
Returns | ||
------- | ||
smoothed_img : object | ||
Image of instance specified by `out_class`, containing data output from | ||
smoothing `img` data by given FWHM kernel. | ||
""" | ||
if out_class is None: | ||
out_class = img.__class__ | ||
n_dim = len(img.shape) | ||
# TODO: make sure time axis is last | ||
# Pad out fwhm from scalar, adding 0 for fourth etc (time etc) dimensions | ||
fwhm = np.asarray(fwhm) | ||
if fwhm.size == 1: | ||
fwhm_scalar = fwhm | ||
fwhm = np.zeros((n_dim,)) | ||
fwhm[:3] = fwhm_scalar | ||
# Voxel sizes | ||
RZS = img.affine[:-1, :n_dim] | ||
vox = np.sqrt(np.sum(RZS ** 2, 0)) | ||
# Smoothing in terms of voxels | ||
vox_fwhm = fwhm / vox | ||
vox_sd = fwhm2sigma(vox_fwhm) | ||
# Do the smoothing | ||
sm_data = spnd.gaussian_filter(img.dataobj, | ||
vox_sd, | ||
mode = mode, | ||
cval = cval) | ||
return out_class(sm_data, img.affine, img.header) |
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