NF: spatial processing module

Add:

* resampling images to images / mapped voxels
* resampling images to output space
* smoothing over voxel axes
* FWHM / sigma conversion

Author: matthew-brett

nibabel/processing.py

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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
+
+import numpy as np
+import numpy.linalg as npl
+
+from .optpkg import optional_package
+spnd, _, _ = optional_package('scipy.ndimage')
+
+from .affines import AffineError, to_matvec, from_matvec, append_diag
+from .spaces import vox2out_vox
+from .nifti1 import Nifti1Image
+
+SIGMA2FWHM = np.sqrt(8 * np.log(2))
+
+
+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
+
+
+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
+
+
+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
+
+
+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)
+
+
+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)
+
+
+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)