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spaces.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.
#
### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ##
"""Routines to work with spaces
A space is defined by coordinate axes.
A voxel space can be expressed by a shape implying an array, where the axes are
the axes of the array.
A mapped voxel space (mapped voxels) is either:
* an image, with attributes ``shape`` (the voxel space) and ``affine`` (the
mapping), or
* a length 2 sequence with the same information (shape, affine).
"""
from itertools import product
import numpy as np
from .affines import apply_affine
def vox2out_vox(mapped_voxels, voxel_sizes=None):
"""output-aligned shape, affine for input implied by `mapped_voxels`
The input (voxel) space, and the affine mapping to output space, are given
in `mapped_voxels`.
The output space is implied by the affine, we don't need to know what that
is, we just return something with the same (implied) output space.
Our job is to work out another voxel space where the voxel array axes and
the output axes are aligned (top left 3 x 3 of affine is diagonal with all
positive entries) and which contains all the voxels of the implied input
image at their correct output space positions, once resampled into the
output voxel space.
Parameters
----------
mapped_voxels : 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.
voxel_sizes : None or sequence
Gives the diagonal entries of `output_affine` (except the trailing 1
for the homogeneous coordinates) (``output_affine == np.diag(voxel_sizes
+ [1])``). If None, return identity `output_affine`.
Returns
-------
output_shape : sequence
Shape of output image that has voxel axes aligned to original image
output space axes, and encloses all the voxel data from the original
image implied by input shape.
output_affine : (4, 4) array
Affine of output image that has voxel axes aligned to the output axes
implied by input affine. Top-left 3 x 3 part of affine is diagonal with
all positive entries. The entries come from `voxel_sizes` if
specified, or are all 1. If the image is < 3D, then the missing
dimensions will have a 1 in the matching diagonal.
"""
try:
in_shape, in_affine = mapped_voxels.shape, mapped_voxels.affine
except AttributeError:
in_shape, in_affine = mapped_voxels
n_axes = len(in_shape)
if n_axes > 3:
raise ValueError('This function can only deal with 3D images')
if n_axes < 3:
in_shape += (1,) * (3 - n_axes)
out_vox = np.ones((3,))
if voxel_sizes is not None:
if not len(voxel_sizes) == n_axes:
raise ValueError('voxel sizes length should match shape')
if not np.all(np.array(voxel_sizes) > 0):
raise ValueError('voxel sizes should all be positive')
out_vox[:n_axes] = voxel_sizes
in_mn_mx = zip([0, 0, 0], np.array(in_shape) - 1)
in_corners = list(product(*in_mn_mx))
out_corners = apply_affine(in_affine, in_corners)
out_mn = out_corners.min(axis=0)
out_mx = out_corners.max(axis=0)
out_shape = np.ceil((out_mx - out_mn) / out_vox) + 1
out_affine = np.diag(list(out_vox) + [1])
out_affine[:3, 3] = out_mn
return tuple(int(i) for i in out_shape[:n_axes]), out_affine
def slice2volume(index, axis, shape=None):
"""Affine expressing selection of a single slice from 3D volume
Imagine we have taken a slice from an image data array, ``s = data[:, :,
index]``. This function returns the affine to map the array coordinates of
``s`` to the array coordinates of ``data``.
This can be useful for resampling a single slice from a volume. For
example, to resample slice ``k`` in the space of ``img1`` from the matching
spatial voxel values in ``img2``, you might do something like::
slice_shape = img1.shape[:2]
slice_aff = slice2volume(k, 2)
whole_aff = np.linalg.inv(img2.affine).dot(img1.affine.dot(slice_aff))
and then use ``whole_aff`` in ``scipy.ndimage.affine_transform``:
rzs, trans = to_matvec(whole_aff)
data = img2.get_fdata()
new_slice = scipy.ndimage.affine_transform(data, rzs, trans, slice_shape)
Parameters
----------
index : int
index of selected slice
axis : {0, 1, 2}
axis to which `index` applies
Returns
-------
slice_aff : shape (4, 3) affine
Affine relating input coordinates in a slice to output coordinates in
the embedded volume
"""
if index < 0:
raise ValueError('Cannot handle negative index')
if not 0 <= axis <= 2:
raise ValueError('Axis should be between 0 and 2')
axes = list(range(4))
axes.remove(axis)
slice_aff = np.eye(4)[:, axes]
slice_aff[axis, -1] = index
return slice_aff