# 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 homogenous 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 not voxel_sizes is 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_data() 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