`affines`¶

Utility routines for working with points and affine transforms

`AffineError`	Errors in calculating or using affines
`append_diag`(aff, steps[, starts])	Add diagonal elements steps and translations starts to affine
`apply_affine`(aff, pts[, inplace])	Apply affine matrix aff to points pts
`dot_reduce`(*args)	Apply numpy dot product function from right to left on arrays
`from_matvec`(matrix[, vector])	Combine a matrix and vector into an homogeneous affine
`obliquity`(affine)	Estimate the obliquity an affine's axes represent.
`rescale_affine`(affine, shape, zooms[, new_shape])	Return a new affine matrix with updated voxel sizes (zooms)
`to_matvec`(transform)	Split a transform into its matrix and vector components.
`voxel_sizes`(affine)	Return voxel size for each input axis given affine

`AffineError`¶

class nibabel.affines.AffineError¶

Bases: ValueError

Errors in calculating or using affines

__init__(*args, **kwargs)¶

append_diag¶

nibabel.affines.append_diag(aff, steps, starts=())¶

Add diagonal elements steps and translations starts to affine

Typical use is in expanding 4x4 affines to larger dimensions. Nipy is the main consumer because it uses NxM affines, whereas we generally only use 4x4 affines; the routine is here for convenience.

Parameters:

aff2D array: N by M affine matrix
stepsscalar or sequence: diagonal elements to append.
startsscalar or sequence: elements to append to last column of aff, representing translations corresponding to the steps. If empty, expands to a vector of zeros of the same length as steps

Returns:

aff_plus2D array: Now P by Q where L = len(steps) and P == N+L, Q=N+L

Examples

>>> aff = np.eye(4)
>>> aff[:3,:3] = np.arange(9).reshape((3,3))
>>> append_diag(aff, [9, 10], [99,100])
array([[  0.,   1.,   2.,   0.,   0.,   0.],
       [  3.,   4.,   5.,   0.,   0.,   0.],
       [  6.,   7.,   8.,   0.,   0.,   0.],
       [  0.,   0.,   0.,   9.,   0.,  99.],
       [  0.,   0.,   0.,   0.,  10., 100.],
       [  0.,   0.,   0.,   0.,   0.,   1.]])

apply_affine¶

nibabel.affines.apply_affine(aff, pts, inplace=False)¶

Apply affine matrix aff to points pts

Returns result of application of aff to the right of pts. The coordinate dimension of pts should be the last.

For the 3D case, aff will be shape (4,4) and pts will have final axis length 3 - maybe it will just be N by 3. The return value is the transformed points, in this case:

res = np.dot(aff[:3,:3], pts.T) + aff[:3,3:4]
transformed_pts = res.T

This routine is more general than 3D, in that aff can have any shape (N,N), and pts can have any shape, as long as the last dimension is for the coordinates, and is therefore length N-1.

Parameters:

aff(N, N) array-like: Homogeneous affine, for 3D points, will be 4 by 4. Contrary to first appearance, the affine will be applied on the left of pts.
pts(…, N-1) array-like: Points, where the last dimension contains the coordinates of each point. For 3D, the last dimension will be length 3.
inplacebool, optional: If True, attempt to apply the affine directly to pts. If False, or in-place application fails, a freshly allocated array will be returned.

Returns:

transformed_pts(…, N-1) array: transformed points

Examples

>>> aff = np.array([[0,2,0,10],[3,0,0,11],[0,0,4,12],[0,0,0,1]])
>>> pts = np.array([[1,2,3],[2,3,4],[4,5,6],[6,7,8]])
>>> apply_affine(aff, pts) 
array([[14, 14, 24],
       [16, 17, 28],
       [20, 23, 36],
       [24, 29, 44]]...)

Just to show that in the simple 3D case, it is equivalent to:

>>> (np.dot(aff[:3,:3], pts.T) + aff[:3,3:4]).T 
array([[14, 14, 24],
       [16, 17, 28],
       [20, 23, 36],
       [24, 29, 44]]...)

But pts can be a more complicated shape:

>>> pts = pts.reshape((2,2,3))
>>> apply_affine(aff, pts) 
array([[[14, 14, 24],
        [16, 17, 28]],

       [[20, 23, 36],
        [24, 29, 44]]]...)

dot_reduce¶

nibabel.affines.dot_reduce(*args)¶

Apply numpy dot product function from right to left on arrays

For passed arrays \(A, B, C, ... Z\) returns \(A \dot B \dot C ... \dot Z\) where “.” is the numpy array dot product.

Parameters:

**argsarrays: Arrays that can be passed to numpy dot function

Returns:

dot_productarray: If there are N arguments, result of arg[0].dot(arg[1].dot(arg[2].dot ... arg[N-2].dot(arg[N-1])))...

from_matvec¶

nibabel.affines.from_matvec(matrix, vector=None)¶

Combine a matrix and vector into an homogeneous affine

Combine a rotation / scaling / shearing matrix and translation vector into a transform in homogeneous coordinates.

Parameters:

matrixarray-like: An NxM array representing the the linear part of the transform. A transform from an M-dimensional space to an N-dimensional space.
vectorNone or array-like, optional: None or an (N,) array representing the translation. None corresponds to an (N,) array of zeros.

Returns:

xformarray: An (N+1, M+1) homogeneous transform matrix.

obliquity¶

nibabel.affines.obliquity(affine)¶

Estimate the obliquity an affine’s axes represent.

The term obliquity is defined here as the rotation of those axes with respect to the cardinal axes. This implementation is inspired by AFNI’s implementation. For further details about obliquity, check AFNI’s documentation.

Parameters:

affine2D array-like: Affine transformation array. Usually shape (4, 4), but can be any 2D array.

Returns:

angles1D array-like: The obliquity of each axis with respect to the cardinal axes, in radians.

rescale_affine¶

nibabel.affines.rescale_affine(affine, shape, zooms, new_shape=None)¶

Return a new affine matrix with updated voxel sizes (zooms)

This function preserves the rotations and shears of the original affine, as well as the RAS location of the central voxel of the image.

Parameters:

affine(N, N) array-like: NxN transform matrix in homogeneous coordinates representing an affine transformation from an (N-1)-dimensional space to an (N-1)-dimensional space. An example is a 4x4 transform representing rotations and translations in 3 dimensions.
shape(N-1,) array-like: The extent of the (N-1) dimensions of the original space
zooms(N-1,) array-like: The size of voxels of the output affine
new_shape(N-1,) array-like, optional: The extent of the (N-1) dimensions of the space described by the new affine. If None, use shape.

Returns:

affine(N, N) array: A new affine transform with the specified voxel sizes

to_matvec¶

nibabel.affines.to_matvec(transform)¶

Split a transform into its matrix and vector components.

The transformation must be represented in homogeneous coordinates and is split into its rotation matrix and translation vector components.

Parameters:

transformarray-like: NxM transform matrix in homogeneous coordinates representing an affine transformation from an (N-1)-dimensional space to an (M-1)-dimensional space. An example is a 4x4 transform representing rotations and translations in 3 dimensions. A 4x3 matrix can represent a 2-dimensional plane embedded in 3 dimensional space.

Returns:

matrix(N-1, M-1) array: Matrix component of transform
vector(M-1,) array: Vector component of transform

voxel_sizes¶

nibabel.affines.voxel_sizes(affine)¶

Return voxel size for each input axis given affine

The affine is the mapping between array (voxel) coordinates and mm (world) coordinates.

The voxel size for the first voxel (array) axis is the distance moved in world coordinates when moving one unit along the first voxel (array) axis. This is the distance between the world coordinate of voxel (0, 0, 0) and the world coordinate of voxel (1, 0, 0). The world coordinate vector of voxel coordinate vector (0, 0, 0) is given by v0 = affine.dot((0, 0, 0, 1)[:3]. The world coordinate vector of voxel vector (1, 0, 0) is v1_ax1 = affine.dot((1, 0, 0, 1))[:3]. The final 1 in the voxel vectors and the [:3] at the end are because the affine works on homogeneous coordinates. The translations part of the affine is trans = affine[:3, 3], and the rotations, zooms and shearing part of the affine is rzs = affine[:3, :3]. Because of the final 1 in the input voxel vector, v0 == rzs.dot((0, 0, 0)) + trans, and v1_ax1 == rzs.dot((1, 0, 0)) + trans, and the difference vector is rzs.dot((0, 0, 0)) - rzs.dot((1, 0, 0)) == rzs.dot((1, 0, 0)) == rzs[:, 0]. The distance vectors in world coordinates between (0, 0, 0) and (1, 0, 0), (0, 1, 0), (0, 0, 1) are given by rzs.dot(np.eye(3)) = rzs. The voxel sizes are the Euclidean lengths of the distance vectors. So, the voxel sizes are the Euclidean lengths of the columns of the affine (excluding the last row and column of the affine).

Parameters:

affine2D array-like: Affine transformation array. Usually shape (4, 4), but can be any 2D array.

Returns:

vox_sizes1D array: Voxel sizes for each input axis of affine. Usually 1D array length 3, but in general has length (N-1) where input affine is shape (M, N).

NiBabel

Access a cacophony of neuro-imaging file formats

Table of Contents

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`affines`¶

`AffineError`¶

append_diag¶

apply_affine¶

dot_reduce¶

from_matvec¶

obliquity¶

rescale_affine¶

to_matvec¶

voxel_sizes¶

NiBabel

Access a cacophony of neuro-imaging file formats

affines¶

AffineError¶

append_diag¶

apply_affine¶

dot_reduce¶

from_matvec¶

obliquity¶

rescale_affine¶

to_matvec¶

voxel_sizes¶

`affines`¶

`AffineError`¶