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Applying coordinate transforms with nibabel.affines.apply_affine
ΒΆ
We often want to apply an affine to an array of coordinates, where the last axis of the array is length 3, containing the x, y and z coordinates.
Nibabel uses nibabel.affines.apply_affine
for this.
For background see: The nibabel.affines module.
>>> import numpy as np
>>> from nibabel.affines import from_matvec, to_matvec, apply_affine
>>> points = np.array([[0, 1, 2], [2, 2, 4], [3, -2, 1], [5, 3, 1]])
>>> points
array([[ 0, 1, 2],
[ 2, 2, 4],
[ 3, -2, 1],
[ 5, 3, 1]])
>>> zooms_plus_translations = from_matvec(np.diag([3, 4, 5]),
... [11, 12, 13])
>>> zooms_plus_translations
array([[ 3, 0, 0, 11],
[ 0, 4, 0, 12],
[ 0, 0, 5, 13],
[ 0, 0, 0, 1]])
>>> apply_affine(zooms_plus_translations, points)
array([[11, 16, 23],
[17, 20, 33],
[20, 4, 18],
[26, 24, 18]])
Of course, this is the same as:
>>> mat, vec = to_matvec(zooms_plus_translations)
>>> mat.dot(points.T).T + vec.reshape((1, 3))
array([[11, 16, 23],
[17, 20, 33],
[20, 4, 18],
[26, 24, 18]])
The advantage of nib.affines.apply_affine
is that it can deal with arrays
of more than two dimensions, and it transposes the transformation matrices for
you to apply the transforms correctly.
A typical use is when applying extra affine transformations to a X by Y by Z by 3 array of coordinates.