Applying coordinate transforms with nibabel.affines.apply_affine

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 @ points.T).T + np.reshape(vec, (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.