8000 ENH: Add a utility to calculate obliquity of affines by oesteban · Pull Request #815 · nipy/nibabel · GitHub
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ENH: Add a utility to calculate obliquity of affines #815

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Merged
merged 6 commits into from
Oct 15, 2019
Merged

ENH: Add a utility to calculate obliquity of affines #815

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3cfff0d
ENH: Add an utility to calculate obliquity of affines
oesteban Sep 20, 2019
c92d560
enh(tests): add not-oblique test, move tests to ``test_affines.py``
oesteban Sep 20, 2019
da8da56
enh: return radians unless degrees=True
oesteban Sep 22, 2019
253a256
enh: address @matthew-brett's comments
oesteban Sep 23, 2019
04584b6
doc: add link to AFNI's documentation about *obliquity* [skip ci]
oesteban Sep 24, 2019
891d85c
fix: incorrect operation ordering caught by @matthew-brett
oesteban Sep 27, 2019
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enh: address @matthew-brett's comments
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@oesteban
oesteban committed Sep 23, 2019
commit 253a256d18d75664001ef3d9872c25952675b7f4
26 changes: 17 additions & 9 deletions nibabel/affines.py
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Expand Up @@ -2,8 +2,6 @@
# vi: set ft=python sts=4 ts=4 sw=4 et:
""" Utility routines for working with points and affine transforms
"""

from math import acos, pi as PI
import numpy as np

from functools import reduce
Expand Down Expand Up @@ -299,17 +297,27 @@ def voxel_sizes(affine):
return np.sqrt(np.sum(top_left ** 2, axis=0))


def obliquity(affine, degrees=False):
def obliquity(affine):
r"""
Estimate the obliquity an affine's axes represent, in degrees from plumb.
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
<https://github.com/afni/afni/blob/b6a9f7a21c1f3231ff09efbd861f8975ad48e525/src/thd_coords.c#L660-L698>`_

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

Returns
-------
angles : 1D array-like
The *obliquity* of each axis with respect to the cardinal axes, in radians.

"""
vs = voxel_sizes(affine)
fig_merit = (affine[:-1, :-1] / vs[np.newaxis, ...]).max(axis=1).min()
radians = abs(acos(fig_merit))
if not degrees:
return radians
return radians * 180 / PI
best_cosines = np.abs((affine[:-1, :-1] / vs).max(axis=1))
return np.arccos(best_cosines)
6 changes: 4 additions & 2 deletions nibabel/tests/test_affines.py
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Expand Up @@ -182,9 +182,11 @@ def test_voxel_sizes():

def test_obliquity():
"""Check the calculation of inclination of an affine axes."""
from math import pi
aligned = np.diag([2.0, 2.0, 2.3, 1.0])
aligned[:-1, -1] = [-10, -10, -7]
R = from_matvec(euler2mat(x=0.09, y=0.001, z=0.001), [0.0, 0.0, 0.0])
oblique = R.dot(aligned)
assert_almost_equal(obliquity(aligned), 0.0)
assert_almost_equal(obliquity(oblique, degrees=True), 5.1569948883)
assert_almost_equal(obliquity(aligned), [0.0, 0.0, 0.0])
assert_almost_equal(obliquity(oblique) * 180 / pi,
[0.0810285, 5.1569949, 5.1569376])
0