Allow homogeneous coordinate transforms in affine_transform

[jni]

There was some discussion in #2255 (comment) about including support for homogeneous coordinate transforms by detecting the shape of the transformation matrix as being 1 + the dimensionality of the image. This implements that change. Hopefully I haven't broken 50 things in the process. =P

[pv]

Test failures.

The main change probably is OK, assuming the offset is applied in the correct order...
The documentation (and maybe examples) probably should also be updated.
In the extended call, maybe check if the last row is all 0 0 0 1.

[jni]

@pv I think I've addressed your comments. I tested the functions manually for a translation -> rotation -> translation sequence to get a rotation about the center. Splitting the resulting homogeneous matrix as is done in the PR gave the correct result using affine_transform.

The scipy.special.orthogonal errors appear unrelated to this PR, am I right there?

[jni]

Here's the code I used to check that the offset is used correctly in the PR:

import numpy as np
from scipy import ndimage as ndi
from skimage import data

camera = data.camera()
θ = np.deg2rad(30)
C = np.cos
S = np.sin

T0 = np.array([[1, 0, -256], [0, 1, -256], [0, 0, 1.]])
Rot = np.array([[C(θ), -S(θ), 0], [S(θ), C(θ), 0], [0, 0, 1]])
T1 = np.array([[1, 0, 256], [0, 1, 256], [0, 0, 1.]])

Forward = T1 @ Rot @ T0
Inverse = np.linalg.inv(Forward)

camera_rot = ndi.affine_transform(camera, Inverse[:2, :2], Inverse[:2, 2], order=1)

plt.imshow(camera_rot)

Result:

[pv]

I think the change is fine, but there are some test failures on travis (test_affine_transform26, test_affine_transform27)

[pv]

Also, the text The given matrix and offset are used ... in docstring probably should be moved to Notes, and adding a paragraph there about the extended affine transform matrices could be useful, even if this is a standard convention.

[jni]

@pv Thanks for the review! Let's hope third time's the charm! =)

[jni]

Oooh Travis is happy. That's a first. =P

[matthew-brett]

Great - thanks for doing this - it's a very nice addition.

[stefanv]

Thank you, Juan; this will certainly lead to more elegant SciPy use downstream.