plot_affine_transformation.py

"""
Visualization of affine resamplings
===================================

This example shows how an affine resampling works.

A Nifti image contains, along with its 3D or 4D data content, a 4x4 matrix
encoding an affine transformation that maps the data array into millimeter
space. If (i, j, k) encodes an integer position (voxel) with the data array,
then adding 1 as a fourth entry, (i, j, k, 1), and multiplying by the affine
matrix yields (x, y, z, 1), a 4-vector containing the millimeter position of
the voxel.

The resampling procedure in :func:`nilearn.image.resample_img` can attribute
a new affine matrix and a new shape to your Nifti image while keeping its
representation in millimeter space exactly the same (up to sampling error and
possible clipping).

This example shows a 2D image in voxel space, and the position of the data in
millimeter space, as encoded by the affine matrix. The image is the resampled
in 3 ways and displayed in millimeter space.

1) 4x4 affine matrix and target shape given
2) 3x3 transformation matrix (only new voxel axes, no offset)
   given and no shape given
3) 4x4 affine matrix given and no shape given

While 1) needs no further explanation (it returns an image exactly as
specified, with a new view on the data in millimeter space), 2) and 3) are
missing some specification, which is subsequently inferred by `resample_img`:
If the affine offset is missing (3x3 transformation, case 2), then the new
image will be the closest bounding box possible around the data along the
new axes. If the affine offset is given, but no shape provided, the
resulting image will be the closest bounding box around the union of the
data points and the affine offset.

Note that specifying a shape without specifying a 3x3 transformation matrix
causes an error message, because `resample_img` will not know where to start
the bounding box (there is no intelligent way of inferring this given the
bounding box shape).
"""

# Create the data with numpy
import numpy as np

from nilearn.image import get_data
from nilearn.plotting import show

# %%
# First make a simple synthetic image


grid = np.mgrid[0:192, 0:128]
circle = (
    np.sum((grid - np.array([32, 32])[:, np.newaxis, np.newaxis]) ** 2, axis=0)
    < 256
)
diamond = (
    np.sum(
        np.abs(grid - np.array([128, 80])[:, np.newaxis, np.newaxis]), axis=0
    )
    < 16
)
rectangle = (
    np.max(
        np.abs(grid - np.array([64, 96])[:, np.newaxis, np.newaxis]), axis=0
    )
    < 16
)

image = np.zeros_like(circle)
image[16:160, 16:120] = 1.0
image = image + 2 * circle + 3 * rectangle + 4 * diamond + 1

vmax = image.max()

source_affine = np.eye(4)
# Use canonical vectors for affine
# Give the affine an offset
source_affine[:2, 3] = np.array([96, 64])

# Rotate it slightly
angle = np.pi / 180 * 15
rotation_matrix = np.array(
    [[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]]
)
source_affine[:2, :2] = rotation_matrix * 2.0  # 2.0mm voxel size

# We need to turn this data into a nibabel image
import nibabel

img = nibabel.Nifti1Image(
    image[:, :, np.newaxis].astype("int32"), affine=source_affine
)

# %%
# Now resample the image
from nilearn.image import resample_img

img_in_mm_space = resample_img(
    img, target_affine=np.eye(4), target_shape=(512, 512, 1)
)

target_affine_3x3 = np.eye(3) * 2
target_affine_4x4 = np.eye(4) * 2
target_affine_4x4[3, 3] = 1.0
img_3d_affine = resample_img(img, target_affine=target_affine_3x3)
img_4d_affine = resample_img(img, target_affine=target_affine_4x4)
target_affine_mm_space_offset_changed = np.eye(4)
target_affine_mm_space_offset_changed[:3, 3] = img_3d_affine.affine[:3, 3]

img_3d_affine_in_mm_space = resample_img(
    img_3d_affine,
    target_affine=target_affine_mm_space_offset_changed,
    target_shape=(np.array(img_3d_affine.shape) * 2).astype(int),
)

img_4d_affine_in_mm_space = resample_img(
    img_4d_affine,
    target_affine=np.eye(4),
    target_shape=(np.array(img_4d_affine.shape) * 2).astype(int),
)

# %%
# Finally, visualize
import matplotlib.pyplot as plt

plt.figure()
plt.imshow(image, interpolation="nearest", vmin=0, vmax=vmax)
plt.title("The original data in voxel space")

plt.figure()
plt.imshow(get_data(img_in_mm_space)[:, :, 0], vmin=0, vmax=vmax)
plt.title("The original data in mm space")

plt.figure()
plt.imshow(get_data(img_3d_affine_in_mm_space)[:, :, 0], vmin=0, vmax=vmax)
plt.title(
    "Transformed using a 3x3 affine -\n leads to "
    "re-estimation of bounding box"
)

plt.figure()
plt.imshow(get_data(img_4d_affine_in_mm_space)[:, :, 0], vmin=0, vmax=vmax)
plt.title(
    "Transformed using a 4x4 affine -\n Uses affine anchor "
    "and estimates bounding box size"
)

show()

# sphinx_gallery_dummy_images=4