This example explains how to compute a transformation to register two 3D volumes by maximization of their Mutual Information [Mattes03]. The optimization strategy is similar to that implemented in ANTS [Avants11].

We will use masks to define which pixels are used in the Mutual Information. Masking can also be done for registration of 2D images rather than 3D volumes.

Masking for registration is useful in a variety of circumstances. For example, in cardiac MRI, where it is usually used to specify a region of interest on a 2D static image, e.g., the left ventricle in a short axis slice. This prioritizes registering the region of interest over other structures that move with respect to the heart.

```
from os.path import join as pjoin
import numpy as np
import matplotlib.pyplot as plt
from dipy.viz import regtools
from dipy.data import fetch_stanford_hardi
from dipy.data.fetcher import fetch_syn_data
from dipy.io.image import load_nifti
from dipy.align.imaffine import (AffineMap,
MutualInformationMetric,
AffineRegistration)
from dipy.align.transforms import (TranslationTransform3D,
RigidTransform3D)
from dipy.align import (affine_registration, translation,
rigid, register_series)
```

Let’s fetch a single b0 volume from the Stanford HARDI dataset.

```
files, folder = fetch_stanford_hardi()
static_data, static_affine, static_img = load_nifti(
pjoin(folder, 'HARDI150.nii.gz'),
return_img=True)
static = np.squeeze(static_data)[..., 0]
# pad array to help with this example
pad_by = 10
static = np.pad(static, [(pad_by, pad_by), (pad_by, pad_by), (0, 0)],
mode='constant', constant_values=0)
static_grid2world = static_affine
```

Let’s create a moving image by transforming the static image.

```
affmat = np.eye(4)
affmat[0, -1] = 4
affmat[1, -1] = 12
theta = 0.1
c, s = np.cos(theta), np.sin(theta)
affmat[0:2, 0:2] = np.array([[c, -s], [s, c]])
affine_map = AffineMap(affmat,
static.shape, static_grid2world,
static.shape, static_grid2world)
moving = affine_map.transform(static)
moving_affine = static_affine.copy()
moving_grid2world = static_grid2world.copy()
regtools.overlay_slices(static, moving, None, 2,
"Static", "Moving", "deregistered.png")
```

Let’s make some registration settings.

```
nbins = 32
sampling_prop = None
metric = MutualInformationMetric(nbins, sampling_prop)
# small number of iterations for this example
level_iters = [100, 10]
sigmas = [1.0, 0.0]
factors = [2, 1]
affreg = AffineRegistration(metric=metric,
level_iters=level_iters,
sigmas=sigmas,
factors=factors)
```

Now let’s register these volumes together without any masking. For the purposes of this example, we will not provide an initial transformation based on centre of mass, but this would work fine with masks.

Note that use of masks is not currently implemented for sparse sampling.

```
transform = TranslationTransform3D()
transl = affreg.optimize(static, moving, transform, None,
static_grid2world, moving_grid2world,
starting_affine=None,
static_mask=None, moving_mask=None)
transform = RigidTransform3D()
transl = affreg.optimize(static, moving, transform, None,
static_grid2world, moving_grid2world,
starting_affine=transl.affine,
static_mask=None, moving_mask=None)
transformed = transl.transform(moving)
transformed = transl.transform(moving)
regtools.overlay_slices(static, transformed, None, 2,
"Static", "Transformed", "transformed.png")
```

We can also use a pipeline to achieve the same thing. For convenience in this tutorial, we will define a function that runs the pipeline and makes a figure.

```
def reg_func(figname, static_mask=None, moving_mask=None):
"""Convenience function for registration using a pipeline.
Uses variables in global scope, except for static_mask and moving_mask.
"""
pipeline = [translation, rigid]
xformed_img, reg_affine = affine_registration(
moving,
static,
moving_affine=moving_affine,
static_affine=static_affine,
nbins=32,
metric='MI',
pipeline=pipeline,
level_iters=level_iters,
sigmas=sigmas,
factors=factors,
static_mask=static_mask,
moving_mask=moving_mask)
regtools.overlay_slices(static, xformed_img, None, 2,
"Static", "Transformed", figname)
return
```

Now we can run this function and hopefully get the same result.

```
reg_func("transformed_pipeline.png")
```

Now let’s modify the images in order to test masking. We will place three squares in the corners of both images, but in slightly different locations.

We will make masks that cover these regions but with an extra border of pixels. This is because the masks need transforming and resampling during optimization, and we want to make sure that we are definitely covering the troublesome features.

```
sz = 15
pd = 10
# modify images
val = static.max()/2.0
static[-sz-pd:-pd, -sz-pd:-pd, :] = val
static[pd:sz+pd, -sz-pd:-pd, :] = val
static[-sz-pd:-pd, pd:sz+pd, :] = val
moving[pd:sz+pd, pd:sz+pd, :] = val
moving[pd:sz+pd, -sz-pd:-pd, :] = val
moving[-sz-pd:-pd, pd:sz+pd, :] = val
# create masks
squares_st = np.zeros_like(static).astype(np.int32)
squares_mv = np.zeros_like(static).astype(np.int32)
squares_st[-sz-1-pd:-pd, -sz-1-pd:-pd, :] = 1
squares_st[pd:sz+1+pd, -sz-1-pd:-pd, :] = 1
squares_st[-sz-1-pd:-pd, pd:sz+1+pd, :] = 1
squares_mv[pd:sz+1+pd, pd:sz+1+pd, :] = 1
squares_mv[pd:sz+1+pd, -sz-1-pd:-pd, :] = 1
squares_mv[-sz-1-pd:-pd, pd:sz+1+pd, :] = 1
regtools.overlay_slices(static, moving, None, 2,
"Static", "Moving", "deregistered_squares.png")
```

```
static_mask = np.abs(squares_st - 1)
moving_mask = np.abs(squares_mv - 1)
fig, ax = plt.subplots(1, 2)
ax[0].imshow(static_mask[:, :, 1].T, cmap="gray", origin="lower")
ax[0].set_title("static image mask")
ax[1].imshow(moving_mask[:, :, 1].T, cmap="gray", origin="lower")
ax[1].set_title("moving image mask")
plt.savefig("masked_static.png", bbox_inches='tight')
```

Let’s try to register these new images without a mask.

```
reg_func("transformed_squares.png")
```

Now we will attempt to register the images using the masks that we defined.

First, use a mask on the static image. Only pixels where the mask is non-zero in the static image will contribute to Mutual Information.

```
reg_func("transformed_squares_mask.png", static_mask=static_mask)
```

We can also attempt the same thing use a moving image mask.

```
reg_func("transformed_squares_mask_2.png", moving_mask=moving_mask)
```

And finally, we can use both masks at the same time.

```
reg_func("transformed_squares_mask_3.png",
static_mask=static_mask, moving_mask=moving_mask)
```

In most use cases, it is likely that only a static mask will be required, e.g., to register a series of images to a single static image.

Let’s make a series of volumes to demonstrate this idea, and register the series to the first image in the series using a static mask:

```
series = np.stack([static, moving, moving], axis=-1)
pipeline = [translation, rigid]
xformed, _ = register_series(series, 0, pipeline,
series_affine=moving_affine,
static_mask=static_mask)
regtools.overlay_slices(np.squeeze(xformed[..., 0]),
np.squeeze(xformed[..., -2]),
None, 2, "Static", "Moving 1", "series_mask_1.png")
regtools.overlay_slices(np.squeeze(xformed[..., 0]),
np.squeeze(xformed[..., -1]),
None, 2, "Static", "Moving 2", "series_mask_2.png")
```

In all of the examples above, different masking choices achieved essentially the same result, but in general the results may differ depending on differences between the static and moving images.

[Mattes03]

Mattes, D., Haynor, D. R., Vesselle, H., Lewellen, T. K., Eubank, W. (2003). PET-CT image registration in the chest using free-form deformations. IEEE Transactions on Medical Imaging, 22(1), 120-8.

[Avants11]

Avants, B. B., Tustison, N., & Song, G. (2011). Advanced Normalization Tools (ANTS), 1-35.

Example source code

You can download `the full source code of this example`

. This same script is also included in the dipy source distribution under the `doc/examples/`

directory.