# Symmetric Diffeomorphic Registration in 3D¶

This example explains how to register 3D volumes using the Symmetric Normalization (SyN) algorithm proposed by Avants et al. [Avants09] (also implemented in the ANTS software [Avants11])

We will register two 3D volumes from the same modality using SyN with the Cross Correlation (CC) metric.

```
import numpy as np
import nibabel as nib
from dipy.align.imwarp import SymmetricDiffeomorphicRegistration
from dipy.align.imwarp import DiffeomorphicMap
from dipy.align.metrics import CCMetric
import os.path
from dipy.viz import regtools
```

Let’s fetch two b0 volumes, the first one will be the b0 from the Stanford HARDI dataset

```
from dipy.data import fetch_stanford_hardi, read_stanford_hardi
fetch_stanford_hardi()
nib_stanford, gtab_stanford = read_stanford_hardi()
stanford_b0 = np.squeeze(nib_stanford.get_data())[..., 0]
```

The second one will be the same b0 we used for the 2D registration tutorial

```
from dipy.data.fetcher import fetch_syn_data, read_syn_data
fetch_syn_data()
nib_syn_t1, nib_syn_b0 = read_syn_data()
syn_b0 = np.array(nib_syn_b0.get_data())
```

We first remove the skull from the b0’s

```
from dipy.segment.mask import median_otsu
stanford_b0_masked, stanford_b0_mask = median_otsu(stanford_b0, 4, 4)
syn_b0_masked, syn_b0_mask = median_otsu(syn_b0, 4, 4)
static = stanford_b0_masked
static_affine = nib_stanford.affine
moving = syn_b0_masked
moving_affine = nib_syn_b0.affine
```

Suppose we have already done a linear registration to roughly align the two images

```
pre_align = np.array([[1.02783543e+00, -4.83019053e-02, -6.07735639e-02, -2.57654118e+00],
[4.34051706e-03, 9.41918267e-01, -2.66525861e-01, 3.23579799e+01],
[5.34288908e-02, 2.90262026e-01, 9.80820307e-01, -1.46216651e+01],
[0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.00000000e+00]])
```

As we did in the 2D example, we would like to visualize (some slices of) the two volumes by overlapping them over two channels of a color image. To do that we need them to be sampled on the same grid, so let’s first re-sample the moving image on the static grid. We create an AffineMap to transform the moving image towards the static image

```
from dipy.align.imaffine import AffineMap
affine_map = AffineMap(pre_align,
static.shape, static_affine,
moving.shape, moving_affine)
resampled = affine_map.transform(moving)
```

plot the overlapped middle slices of the volumes

```
regtools.overlay_slices(static, resampled, None, 1, 'Static', 'Moving', 'input_3d.png')
```

We want to find an invertible map that transforms the moving image into the static image. We will use the Cross Correlation metric

```
metric = CCMetric(3)
```

Now we define an instance of the registration class. The SyN algorithm uses a multi-resolution approach by building a Gaussian Pyramid. We instruct the registration object to perform at most \([n_0, n_1, ..., n_k]\) iterations at each level of the pyramid. The 0-th level corresponds to the finest resolution.

```
level_iters = [10, 10, 5]
sdr = SymmetricDiffeomorphicRegistration(metric, level_iters)
```

Execute the optimization, which returns a DiffeomorphicMap object, that can be used to register images back and forth between the static and moving domains. We provide the pre-aligning matrix that brings the moving image closer to the static image

```
mapping = sdr.optimize(static, moving, static_affine, moving_affine, pre_align)
```

Now let’s warp the moving image and see if it gets similar to the static image

```
warped_moving = mapping.transform(moving)
```

We plot the overlapped middle slices

```
regtools.overlay_slices(static, warped_moving, None, 1, 'Static', 'Warped moving', 'warped_moving.png')
```

And we can also apply the inverse mapping to verify that the warped static image is similar to the moving image

```
warped_static = mapping.transform_inverse(static)
regtools.overlay_slices(warped_static, moving, None, 1, 'Warped static', 'Moving', 'warped_static.png')
```

## References¶

[Avants09] | Avants, B. B., Epstein, C. L., Grossman, M., & Gee, J. C. (2009). Symmetric Diffeomorphic Image Registration with Cross- Correlation: Evaluating Automated Labeling of Elderly and Neurodegenerative Brain, 12(1), 26-41. |

[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.