# 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
from dipy.align.imwarp import SymmetricDiffeomorphicRegistration
from dipy.align.metrics import CCMetric
from dipy.data import get_fnames
from dipy.io.image import load_nifti
from dipy.viz import regtools


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

hardi_fname, hardi_bval_fname, hardi_bvec_fname = get_fnames('stanford_hardi')

stanford_b0, stanford_b0_affine = load_nifti(hardi_fname)
stanford_b0 = np.squeeze(stanford_b0)[..., 0]


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

t1_fname, b0_fname = get_fnames('syn_data')
syn_b0, syn_b0_affine = load_nifti(b0_fname)


We first remove the skull from the b0’s

from dipy.segment.mask import median_otsu
numpass=4)

static_affine = stanford_b0_affine
moving_affine = 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.