Symmetric Diffeomorphic Registration in 3D

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')
../../_images/input_3d.png

Static image in red on top of the pre-aligned moving image (in green).

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')
../../_images/warped_moving.png

Moving image transformed under the (direct) transformation in green on top of the static image (in red).

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')
../../_images/warped_static.png

Static image transformed under the (inverse) transformation in red on top of the moving image (in green). Note that the moving image has lower resolution.

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.