This example explains how to register 2D images using the Symmetric
Normalization (SyN) algorithm proposed by Avants et al. [Avants09]
(also implemented in the ANTs software [Avants11]) We will perform the classic Circle-To-C experiment for diffeomorphic
registration To visually check the overlap of the static image with the transformed moving
image, we can plot them on top of each other with different channels to see
where the differences are located We want to find an invertible map that transforms the moving image (circle)
into the static image (the C letter). The first decision we need to make is what similarity metric is appropriate
for our problem. In this example we are using two binary images, so the Sum
of Squared Differences (SSD) is a good choice. 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 instance 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. Now we execute the optimization, which returns a DiffeomorphicMap object,
that can be used to register images back and forth between the static and
moving domains It is a good idea to visualize the resulting deformation map to make sure the
result is reasonable (at least, visually) Now let’s warp the moving image and see if it gets similar to the static image 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 Static image transformed under the (inverse) transformation in red on top
of the moving image (in green). Now let’s register a couple of slices from a b0 image using the Cross
Correlation metric. Also, let’s inspect the evolution of the registration.
To do this we will define a function that will be called by the registration
object at each stage of the optimization process. We will draw the current
warped images after finishing each resolution. Now we are ready to configure and run the registration. First load the data We first remove the skull from the b0 volume And select two slices to try the 2D registration After loading the data, we instantiate the Cross-Correlation metric. The metric
receives three parameters: the dimension of the input images, the standard
deviation of the Gaussian Kernel to be used to regularize the gradient and the
radius of the window to be used for evaluating the local normalized cross
correlation. Let’s use a scale space of 3 levels And execute the optimization We can see the effect of the warping by switching between the images before and
after registration Moving image transformed under the (direct) transformation in green on top
of the static image (in red). And we can apply the inverse warping too Static image transformed under the (inverse) transformation in red on top
of the moving image (in green). Finally, let’s see the deformation 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. Avants, B. B., Tustison, N., & Song, G. (2011). Advanced
Normalization Tools (ANTS), 1-35. Example source code You can download Symmetric Diffeomorphic Registration in 2D
import numpy as np
from dipy.align.imwarp import SymmetricDiffeomorphicRegistration
from dipy.align.metrics import SSDMetric, CCMetric
import dipy.align.imwarp as imwarp
from dipy.data import get_fnames
from dipy.io.image import load_nifti_data
from dipy.segment.mask import median_otsu
from dipy.viz import regtools
fname_moving = get_fnames('reg_o')
fname_static = get_fnames('reg_c')
moving = np.load(fname_moving)
static = np.load(fname_static)
regtools.overlay_images(static, moving, 'Static', 'Overlay', 'Moving',
'input_images.png')
dim = static.ndim
metric = SSDMetric(dim)
level_iters = [200, 100, 50, 25]
sdr = SymmetricDiffeomorphicRegistration(metric, level_iters, inv_iter=50)
mapping = sdr.optimize(static, moving)
regtools.plot_2d_diffeomorphic_map(mapping, 10, 'diffeomorphic_map.png')
warped_moving = mapping.transform(moving, 'linear')
regtools.overlay_images(static, warped_moving, 'Static', 'Overlay',
'Warped moving', 'direct_warp_result.png')
warped_static = mapping.transform_inverse(static, 'linear')
regtools.overlay_images(warped_static, moving, 'Warped static', 'Overlay',
'Moving', 'inverse_warp_result.png')
def callback_CC(sdr, status):
# Status indicates at which stage of the optimization we currently are
# For now, we will only react at the end of each resolution of the scale
# space
if status == imwarp.RegistrationStages.SCALE_END:
# get the current images from the metric
wmoving = sdr.metric.moving_image
wstatic = sdr.metric.static_image
# draw the images on top of each other with different colors
regtools.overlay_images(wmoving, wstatic, 'Warped moving', 'Overlay',
'Warped static')
t1_name, b0_name = get_fnames('syn_data')
data = load_nifti_data(b0_name)
b0_mask, mask = median_otsu(data, median_radius=4, numpass=4)
static = b0_mask[:, :, 40]
moving = b0_mask[:, :, 38]
sigma_diff = 3.0
radius = 4
metric = CCMetric(2, sigma_diff, radius)
level_iters = [100, 50, 25]
sdr = SymmetricDiffeomorphicRegistration(metric, level_iters)
sdr.callback = callback_CC
mapping = sdr.optimize(static, moving)
warped = mapping.transform(moving)
regtools.overlay_images(static, moving, 'Static', 'Overlay', 'Moving',
't1_slices_input.png')
regtools.overlay_images(static, warped, 'Static', 'Overlay', 'Warped moving',
't1_slices_res.png')
inv_warped = mapping.transform_inverse(static)
regtools.overlay_images(inv_warped, moving, 'Warped static', 'Overlay',
'moving', 't1_slices_res2.png')
regtools.plot_2d_diffeomorphic_map(mapping, 5, 'diffeomorphic_map_b0s.png')
References
the full source code of this example. This same script is also included in the dipy source distribution under the doc/examples/ directory.