Voxel-wise features were extracted in a common template space (Ω
Template, see Figure
2) based on the data of the training set. This common template space was constructed using a procedure that avoids bias toward any of the individual training images (Seghers et al., 2004 ). In this approach, the coordinate transformations from the template space to the subject's image space (
Vi: Ω
Template → Ω
Ii) were derived from pairwise image registrations. For computation of
Vi, the image of an individual training subject (
Ii) was registered to all other training images (
Ij) using
Ii as the fixed image. This resulted in a set of transformations
Wi,j : Ω
Ii→Ω
Ij. By averaging the transformations
Wi, j, the transformation
Ui : Ω
Ii→Ω
Template was calculated:
The transformation
Vi was calculated as an inversion of
Ui:
Vi =
Ui−1. Note that the identity transformation
Wi,i is also included in (5). The pairwise registrations were performed using a similarity (rigid plus isotropic scaling), affine, and nonrigid B-spline transformation model consecutively. The nonrigid B-spline registration used a three-level multi-resolution framework with isotropic control-point spacings of 24, 12, and 6 mm in the three resolutions respectively.
A template image was built using:
with
Ii(
Vi) representing the deformed individual training images. The test images were not included in the construction of Ω
Template. For the test images, the transformation to template space (
Vi) was obtained using the same procedure described above: using pairwise registration of each image with all training images, followed by averaging and inversion. Brain masks and tissue maps were transformed to template space using
Vi.
For extraction of the region-wise features, a set of 72 brain ROIs was defined for each subject individually in subject space (Ω
I) using a multi-atlas segmentation procedure (Figure
3). Thirty labeled T1w images containing 83 ROIs each (Hammers et al., 2003 (
link); Gousias et al., 2008 (
link)) were used as atlas images. The atlas images were registered to the subject's T1w image using a rigid, affine, and nonrigid B-spline transformation model consecutively resulting in transformation
Si,k : Ω
Ii → Ω
Atlask. Registration was performed by maximization of mutual information within dilated brain masks (Smith, 2002 (
link)). For initialization, the dilated brain masks were rigidly registered. For nonrigid registration, the same multi-resolution settings were used as in the template space construction. For this step, the subjects' images were corrected for inhomogeneities (Tustison et al., 2010 (
link)). Labels were propagated to Ω
Ii using
Si,k and fused using a majority voting algorithm (Heckemann et al., 2006 (
link)). The brain stem, corpus callosum, third ventricle, lateral ventricles, cerebellum, and substantia nigra were excluded.
Shamonin D.P., Bron E.E., Lelieveldt B.P., Smits M., Klein S, & Staring M. (2014). Fast parallel image registration on CPU and GPU for diagnostic classification of Alzheimer's disease. Frontiers in Neuroinformatics, 7, 50.