Software - High Dimensional Warping

High Dimensional Warping using Cubic B-Splines

For cross-sectional studies we do linear image alignment followed by high-dimensional warping. Warps are also useful in longitudinal studies for capturing small local changes over time.

The warp is based on local cubic B-spline shape adjustment to optimize a local intensity matching –usually cross-correlation which we have found works better than normalized mutual information.

The following images illustrate the warping process. In the first row, two subjects and the template brain are shown at the same slice. Next we show the warped images of the same subjects along with an average image of 96 warped subjects.

Before Warping
Subject 1 Subject 2 Template
After Warping
Subject 1 Subject 2 Average of 96 subjects

These subjects have been chosen to illustrate the range of anatomical variation that can be handled by the warping process. In each subject, the ventricles, starting from very disparate sizes and shapes, have been well-aligned with those of the template.

But the images also illustrate limitations of the warp. There are cortical differences in each subject compared to the template that could not be successfully resolved. These areas can be seen as pinched sulci and gyri at the cortical rim in the warped images. Two techniques to limit these artefacts include placing upper and lower bounds on the values of the jacobians allowed at a point, and placing a cap on the strain energy of the deformation at a point.

The averaged warp image smoothes out many of these local random differences and thus resembles the template very closely. The real power of the average image is to show the improvement possible over the averaged linearly aligned images commonly used in techniques such as VBM.

Applications of High Dimensional Warping

Uses of the spline warp in our lab include the following:

  1. Cross sectional studies of multiple subjects in which anatomical features may be directly compared for all subjects by being displayed on the same anatomical template. This permits generating statistics for multiple subjects in the same space.

  2. Longitudinal studies in which the jacobian values of the warp from time 1 to time 2 can be used to indicate areas of shape change. In particular, the volume change at time 2 of structures such as the hippocampus may be automatically computed using ROIs traced out at time 1 and the jacobian values of the voxels in those ROIs.
  3. The warp is used in our template-based inhomogeneity correction.

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