In this talk, I will introduce the problem of registering tensor-valued data obtained from
diffusion tensor magnetic resonance imaging (DT-MRI). In addition to an overview of
existing approaches and a summary of avenues for future work, I will sketch three ideas
in more detail. First, a novel similarity metric with which to drive diffusion tensor
registration is described that exploits the unique shape and orientation characteristics of
our diffusion ellipsoids. Specifically, the pattern of pairwise orientation differences
between the voxel of interest located at x and every voxel within a neighborhood
centered at x is proposed as a more robust and accurate replacement of the usual
voxelwise comparison of orientation information (either at a voxel or over a region).
Preliminary results indicate this new metric may reduce the number of local minima
typically observed with standard applications of diffusion orientation in tensor
registration. The second part of the presentation will consider the diffusion MRI
registration problem from the more general perspective of abitrary diffusion profiles
as opposed to the Gaussian distributions assumed in DT-MRI. In practice, non-
Gaussian diffusion profiles occur whenever fibers cross in white matter, thus MRI
reconstruction techniques that can accommodate multiple fiber orientations are an active
area of research. The naturally induced L2 distance between positive-valued spherical
functions is specialized to the case of diffusion tensors, and this is coupled with a nonstandard
affine parameterization that facilitates the finite strain-based reorientation of
tensors adopted in this work. Preliminary results demonstrating the piecewise affine
extension to high dimensional non-rigid registration of DT-MRI data will be shown. The
final topic I will discuss leverages image registration to warp a labeled brain atlas to
segment extracted fiber tracts from an individual, thus enabling an anatomical basis for
the visualization of white matter tracts.
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