Density-based Similarity in the Registration of Diffusion-Weighted Images

Diffusion-Weighted Magnetic Resonance Imaging (DW-MRI or DWI) is a
non-invasive scanning protocol aimed at inferring the structure of biological
tissue by tracking the movement of water molecules. As molecules diffuse
along and around obstacles, in-vivo images of the diffusion can be used
to reconstruct the minuscule anatomy that would otherwise be invisible
in standard MRI. The applications of DWI ranges from tumor detection to
tracing the neuronal pathways connecting the brain.
DWI is also a complex modality and difficult to both validate and compare.
The data is directional and exhibits a non-linear behaviour for high-resolution
images. It requires longer scanning times and high magnetic gradients, resulting
in an increased amount of noise from motion and external factors.
DWI also has no gold standard datasets for comparable quantitative validation.
Group studies often present results through private segmentations
from trained experts or by qualitative visual evaluation. This is a significant
problem as DWI is becoming an issue of Big Data due to increasing amounts
of open and freely available datasets. As such, our first contribution is a
critical review of image registration and validation of group-wise alignment
of DWI. We investigate common approaches to compare DWI data in terms
of voxel- and connectivity-based methods.
Image registration is the process of spatially aligning images in a way that
allow us to define a shared coordinate system between them. For DWI, the
reorientation of the directional information presents a difficult challenge.
In many cases, DWI is simply registered using standard 3D algorithms
and without considering their non-linear relationship. Our second contribution
is a density-based scale-space formulation for DWI that gives access to
information-theoretic similarity measures, based on the full diffusion profile.
The presented framework is a global registration method that optimizes the
mutual information between DWI with explicit reorientation of the gradient
vectors. We show that the directional scale is important for aligning DWI.
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