Quantifying error in estimates of human brain fiber directions using Earth Mover's Distance
This work addresses the need for accurate error measurement in brain connectivity mapping, which is incremental as it compares existing metrics rather than introducing a new method.
The paper tackles the problem of quantifying error in estimates of human brain fiber orientation distribution functions (fODFs) from diffusion-weighted MRI, proposing the Earth Mover's Distance (EMD) as a suitable metric for this purpose.
Diffusion-weighted MR imaging (DWI) is the only method we currently have to measure connections between different parts of the human brain in vivo. To elucidate the structure of these connections, algorithms for tracking bundles of axonal fibers through the subcortical white matter rely on local estimates of the fiber orientation distribution function (fODF) in different parts of the brain. These functions describe the relative abundance of populations of axonal fibers crossing each other in each location. Multiple models exist for estimating fODFs. The quality of the resulting estimates can be quantified by means of a suitable measure of distance on the space of fODFs. However, there are multiple distance metrics that can be applied for this purpose, including smoothed $L_p$ distances and the Wasserstein metrics. Here, we give four reasons for the use of the Earth Mover's Distance (EMD) equipped with the arc-length, as a distance metric. (continued)