Quantifying error in estimates of human brain fiber directions using Earth Mover's Distance

TL;DR

This paper evaluates the accuracy of human brain fiber direction estimates in diffusion MRI using Earth Mover's Distance, highlighting its advantages over other metrics for quantifying errors in fiber orientation distributions.

Contribution

The study advocates for using Earth Mover's Distance with arc-length to measure errors in fODF estimates, providing a detailed rationale and comparison with other metrics.

Findings

EMD effectively quantifies errors in fiber orientation estimates.

EMD with arc-length offers advantages over smoothed Lp distances.

The paper provides a theoretical and practical comparison of distance metrics.

Abstract

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)