Comparing vector fields across surfaces: interest for characterizing the orientations of cortical folds
This work addresses a niche problem in medical imaging for researchers analyzing cortical folds, but it is incremental as it builds on existing differential geometry concepts.
The authors tackled the problem of comparing vector fields across surfaces of the same genus by proposing a framework that maps them onto a common space using differential geometry, enabling statistical analysis. They demonstrated its utility with real data, quantitatively assessing the reproducibility of curvature directions in cortical folding patterns.
Vectors fields defined on surfaces constitute relevant and useful representations but are rarely used. One reason might be that comparing vector fields across two surfaces of the same genus is not trivial: it requires to transport the vector fields from the original surfaces onto a common domain. In this paper, we propose a framework to achieve this task by mapping the vector fields onto a common space, using some notions of differential geometry. The proposed framework enables the computation of statistics on vector fields. We demonstrate its interest in practice with an application on real data with a quantitative assessment of the reproducibility of curvature directions that describe the complex geometry of cortical folding patterns. The proposed framework is general and can be applied to different types of vector fields and surfaces, allowing for a large number of high potential applications in medical imaging.