Comparing Vector Fields Across Surfaces: Interest for Characterizing the Orientations of Cortical Folds

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 grounded on differential geometry to achieve this task. The proposed framework enables the computation of statistics on vector fields. We demonstrate its interest in practice with an application on real neuroimaging data. We provide 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.