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Vectors fields defined on surfaces constitute relevant and usefulrepresentations but are rarely used. One reason might be that comparing vectorfields across two surfaces of the same genus is not trivial: it requires totransport the vector fields from the original surfaces onto a common domain. Inthis paper, we propose a framework to achieve this task by mapping the vectorfields onto a common space, using some notions of differential geometry. Theproposed framework enables the computation of statistics on vector fields. Wedemonstrate its interest in practice with an application on real data with aquantitative assessment of the reproducibility of curvature directions thatdescribe the complex geometry of cortical folding patterns. The proposedframework is general and can be applied to different types of vector fields andsurfaces, allowing for a large number of high potential applications in medicalimaging.

Comparing vector fields across surfaces: interest for characterizing the orientations of cortical folds