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

TL;DR

This paper introduces a framework for comparing vector fields on surfaces, particularly applied to cortical folds, enabling statistical analysis and reproducibility assessment in medical imaging.

Contribution

It proposes a novel method to map vector fields onto a common domain using differential geometry, facilitating comparison and analysis across surfaces.

Findings

Framework successfully compares vector fields on cortical surfaces.

Application demonstrates high reproducibility of curvature directions.

Method is general and adaptable to various surface types.

Abstract

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.