Normal and Equivolumetric Coordinate Systems for Cortical Areas

TL;DR

This paper introduces coordinate systems for the complex folded cortex, using geometric priors like normality and equivolumetric conditions, with mathematical formulation and numerical simulations to compare methods.

Contribution

It presents a novel mathematical framework and numerical approach for estimating coordinate systems adapted to cortical surfaces, incorporating geometric priors.

Findings

Coordinate systems satisfy geometric priors such as streamline normality and equivolumetric conditions.

Numerical simulations demonstrate the effectiveness of the proposed methods.

Comparison with recent approaches shows advantages in accuracy and consistency.

Abstract

We describe coordinate systems adapted for the space between two surfaces, such as those delineating the highly folded cortex in mammalian brains. These systems are estimated in order to satisfy geometric priors, including streamline normality or equivolumetric conditions on layers. We give a precise mathematical formulation of these problems, and present numerical simulations based on diffeomorphic registration methods, comparing them with recent approaches.