Unfolding the Cerebral Cortex Using Level Set Methods

Level set methods provide a robust way to implement geometric flows, but they suffer from two problems which are relevant when using smoothing flows to unfold the cortex: the lack of point-correspondence between scales and the inability to implement tangential velocities. In this paper, we suggest to solve these problems by driving the nodes of a mesh with an ordinary Differential equation. We state that this approach does not suffer from the known problems of Lagrangian methods since all geometrical properties are computed on the fixed (Eulerian) grid. Additionally, tangential velocities can be given to the nodes, allowing the mesh to follow general evolution equations, which could be crucial to achieving the final goal of minimizing local metric distortions. To experiment with this approach, we derive area and volume preserving mean curvature flows and use them to unfold surfaces extracted from MRI data of the human brain.

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