Area-preserving surface flattening using lie advection

In this paper, we propose a novel area-preserving surface flattening method, which is rigorous in theory, efficient in computation, yet general in application domains. Leveraged on the state-of-the-art flattening techniques, an infinitesimal area restoring diffeomorphic flow is constructed as a Lie advection of differential 2-forms on the manifold, which yields strict equality of area elements between the flattened and the original surfaces at its final state. With a surface represented by a triangular mesh, we present how an deterministic algorithm can be faithfully implemented to its continuous counterpart. To demonstrate the utility of this method, we have applied our method to both the cortical hemisphere and the entire cortex. Highly complied results are obtained in a matter of seconds.