Algorithms to Improve the Reparameterization of Spherical Mappings of Brain Surface Meshes

A spherical map of a cortical surface is often used for improved brain registration, for advanced morphometric analysis (eg, of brain shape), and for surface-based analysis of functional signals recorded from the cortex. Furthermore, for intersubject analysis, it is usually necessary to reparameterize the surface mesh into a common coordinate system. An isometric map conserves all angle and area information in the original cortical mesh; however, in practice, spherical maps contain some distortion. Here, we propose fast new algorithms to reduce the distortion of initial spherical mappings generated using one of three common spherical mapping methods. The algorithms iteratively solve a nonlinear optimization problem to reduce distortion. Our results demonstrate that our correction process is computationally inexpensive and the resulting spherical maps have improved distortion metrics. We show that our corrected spherical maps improve reparameterization of the cortical surface mesh, such that the distance error measures between the original and reparameterized surface are significantly decreased.