Encoding Neuroanatomical Information using Weighted Spherical Harmonic Representation

Cortical surfaces can be modeled using the recently developed weighed spherical harmonic (SPHARM) representation. The weighted-SPHARM representation incorporates data smoothing, parametrization and surface registration in a unified mathematical framework. The weighted-SPHARM represents the surface coordinates as a weighted linear combination of spherical harmonics in such a way that it solves a heat equation. The representation can decomposes an arbitrary surface into symmetric and asymmetric parts with respect to mirror reflection. By analyzing this unique decomposition, surface asymmetry can be quantified. We have applied our technique in quantifying abnormal brain asymmetry in autistic subjects.