Computational Functional Anatomy

Abstract

We present a novel kernel smoothing framework using the Laplace-Beltrami eigenfunctions. The Green's function of an isotropic diffusion equation on a manifold is analytically represented using the eigenfunctions of the Laplace-Beltraimi operator. The Green's function is then used in explicitly constructing heat kernel smoothing as a series expansion of the eigenfunctions. Unlike many previous surface diffusion approaches, diffusion is analytically represented using the eigenfunctions substantially improving numerical accuracy. Our numerical implementation is validated against the spherical harmonic representation of heat kernel smoothing on a unit sphere. The proposed framework is illustrated with mandible, hippocampus and cortical surfaces, and is compared to a widely used iterative kernel smoothing method in computational anatomy.??