Heat kernel smoothing using Laplace-Beltrami eigenfunctions.

We present a novel surface smoothing framework using the Laplace-Beltrami eigenfunctions. The Green's function of an isotropic diffusion equation on a manifold is constructed as a linear combination of the Laplace-Beltraimi operator. The Green's function is then used in constructing heat kernel smoothing. Unlike many previous approaches, diffusion is analytically represented as a series expansion avoiding numerical instability and inaccuracy issues. This proposed framework is illustrated with mandible surfaces, and is compared to a widely used iterative kernel smoothing technique in computational anatomy. The MATLAB source code is freely available at https://brainimaging.waisman.wisc.edu/ chung/lb.