Point-set registration in bounded domains via the Fokker–Planck equation

We present a point set registration method in bounded domains based on the solution to the Fokker–Planck equation. Our approach leverages (i) density estimation based on Gaussian mixture models; (ii) a stabilized finite element discretization of the Fokker–Planck equation; (iii) a specialized method for the integration of the particles. We review relevant properties of the Fokker–Planck equation that provide the foundations for the numerical method. We discuss two strategies for the integration of the particles and we propose a regularization technique to control the distance of the particles from the boundary of the domain. We perform extensive numerical experiments for two two-dimensional model problems to illustrate the many features of the method.