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

TL;DR

This paper introduces a novel point set registration method in bounded domains utilizing the Fokker-Planck equation, combining density estimation, finite element discretization, and particle integration techniques.

Contribution

It presents a new approach that integrates the Fokker-Planck equation with density estimation and specialized particle integration for improved registration in bounded domains.

Findings

Effective registration demonstrated on 2D model problems

Stable numerical method with boundary regularization

Versatile approach applicable to complex bounded domains

Abstract

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.