Work

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

Year: 2025

Type: article

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.

Source: Comptes Rendus Mathématique

DOI: 10.5802/crmath.753

Authors: Angelo Iollo, Tommaso Taddei

Institutions: Université de Bordeaux, Centre Inria de l'université de Bordeaux, Institut de Mathématiques de Bordeaux, MEMPHIS: Modèles et méthodes pour les problèmes multiphysiques et interactions

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4412035968

FWCI:

Cites: 29

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Related to: 10