Median filter method for mean curvature flow using a random Jacobi algorithm

TL;DR

This paper introduces an efficient median filter-based scheme for level set mean curvature flow, proving convergence and extending results for the MBO thresholding scheme in data clustering, with discussions on boundary conditions.

Contribution

It presents a novel median filter method for mean curvature flow with proven convergence and extends weak convergence results for the MBO scheme to strong convergence in heat flow.

Findings

Proven convergence in $L^inity$-norm for the proposed scheme.

Extended weak to strong convergence for the MBO scheme.

Discussed boundary conditions for the scheme.

Abstract

We present an efficient scheme for level set mean curvature flow using a domain discretization and median filters. For this scheme, we show convergence in $L^\infty$-norm under mild assumptions on the number of points in the discretization. In addition, we strengthen the weak convergence result for the MBO thresholding scheme applied to data clustering of Lelmi and one of the authors. This is done through a strong convergence of the discretized heat flow in the optimal regime. Different boundary conditions are also discussed.