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

2024/10/10 by Anton Ullrich, Tim Laux, Ullrich, Anton +1 · 2 citations
Computer Science · Engineering · #35D40 #3D Shape Modeling and Analysis #53E10 (Primary) #60D05 (Secondary) #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #Computer Graphics and Visualization Techniques #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2410.07776

openalex publication_date 2024/10/10 · openalex created_date 2024/10/13 · openalex updated_date 2026/07/28

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^∞-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.

Cited by

• Obstacle Mean Curvature Flow: Efficient Approximation and Convergence Analysis
• Elementary discrete diffusion/redistancing schemes for the mean curvature flow

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