2022/12/09 by Selim Esedoḡlu, Esedoglu, Selim, Jiajia Guo +3
Computer Science · Engineering · Physics and Astronomy · #35K93 (Secondary) #65M12 (Primary) #Computer Graphics and Visualization Techniques #FOS: Mathematics #Lattice Boltzmann Simulation Studies #Numerical Analysis (math.NA) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2212.04943
openalex publication_date 2022/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The median filter scheme is an elegant, monotone discretization of the level set formulation of motion by mean curvature. It turns out to evolve every level set of the initial condition precisely by another class of methods known as threshold dynamics. Median filters are, in other words, the natural level set versions of threshold dynamics algorithms. Exploiting this connection, we revisit median filters in light of recent progress on the threshold dynamics method. In particular, we give a variational formulation of, and exhibit a Lyapunov function for, median filters, resulting in energy based unconditional stability properties. The connection also yields analogues of median filters in the multiphase setting of mean curvature flow of networks. These new multiphase level set methods do not require frequent redistancing, and can accommodate a wide range of surface tensions.