Numerical methods for motion of level sets by affine curvature

TL;DR

This paper develops stable, convergent finite difference schemes for simulating the motion of level sets driven by affine curvature, ensuring accurate and invariant morphological evolution.

Contribution

It introduces new finite difference schemes based on viscosity solutions that are stable and preserve affine invariance for curvature-driven level set motion.

Findings

Standard schemes are nonlinearly unstable.

Proposed schemes are convergent and stable.

Numerical experiments confirm accuracy and invariance.

Abstract

We study numerical methods for the nonlinear partial differential equation that governs the motion of level sets by affine curvature. We show that standard finite difference schemes are nonlinearly unstable. We build convergent finite difference schemes, using the theory of viscosity solutions. We demonstrate that our approximate solutions capture the affine invariance and morphological properties of the evolution. Numerical experiments demonstrate the accuracy and stability of the discretization.