A diffusion driven curvature flow

TL;DR

This paper proves that a modified diffusion-driven algorithm, inspired by the Bence-Merriman-Osher method and Evans' convergence proof, effectively models curvature-driven surface evolution, with applications to visual cortex modeling.

Contribution

It introduces a new version of the diffusion-driven curvature flow algorithm with a different surface evolution definition, extending previous methods and linking to neural modeling.

Findings

The modified algorithm converges to curvature flow.

The approach is applicable to visual cortex models.

It bridges heat equation solutions with geometric surface evolution.

Abstract

Bence-Merriman-Osher algorithm computes numerically mean curvature flow via solutions of heat equation iteratively initialized at the end of each short time interval. Inspired by the convergence proof of Evans of this algorithm where he employed nonlinear semigroup theory and level set approach to mean curvature flow, we prove here that a similar procedure, but now with a different definition of evolved surface at the end of each short time interval, results in a motion by curvature. The interest of this version of the algorithm is its application corresponding to model of the visual cortex.