Static, quasistatic and dynamic analysis for scaled Perona-Malik functionals

TL;DR

This paper provides an asymptotic analysis of scaled Perona-Malik functionals, describing their local minimization, quasi-static, and dynamic evolutions, which converge to the Mumford-Shah functional as the scale changes.

Contribution

It offers a detailed asymptotic description of the local minimization and evolution problems for scaled Perona-Malik functionals, connecting them to the Mumford-Shah functional.

Findings

Convergence of scaled Perona-Malik energies to Mumford-Shah functional

Asymptotic characterization of local minimizers

Analysis of quasi-static and dynamic evolutions

Abstract

We present an asymptotic description of local minimization problems, and of quasi-static and dynamic evolutions of scaled Perona-Malik functionals. The scaling is chosen such that these energies $\Gamma$-converge to the Mumford-Shah functional by a result by Morini and Negri.