# Mumford-Shah Mesh Processing using the Ambrosio-Tortorelli Functional

### Abstract

The Mumford-Shah functional approximates a function by a piecewise smooth function. Its versatility makes it ideal for tasks such as image segmentation or restoration, and it is now a widespread tool of image processing. Recent work has started to investigate its use for mesh segmentation and feature lines detection, but we take the stance that the power of this func- tional could reach far beyond these tasks and integrate the everyday mesh processing toolbox. In this paper, we discretize an Ambrosio-Tortorelli approximation via a Discrete Exterior Calculus formulation. We show that, combined with a new shape optimization routine, several mesh processing problems can be readily tackled within the same framework. In particular, we illustrate applications in mesh denoising, normal map embossing, mesh inpainting and mesh segmentation.

Type

Caption: Our discretization of the MS functional along with our new vertex projection technique allows for applications such as mesh denoising, segmentation, inpainting and normal map embossing. (b) Our method removes heavy noise while preserving sharp features shown in yellow. (c) We remove vertices highlighted in cyan from the original mesh (a): our method finds sharp features (shown in yellow) and sucessfully inpaints the missing area. (d) We decompose the original mesh (a) into piecewise smooth segments whose boundaries are characterized by sharp features shown on edges in red. (e) We emboss a normal map into the mesh vertices.

@techreport{bonneel18ATRR,
author = {Nicolas Bonneel and David Coeurjolly and Pierre Gueth and Jacques-Olivier Lachaud},
institution = {arXiv},
month = {June},
note = {working paper or preprint},
title = {Mumford-Shah Mesh Processing using the Ambrosio-Tortorelli Functional},
url = {https://arxiv.org/abs/1806.05999},
year = {2018}
}