  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 functional 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.
