Mumford-Shah Mesh Processing using the Ambrosio-Tortorelli Functional

Nicolas Bonneel 1, 2 David Coeurjolly 1 Pierre Gueth 3 Jacques-Olivier Lachaud 4
1 M2DisCo - Geometry Processing and Constrained Optimization
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
2 GeoMod - Modélisation Géométrique, Géométrie Algorithmique, Fractales
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
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 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.
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Nicolas Bonneel, David Coeurjolly, Pierre Gueth, Jacques-Olivier Lachaud. Mumford-Shah Mesh Processing using the Ambrosio-Tortorelli Functional. Computer Graphics Forum, Wiley, 2018, Proceedings of Pacific Graphics 2018, 37 (7), pp.75-85. ⟨10.1111/cgf.13549⟩. ⟨hal-01870901⟩

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