Mumford‐Shah Mesh Processing using the Ambrosio‐Tortorelli Functional

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 featur...

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Bibliographic Details
Published inComputer graphics forum Vol. 37; no. 7; pp. 75 - 85
Main Authors Bonneel, Nicolas, Coeurjolly, David, Gueth, Pierre, Lachaud, Jacques‐Olivier
Format Journal Article
LanguageEnglish
Published Oxford Blackwell Publishing Ltd 01.10.2018
Wiley
SeriesProceedings of Pacific Graphics 2018
Subjects
Computational Geometry
Computer Science
Embossing
Image Processing
Image processing systems
Image segmentation
Noise reduction
Restoration
Shape optimization
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Summary: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.
Bibliography:joint first authors
ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.13549