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Compressed Manifold Modes for Mesh Processing

Thomas Neumann, Kiran Varanasi, Christian Theobalt, Marcus Magnor, Markus Wacker Computer Graphics Forum (Proc. of Symposium on Geometry Processing SGP), vol. 33, no. 5. 2014
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Bibtex 
@article {CMM2014,
  author = {Neumann, T. and Varanasi, K. and Theobalt, C. and Magnor, M. and Wacker, M.},
  title = {Compressed Manifold Modes for Mesh Processing},
  journal = {Computer Graphics Forum},
  volume = {33},
  number = {5},
  issn = {1467-8659},
  pages = {35--44},
  year = {2014},
}}
Compressed Manifold Modes for Mesh Processing

Abstract

This paper introduces compressed eigenfunctions of the Laplace-Beltrami operator on 3D manifold surfaces. They constitute a novel functional basis, called the compressed manifold basis, where each function has local support. We derive an algorithm, based on the alternating direction method of multipliers (ADMM), to compute this basis on a given triangulated mesh. We show that compressed manifold modes identify key shape features, yielding an intuitive understanding of the basis for a human observer, where a shape can be processed as a collection of parts. We evaluate compressed manifold modes for potential applications in in shape matching and mesh abstraction. Our results show that this basis has distinct advantages over existing alternatives, indicating high potential for a wide range of use-cases in mesh processing.

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