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Compressed Manifold Modes for Mesh Processing
Author(s) -
Neumann T.,
Varanasi K.,
Theobalt C.,
Magnor M.,
Wacker M.
Publication year - 2014
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.12429
Subject(s) - basis (linear algebra) , computer science , basis function , manifold (fluid mechanics) , eigenfunction , algorithm , topology (electrical circuits) , mathematics , geometry , mathematical analysis , eigenvalues and eigenvectors , combinatorics , engineering , mechanical engineering , physics , quantum mechanics
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 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.