Compressed Manifold Modes for Mesh Processing

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 multip...

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Bibliographic Details
Published in:Computer graphics forum Vol. 33; no. 5; pp. 35 - 44
Main Authors: Neumann, T., Varanasi, K., Theobalt, C., Magnor, M., Wacker, M.
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.08.2014
Subjects:
Algorithms
Analysis
Categories and Subject Descriptors (according to ACM CCS)
Collection
Compressed
Computer graphics
Eigenvalues
Human
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Hierarchy and geometric transformations
Manifolds
Mathematical analysis
Operators
Studies
Three dimensional
Topological manifolds
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary: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 ion. 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.
Bibliography:Supporting InformationSupporting Information
ark:/67375/WNG-Z2D226GQ-H
ArticleID:CGF12429
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12429