Spectral Mesh Processing

Spectral methods for mesh processing and analysis rely on the eigenvalues, eigenvectors, or eigenspace projections derived from appropriately defined mesh operators to carry out desired tasks. Early work in this area can be traced back to the seminal paper by Taubin in 1995, where spectral analysis...

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Bibliographic Details
Published in:Computer graphics forum Vol. 29; no. 6; pp. 1865 - 1894
Main Authors: Zhang, H., Van Kaick, O., Dyer, R.
Format: Journal Article
Language:English
Published: Oxford, UK Blackwell Publishing Ltd 01.09.2010
Subjects:
Aids
Combinatorial analysis
Computer based modeling
Computer graphics
Computer Graphics [I.3.5]: Computational Geometry and Object Modeling
Computer vision
Eigenvalues
Eigenvectors
Filtering
Focusing
Geometry
geometry processing
Graph theory
High performance computing
Linear algebra
Lists
Machine learning
Operators
Spectra
Studies
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:Spectral methods for mesh processing and analysis rely on the eigenvalues, eigenvectors, or eigenspace projections derived from appropriately defined mesh operators to carry out desired tasks. Early work in this area can be traced back to the seminal paper by Taubin in 1995, where spectral analysis of mesh geometry based on a combinatorial Laplacian aids our understanding of the low‐pass filtering approach to mesh smoothing. Over the past 15 years, the list of applications in the area of geometry processing which utilize the eigenstructures of a variety of mesh operators in different manners have been growing steadily. Many works presented so far draw parallels from developments in fields such as graph theory, computer vision, machine learning, graph drawing, numerical linear algebra, and high‐performance computing. This paper aims to provide a comprehensive survey on the spectral approach, focusing on its power and versatility in solving geometry processing problems and attempting to bridge the gap between relevant research in computer graphics and other fields. Necessary theoretical background is provided. Existing works covered are classified according to different criteria: the operators or eigenstructures employed, application domains, or the dimensionality of the spectral embeddings used. Despite much empirical success, there still remain many open questions pertaining to the spectral approach. These are discussed as we conclude the survey and provide our perspective on possible future research.
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ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2010.01655.x