Localized Manifold Harmonics for Spectral Shape Analysis

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dc.contributor.authorMelzi, S.en_US
dc.contributor.authorRodolà, E.en_US
dc.contributor.authorCastellani, U.en_US
dc.contributor.authorBronstein, M. M.en_US
dc.contributor.editorChen, Min and Benes, Bedrichen_US
dc.date.accessioned2018-08-29T06:55:56Z
dc.date.available2018-08-29T06:55:56Z
dc.date.issued2018
dc.description.abstractThe use of Laplacian eigenfunctions is ubiquitous in a wide range of computer graphics and geometry processing applications. In particular, Laplacian eigenbases allow generalizing the classical Fourier analysis to manifolds. A key drawback of such bases is their inherently global nature, as the Laplacian eigenfunctions carry geometric and topological structure of the entire manifold. In this paper, we introduce a new framework for local spectral shape analysis. We show how to efficiently construct localized orthogonal bases by solving an optimization problem that in turn can be posed as the eigendecomposition of a new operator obtained by a modification of the standard Laplacian. We study the theoretical and computational aspects of the proposed framework and showcase our new construction on the classical problems of shape approximation and correspondence. We obtain significant improvement compared to classical Laplacian eigenbases as well as other alternatives for constructing localized bases.The use of Laplacian eigenfunctions is ubiquitous in a wide range of computer graphics and geometry processing applications. In particular, Laplacian eigenbases allow generalizing the classical Fourier analysis to manifolds. A key drawback of such bases is their inherently global nature, as the Laplacian eigenfunctions carry geometric and topological structure of the entire manifold. In this paper, we introduce a new framework for local spectral shape analysis. We show how to efficiently construct localized orthogonal bases by solving an optimization problem that in turn can be posed as the eigendecomposition of a new operator obtained by a modification of the standard Laplacian.en_US
dc.description.number6
dc.description.sectionheadersArticles
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume37
dc.identifier.doi10.1111/cgf.13309
dc.identifier.issn1467-8659
dc.identifier.pages20-34
dc.identifier.urihttps://doi.org/10.1111/cgf.13309
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf13309
dc.publisher© 2018 The Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectsignal processing
dc.subjectmethods and applications
dc.subject3D shape matching
dc.subjectmodelling
dc.subjectcomputational geometry
dc.subjectmodelling
dc.subjectCategories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling—Shape Analysis, 3D Shape Matching, Geometric Modelling
dc.titleLocalized Manifold Harmonics for Spectral Shape Analysisen_US
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