Localized Manifold Harmonics for Spectral Shape Analysis

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Date
2017
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association
Abstract
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. 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.
Description

        
@inproceedings{
10.2312:sgp.20171203
, booktitle = {
Symposium on Geometry Processing 2017- Posters
}, editor = {
Jakob Andreas Bærentzen and Klaus Hildebrandt
}, title = {{
Localized Manifold Harmonics for Spectral Shape Analysis
}}, author = {
Melzi, Simone
and
RodolĂ , Emanuele
and
Castellani, Umberto
and
Bronstein, Michael M.
}, year = {
2017
}, publisher = {
The Eurographics Association
}, ISSN = {
1727-8384
}, ISBN = {
978-3-03868-047-5
}, DOI = {
10.2312/sgp.20171203
} }
Citation