TY - JOUR
T1 - Localized Manifold Harmonics for Spectral Shape Analysis
AU - Melzi, S.
AU - Rodolà, E.
AU - Castellani, U.
AU - Bronstein, M. M.
N1 - Publisher Copyright:
© 2017 The Author(s) Eurographics Proceedings © 2017 The Eurographics Association.
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85122695323&partnerID=8YFLogxK
U2 - 10.2312/sgp.20171203
DO - 10.2312/sgp.20171203
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AN - SCOPUS:85122695323
SN - 1727-8384
SP - 5
EP - 6
JO - Eurographics Symposium on Geometry Processing
JF - Eurographics Symposium on Geometry Processing
T2 - 15th Eurographics Symposium on Geometry Processing, SGP 2017
Y2 - 3 July 2017 through 5 July 2017
ER -