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.

Melzi, S., Rodolà, E., Castellani, U., Bronstein, M. (2017). Localized Manifold Harmonics for Spectral Shape Analysis. In Conference Proceedings (Poster) (pp.5-6) [10.2312/sgp.20171203].

Localized Manifold Harmonics for Spectral Shape Analysis

Simone Melzi;
2017

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.
Si
poster
Scientifica
Spectral geometry processing; Shape analysis; LBO; Localization
English
15th Eurographics Symposium on Geometry Processing, SGP 2017 - 3 July 2017 through 5 July 2017
Melzi, S., Rodolà, E., Castellani, U., Bronstein, M. (2017). Localized Manifold Harmonics for Spectral Shape Analysis. In Conference Proceedings (Poster) (pp.5-6) [10.2312/sgp.20171203].
Melzi, S; Rodolà, E; Castellani, U; Bronstein, M
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/389392
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