Localized Manifold Harmonics for Spectral Shape Analysis

Melzi, Simone; Rodolà, Emanuele; Castellani, Umberto; Bronstein, Michael M.

Localized Manifold Harmonics for Spectral Shape Analysis

Files

005-006.pdf (2.87 MB)

Date

2017

Authors

Melzi, Simone
Rodolà, Emanuele
Castellani, Umberto
Bronstein, Michael M.

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.

        @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 
Rodolà, 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
}
}