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@article{Melzi:2018:10.1111/cgf.13309,
author = {Melzi, S and Rodolà, E and Castellani, U and Bronstein, MM},
doi = {10.1111/cgf.13309},
journal = {Computer Graphics Forum},
pages = {20--34},
title = {Localized Manifold Harmonics for Spectral Shape Analysis},
url = {http://dx.doi.org/10.1111/cgf.13309},
volume = {37},
year = {2018}
}

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TY  - JOUR
AB  - © 2017 The Authors Computer Graphics Forum © 2017 The Eurographics Association and John Wiley  &  Sons Ltd. 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. We obtain significant improvement compared to classical Laplacian eigenbases as well as other alternatives for constructing localized bases.
AU  - Melzi,S
AU  - Rodolà,E
AU  - Castellani,U
AU  - Bronstein,MM
DO  - 10.1111/cgf.13309
EP  - 34
PY  - 2018///
SN  - 0167-7055
SP  - 20
TI  - Localized Manifold Harmonics for Spectral Shape Analysis
T2  - Computer Graphics Forum
UR  - http://dx.doi.org/10.1111/cgf.13309
VL  - 37
ER  -

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