Localized Manifold Harmonics for Spectral Shape Analysis

S. Melzi, E. Rodolà, U. Castellani, M. M. Bronstein

Research output: Contribution to journalConference articlepeer-review


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.

Original languageEnglish
Pages (from-to)5-6
Number of pages2
JournalEurographics Symposium on Geometry Processing
StatePublished - 2017
Event15th Eurographics Symposium on Geometry Processing, SGP 2017 - London, United Kingdom
Duration: 3 Jul 20175 Jul 2017


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