Fakultät Informatik

14.07.2017

Kolloq. Simone Melzi, PhD, topic: Localized Manifold Harmonics for Spectral Shape Analysis

Friday, 14th of July 2017, 11:00 am FMI 02.09.023 (MI-Building, Campus Garching)

Abstract:
The use of Laplacian eigenfunctions is ubiquitous in a wide range of computergraphics and geometry processing applications. In particular, Laplacia eigenbases allow generalizing the classical Fourier analysis to manifolds. Akey drawback of such bases is their inherently global nature, as the Laplacianeigenfunctions carry geometric and topological structure of the entiremanifold. In this talk, we introduce a new framework for local spectral shapeanalysis. We show how to efficiently construct localized orthogonal bases bysolving an optimization problem that in turn can be posed as theeigendecomposition of a new operator obtained by a modification of the standardLaplacian. We study the theoretical and computational aspects of the proposedframework and showcase our new construction on the classical problems of shapeapproximation and correspondence. We obtain significant improvement compared to classical Laplacian eigenbases as well as other alternatives for constructinglocalized bases.

Bio:
Simone Melzi is a PhD student at the University of Verona (Italy), where he works under the supervision of Prof. Castellani on extending, applying and formulating signal processing techniques for (possibly high-dimensional) signals on surfaces. He has published about 10 papers on this topic in top-tier venues and journals in computer vision and graphics (TOG, ICCV, SGP, etc.) and maintains fruitful collaborations with world leaders in this area (Ecole polytechnique, USI Lugano, Sapienza U Rome).

contact person:
--------------------
Daniel Cremers
Phone: +49.89.289.17755
Email: cremers(at)tum.de

 

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