Localized Manifold Harmonics for Spectral Shape Analysis
| Autor: | Melzi, S., Rodolà, E., Castellani, U., Bronstein, M. M. |
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| Přispěvatelé: | Melzi, S, Rodolà, E, Castellani, U, Bronstein, M |
| Rok vydání: | 2017 |
| Předmět: |
FOS: Computer and information sciences
Spectral geometry processing Shape analysi methods and application 3D shape matching Mathematics::Spectral Theory Computational geometry Methods and applications Graphics (cs.GR) modelling Computer Science - Graphics LBO signal processing 3D shape matching computational geometry Localization signal processing ComputingMethodologies_COMPUTERGRAPHICS |
| DOI: | 10.48550/arxiv.1707.02596 |
| Popis: | 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. Comment: Accepted to Computer Graphics Forum |
| Databáze: | OpenAIRE |
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