Localized Manifold Harmonics for Spectral Shape Analysis (Unknown language)

in Symposium on Geometry Processing 2017- Posters; 5-6
Symposium on Geometry Processing 2017- Posters

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.

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Sequentially-Defined Compressed Modes via ADMM
Houston, Kevin | 2017
DepthCut: Improved Depth Edge Estimation Using Multiple Unreliable Channels
Guerrero, Paul / Winnemöller, Holger / Li, Wilmot / Mitra, Niloy J. | 2017
Localized Manifold Harmonics for Spectral Shape Analysis
Melzi, Simone / Rodolà, Emanuele / Castellani, Umberto / Bronstein, Michael M. | 2017
A Primal-to-Primal Discretization of Exterior Calculus on Polygonal Meshes
Ptackova, Lenka / Velho, Luiz | 2017
Schrödinger Operator for Sparse Approximation of 3D Meshes
Choukroun, Yoni / Pai, Gautam / Kimmel, Ron | 2017
PCR: A Geometric Cocktail for Triangulating Point Clouds Beautifully Without Angle Bounds
Leitão, Gonçalo N. V. / Gomes, Abel J. P. | 2017

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