Localized Manifold Harmonics for Spectral Shape Analysis
- New search for: Melzi, Simone
- New search for: Rodolà, Emanuele
- New search for: Castellani, Umberto
- New search for: Bronstein, Michael M.
- New search for: The Eurographics Association
|commercial customers||academic customers|
|All round price||€17.50||€4.50|
Type of media:Conference paper
Type of material:Electronic Resource
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.