Schrödinger Operator for Sparse Approximation of 3D Meshes (Unknown language)

in Symposium on Geometry Processing 2017- Posters; 9-10
Symposium on Geometry Processing 2017- Posters

We introduce a Schrödinger operator for spectral approximation of meshes representing surfaces in 3D. The operator is obtained by modifying the Laplacian with a potential function which defines the rate of oscillation of the harmonics on different regions of the surface. We design the potential using a vertex ordering scheme which modulates the Fourier basis of a 3D mesh to focus on crucial regions of the shape having high-frequency structures and employ a sparse approximation framework to maximize compression performance. The combination of the spectral geometry of the Hamiltonian in conjunction with a sparse approximation approach outperforms existing spectral compression schemes.

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A Primal-to-Primal Discretization of Exterior Calculus on Polygonal Meshes
Ptackova, Lenka / Velho, Luiz | 2017
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Choukroun, Yoni / Pai, Gautam / Kimmel, Ron | 2017
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