Schrödinger Operator for Sparse Approximation of 3D Meshes

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Date
2017
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association
Abstract
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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@inproceedings{
10.2312:sgp.20171205
, booktitle = {
Symposium on Geometry Processing 2017- Posters
}, editor = {
Jakob Andreas Bærentzen and Klaus Hildebrandt
}, title = {{
Schrödinger Operator for Sparse Approximation of 3D Meshes
}}, author = {
Choukroun, Yoni
and
Pai, Gautam
and
Kimmel, Ron
}, year = {
2017
}, publisher = {
The Eurographics Association
}, ISSN = {
1727-8384
}, ISBN = {
978-3-03868-047-5
}, DOI = {
10.2312/sgp.20171205
} }
Citation