Schrödinger Operator for Sparse Approximation of 3D Meshes
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Date
2017
Authors
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.
Description
@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}
}