Schrödinger Operator for Sparse Approximation of 3D Meshes

Choukroun, Yoni; Pai, Gautam; Kimmel, Ron

Schrödinger Operator for Sparse Approximation of 3D Meshes

Files

009-010.pdf (689.35 KB)

Date

2017

Authors

Choukroun, Yoni
Pai, Gautam
Kimmel, Ron

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.

        @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
}
}