Steklov Spectral Geometry for Extrinsic Shape Analysis
Name
a7-wang.pdf
Description
Published version
Size
18.95 MB
Format
Adobe PDF
Checksum (MD5)
a543720da3ab76d69262759d25eeb273
Author(s)
Wang, Yu
Ben-Chen, Mirela
Polterovich, Iosif
Solomon, Justin
Date Issued
2019
Journal
ACM Transactions on Graphics
Publisher
Association for Computing Machinery (ACM)
Version
Final published version
Abstract
© 2018 held by Owner/Author We propose using the Dirichlet-to-Neumann operator as an extrinsic alternative to the Laplacian for spectral geometry processing and shape analysis. Intrinsic approaches, usually based on the Laplace-Beltrami operator, cannot capture the spatial embedding of a shape up to rigid motion, and many previous extrinsic methods lack theoretical justification. Instead, we consider the Steklov eigenvalue problem, computing the spectrum of the Dirichlet-to-Neumann operator of a surface bounding a volume. A remarkable property of this operator is that it completely encodes volumetric geometry. We use the boundary element method (BEM) to discretize the operator, accelerated by hierarchical numerical schemes and preconditioning; this pipeline allows us to solve eigenvalue and linear problems on large-scale meshes despite the density of the Dirichlet-to-Neumann discretization. We further demonstrate that our operators naturally fit into existing frameworks for geometry processing, making a shift from intrinsic to extrinsic geometry as simple as substituting the Laplace-Beltrami operator with the Dirichlet-to-Neumann operator.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1145/3152156
