Functional Maps Representation On Product Manifolds
Name
1809.10940.pdf
Description
Submitted version
Size
3.34 MB
Format
Adobe PDF
Checksum (MD5)
7252eebff39de935415c2219c8f3b57f
Author(s)
Rodolà, E
Lähner, Z
Bronstein, AM
Bronstein, MM
Solomon, J
Date Issued
2019
Journal
Computer Graphics Forum
Publisher
Wiley
Version
Original manuscript
Abstract
© 2019 The Authors Computer Graphics Forum © 2019 The Eurographics Association and John Wiley & Sons Ltd. We consider the tasks of representing, analysing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the language of signal processing on manifolds. Being a manifold itself, the product space endows the set of maps with a geometry of its own, which we exploit to define map operations in the spectral domain; we also derive relationships with other existing representations (soft maps and functional maps). To apply these ideas in practice, we discretize product manifolds and their Laplace–Beltrami operators, and we introduce localized spectral analysis of the product manifold as a novel tool for map processing. Our framework applies to maps defined between and across 2D and 3D shapes without requiring special adjustment, and it can be implemented efficiently with simple operations on sparse matrices.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1111/cgf.13598
