Isospectralization, or how to hear shape, style, and correspondence

Luca Cosmo, Mikhail Panine, Arianna Rampini, Maks Ovsjanikov, Michael M. Bronstein, Emanuele Rodola

Research output: Chapter in Book/Report/Conference proceedingConference contribution

32 Scopus citations

Abstract

The question whether one can recover the shape of a geometric object from its Laplacian spectrum ('hear the shape of the drum') is a classical problem in spectral geometry with a broad range of implications and applications. While theoretically the answer to this question is negative (there exist examples of iso-spectral but non-isometric manifolds), little is known about the practical possibility of using the spectrum for shape reconstruction and optimization. In this paper, we introduce a numerical procedure called isospectralization, consisting of deforming one shape to make its Laplacian spectrum match that of another. We implement the isospectralization procedure using modern differentiable programming techniques and exemplify its applications in some of the classical and notoriously hard problems in geometry processing, computer vision, and graphics such as shape reconstruction, pose and style transfer, and dense deformable correspondence.
Original languageEnglish (US)
Title of host publication2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)
PublisherIEEE
Pages7521-7530
Number of pages10
ISBN (Print)9781728132938
DOIs
StatePublished - Jan 9 2020
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2022-06-24
Acknowledged KAUST grant number(s): OSR-CRG2017-3426
Acknowledgements: The authors wish to thank Alex Bronstein for useful discussions. ER and AR are supported by the ERC Starting Grant No. 802554 (SPECGEO). MB and LC are partially supported by ERC Consolidator Grant No. 724228 (LEMAN) and Google Research Faculty awards. MB is also partially supported by the Royal Society Wolfson Research Merit award and Rudolf Diesel industrial fellowship at TU Munich. Parts of this work were supported by a Google Focused Research Award, KAUST OSR Award No. OSR-CRG2017-3426, a gift from the NVIDIA Corporation and the ERC Starting Grant No. 758800 (EXPROTEA).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

Fingerprint

Dive into the research topics of 'Isospectralization, or how to hear shape, style, and correspondence'. Together they form a unique fingerprint.

Cite this