Surface Networks

Ilya Kostrikov, Zhongshi Jiang, Daniele Panozzo, Denis Zorin, Joan Bruna

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

Abstract

We study data-driven representations for three-dimensional triangle meshes, which are one of the prevalent objects used to represent 3D geometry. Recent works have developed models that exploit the intrinsic geometry of manifolds and graphs, namely the Graph Neural Networks (GNNs) and its spectral variants, which learn from the local metric tensor via the Laplacian operator. Despite offering excellent sample complexity and built-in invariances, intrinsic geometry alone is invariant to isometric deformations, making it unsuitable for many applications. To overcome this limitation, we propose several upgrades to GNNs to leverage extrinsic differential geometry properties of three-dimensional surfaces, increasing its modeling power. In particular, we propose to exploit the Dirac operator, whose spectrum detects principal curvature directions - this is in stark contrast with the classical Laplace operator, which directly measures mean curvature. We coin the resulting models Surface Networks (SN). We prove that these models define shape representations that are stable to deformation and to discretization, and we demonstrate the efficiency and versatility of SNs on two challenging tasks: temporal prediction of mesh deformations under non-linear dynamics and generative models using a variational autoencoder framework with encoders/decoders given by SNs.

Original languageEnglish (US)
Title of host publicationProceedings - 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2018
PublisherIEEE Computer Society
Pages2540-2548
Number of pages9
ISBN (Electronic)9781538664209
DOIs
StatePublished - Dec 14 2018
Event31st Meeting of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2018 - Salt Lake City, United States
Duration: Jun 18 2018Jun 22 2018

Publication series

NameProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
ISSN (Print)1063-6919

Conference

Conference31st Meeting of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2018
CountryUnited States
CitySalt Lake City
Period6/18/186/22/18

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition

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