Tangent Space Backpropagation for 3D Transformation Groups

Zachary Teed, Jia Deng

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

3 Scopus citations

Abstract

We address the problem of performing backpropagation for computation graphs involving 3D transformation groups SO(3), SE(3), and Sim(3). 3D transformation groups are widely used in 3D vision and robotics, but they do not form vector spaces and instead lie on smooth manifolds. The standard backpropagation approach, which embeds 3D transformations in Euclidean spaces, suffers from numerical difficulties. We introduce a new library, which exploits the group structure of 3D transformations and performs backpropagation in the tangent spaces of manifolds. We show that our approach is numerically more stable, easier to implement, and beneficial to a diverse set of tasks. Our plug-and-play PyTorch library is available at https://github.com/princeton-vl/lietorch.

Original languageEnglish (US)
Title of host publicationProceedings - 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2021
PublisherIEEE Computer Society
Pages10333-10342
Number of pages10
ISBN (Electronic)9781665445092
DOIs
StatePublished - 2021
Event2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2021 - Virtual, Online, United States
Duration: Jun 19 2021Jun 25 2021

Publication series

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

Conference

Conference2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2021
Country/TerritoryUnited States
CityVirtual, Online
Period6/19/216/25/21

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Vision and Pattern Recognition

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