3D Equivariant Graph Implicit Functions

Yunlu Chen, Basura Fernando, Hakan Bilen, Matthias Nießner, Efstratios Gavves

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

Abstract

In recent years, neural implicit representations have made remarkable progress in modeling of 3D shapes with arbitrary topology. In this work, we address two key limitations of such representations, in failing to capture local 3D geometric fine details, and to learn from and generalize to shapes with unseen 3D transformations. To this end, we introduce a novel family of graph implicit functions with equivariant layers that facilitates modeling fine local details and guaranteed robustness to various groups of geometric transformations, through local $k$-NN graph embeddings with sparse point set observations at multiple resolutions. Our method improves over the existing rotation-equivariant implicit function from 0.69 to 0.89 (IoU) on the ShapeNet reconstruction task. We also show that our equivariant implicit function can be extended to other types of similarity transformations and generalizes to unseen translations and scaling.
Original languageEnglish
Title of host publicationComputer Vision – ECCV 2022: 17th European Conference, Tel Aviv, Israel, October 23–27, 2022, Proceedings, Part III
EditorsShai Avidan, Gabriel Brostow, Moustapha Cissé, Giovanni Maria Farinella, Tal Hassner
PublisherSpringer, Cham
Pages485-502
Number of pages17
ISBN (Electronic)978-3-031-20062-5
ISBN (Print)978-3-031-20061-8
DOIs
Publication statusPublished - 11 Nov 2022
EventEuropean Conference on Computer Vision 2022 - Israel, Tel Aviv, Israel
Duration: 23 Oct 202227 Oct 2022
https://eccv2022.ecva.net/

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Cham
Volume13663
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceEuropean Conference on Computer Vision 2022
Abbreviated titleECCV 2022
Country/TerritoryIsrael
CityTel Aviv
Period23/10/2227/10/22
Internet address

Keywords

  • Implicit neural representations
  • equivariance
  • graph neural networks
  • 3D reconstruction
  • transformation

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