mlsanityData to 7 Oct 2026

Moving Frame Net: SE(3)-Equivariant Network for Volumes

arXiv 2211.03420 ↗First posted 7 Nov 2022cs.CV stat.MLcited by 6

Not on the map. Why?

Abstract (arXiv)

Equivariance of neural networks to transformations helps to improve their performance and reduce generalization error in computer vision tasks, as they apply to datasets presenting symmetries (e.g. scalings, rotations, translations). The method of moving frames is classical for deriving operators invariant to the action of a Lie group in a manifold.Recently, a rotation and translation equivariant neural network for image data was proposed based on the moving frames approach. In this paper we significantly improve that approach by reducing the computation of moving frames to only one, at the input stage, instead of repeated computations at each layer. The equivariance of the resulting architecture is proved theoretically and we build a rotation and translation equivariant neural network to process volumes, i.e. signals on the 3D space. Our trained model overperforms the benchmarks in the medical volume classification of most of the tested datasets from MedMNIST3D.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 21 of its 27 references that are in the map. First posted on arXiv 7 Nov 2022.

Builds on

21 of 27 references.

References · 21

  1. 2016Group Equivariant Convolutional Networkscited by 1,154
  2. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  3. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  4. 2021MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classificationcited by 682
  5. 2016Harmonic Networks: Deep Translation and Rotation Equivariancecited by 293
  6. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 223
  7. 2020MedMNIST Classification Decathlon: A Lightweight AutoML Benchmark for Medical Image Analysiscited by 206
  8. 2017Learning Steerable Filters for Rotation Equivariant CNNscited by 193
  9. 2018Deep Neural Networks Motivated by Partial Differential Equationscited by 187
  10. 2020Lorentz Group Equivariant Neural Network for Particle Physicscited by 120
  11. 2021Equivariant Point Network for 3D Point Cloud Analysiscited by 81
  12. 2018CubeNet: Equivariance to 3D Rotation and Translationcited by 59
9 more
  1. 2020PDO-eConvs: Partial Differential Operator Based Equivariant Convolutionscited by 34
  2. 2016Structured Receptive Fields in CNNscited by 32
  3. 20213D Medical Point Transformer: Introducing Convolution to Attention Networks for Medical Point Cloud Analysiscited by 23
  4. 2021Steerable Partial Differential Operators for Equivariant Neural Networkscited by 22
  5. 2020Embed Me If You Can: A Geometric Perceptroncited by 10
  6. 2022Fully trainable Gaussian derivative convolutional layercited by 10
  7. 2020Rotation-Invariant Point Convolution With Multiple Equivariant Alignmentscited by 7
  8. 2022Differential invariants for SE(2)-equivariant networkscited by 6
  9. 2022PDO-s3DCNNs: Partial Differential Operator Based Steerable 3D CNNscited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 3; 2025: 1; 2026: 1.

6 papers.

  1. 2024ILPO-NET: Network for the invariant recognition of arbitrary volumetric patterns in 3Dcited by 3
  2. 2024On the Fourier analysis in the SO(3) space : EquiLoPO Networkcited by 1
  3. 2025Equivariant Eikonal Neural Networks: Grid-Free, Scalable Travel-Time Prediction on Homogeneous Spacescited by 1
  4. 2023Entropy Transformer Networks: A Learning Approach via Tangent Bundle Data Manifoldcited by 0
  5. 2024Adaptive Sampling for Continuous Group Equivariant Neural Networkscited by 0
  6. 2026bispectrum: Selective G-Bispectra Made Practicalcited by 0