mlsanityData to 14 Oct 2026

Regular SE(3) Group Convolutions for Volumetric Medical Image Analysis

arXiv 2306.13960 ↗First posted 24 Jun 2023cs.CV cs.AI cs.LGcited by 6

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Abstract (arXiv)

Regular group convolutional neural networks (G-CNNs) have been shown to increase model performance and improve equivariance to different geometrical symmetries. This work addresses the problem of SE(3), i.e., roto-translation equivariance, on volumetric data. Volumetric image data is prevalent in many medical settings. Motivated by the recent work on separable group convolutions, we devise a SE(3) group convolution kernel separated into a continuous SO(3) (rotation) kernel and a spatial kernel. We approximate equivariance to the continuous setting by sampling uniform SO(3) grids. Our continuous SO(3) kernel is parameterized via RBF interpolation on similarly uniform grids. We demonstrate the advantages of our approach in volumetric medical image analysis. Our SE(3) equivariant models consistently outperform CNNs and regular discrete G-CNNs on challenging medical classification tasks and show significantly improved generalization capabilities. Our approach achieves up to a 16.5% gain in accuracy over regular CNNs.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 16 of its 29 references that are in the map. First posted on arXiv 24 Jun 2023.

Builds on

16 of 29 references.

References · 16

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  3. 2016Group Equivariant Convolutional Networkscited by 1,165
  4. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
  5. 2021MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classificationcited by 690
  6. 2018PointConv: Deep Convolutional Networks on 3D Point Cloudscited by 657
  7. 2019The Liver Tumor Segmentation Benchmark (LiTS)cited by 509
  8. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 354
  9. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 300
  10. 2016Harmonic Networks: Deep Translation and Rotation Equivariancecited by 295
  11. 2016Volumetric and Multi-View CNNs for Object Classification on 3D Datacited by 240
  12. 2020MedMNIST Classification Decathlon: A Lightweight AutoML Benchmark for Medical Image Analysiscited by 206
4 more
  1. 2018Roto-Translation Covariant Convolutional Networks for Medical Image Analysiscited by 92
  2. 2018CubeNet: Equivariance to 3D Rotation and Translationcited by 59
  3. 20183D G-CNNs for Pulmonary Nodule Detectioncited by 36
  4. 2021Exploiting Redundancy: Separable Group Convolutional Networks on Lie Groupscited by 22

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 2; 2025: 1; 2026: 2.

6 papers.

  1. 2023Fast, Expressive SE(n) Equivariant Networks through Weight-Sharing in Position-Orientation Spacecited by 41
  2. 2025Probing Equivariance and Symmetry Breaking in Convolutional Networkscited by 12
  3. 2026Flow Equivariant World Models: Memory for Partially Observed Dynamic Environmentscited by 8
  4. 2024Current Symmetry Group Equivariant Convolution Frameworks for Representation Learningcited by 2
  5. 2024On the Fourier analysis in the SO(3) space : EquiLoPO Networkcited by 1
  6. 2026bispectrum: Selective G-Bispectra Made Practicalcited by 0