mlsanityData to 14 Oct 2026

SE(3)-Equivariant and Noise-Invariant 3D Rigid Motion Tracking in Brain MRI

arXiv 2312.13534 ↗First posted 21 Dec 2023eess.IV cs.CVcited by 10

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Abstract (arXiv)

Rigid motion tracking is paramount in many medical imaging applications where movements need to be detected, corrected, or accounted for. Modern strategies rely on convolutional neural networks (CNN) and pose this problem as rigid registration. Yet, CNNs do not exploit natural symmetries in this task, as they are equivariant to translations (their outputs shift with their inputs) but not to rotations. Here we propose EquiTrack, the first method that uses recent steerable SE(3)-equivariant CNNs (E-CNN) for motion tracking. While steerable E-CNNs can extract corresponding features across different poses, testing them on noisy medical images reveals that they do not have enough learning capacity to learn noise invariance. Thus, we introduce a hybrid architecture that pairs a denoiser with an E-CNN to decouple the processing of anatomically irrelevant intensity features from the extraction of equivariant spatial features. Rigid transforms are then estimated in closed-form. EquiTrack outperforms state-of-the-art learning and optimisation methods for motion tracking in adult brain MRI and fetal MRI time series. Our code is available at https://github.com/BBillot/EquiTrack.

Key facts. Cited by 10 papers in the map (data through 14 Oct 2026). Builds on 33 of its 78 references that are in the map. First posted on arXiv 21 Dec 2023.

Builds on

33 of 78 references.

References · 33

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21 more
  1. 2018A Deep Learning Framework for Unsupervised Affine and Deformable Image Registrationcited by 160
  2. 2020SynthMorph: learning contrast-invariant registration without acquired imagescited by 140
  3. 2019Scale-Equivariant Steerable Networkscited by 110
  4. 2018Roto-Translation Covariant Convolutional Networks for Medical Image Analysiscited by 92
  5. 2021Residual Pathway Priors for Soft Equivariance Constraintscited by 75
  6. 2019Disentangled Representation Learning in Cardiac Image Analysiscited by 69
  7. 2018CubeNet: Equivariance to 3D Rotation and Translationcited by 59
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  11. 2018Real-time Deep Pose Estimation with Geodesic Loss for Image-to-Template Rigid Registrationcited by 40
  12. 20183D G-CNNs for Pulmonary Nodule Detectioncited by 36
  13. 2020Roto-Translation Equivariant Convolutional Networks: Application to Histopathology Image Analysiscited by 32
  14. 2023A Robust and Interpretable Deep Learning Framework for Multi-modal Registration via Keypointscited by 25
  15. 2016An Artificial Agent for Robust Image Registrationcited by 23
  16. 2021Equivariant Filters for Efficient Tracking in 3D Imagingcited by 17
  17. 2018Intertwiners between Induced Representations (with Applications to the Theory of Equivariant Neural Networks)cited by 16
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  19. 2019Fetal Pose Estimation in Volumetric MRI using a 3D Convolution Neural Networkcited by 9
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  21. 2023Dynamic Neural Fields for Learning Atlases of 4D Fetal MRI Time-seriescited by 4

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 3; 2025: 5; 2026: 2.

10 papers.

  1. 2024Segment as You Wish -- Free-Form Language-Based Segmentation for Medical Imagescited by 2
  2. 2024CABLD: Contrast-Agnostic Brain Landmark Detection with Consistency-Based Regularizationcited by 2
  3. 2025Spatial regularisation for improved accuracy and interpretability in keypoint-based registrationcited by 1
  4. 2025Fetuses Made Simple: Modeling and Tracking of Fetal Shape and Posecited by 1
  5. 2025Intraoperative 2D/3D Registration via Spherical Similarity Learning and Differentiable Levenberg-Marquardt Optimizationcited by 1
  6. 2024A Unified Deep Learning Framework for Motion Correction in Medical Imagingcited by 0
  7. 2025Moment kernels: a simple and scalable approach for equivariance to rotations and reflections in deep convolutional networkscited by 0
  8. 2025Equivariant symmetry-aware head pose estimation for fetal MRIcited by 0
  9. 2026Rotation Equivariant Convolutions in Deformable Registration of Brain MRIcited by 0
  10. 2026Patient-Agnostic Synthetic Pretraining for Efficient Patient-Specific Intraoperative 2D/3D Registrationcited by 0