# SpaER: Learning Spatio-temporal Equivariant Representations for Fetal Brain Motion Tracking

arXiv: https://arxiv.org/abs/2407.20198 · HTML: https://mlsanity.com/paper/2407.20198/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 33 references that are in the map.
- First posted on arXiv 29 Jul 2024.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Real-time Deep Pose Estimation with Geodesic Loss for Image-to-Template Rigid Registration](https://mlsanity.com/paper/1803.05982/) (2018)
- [SVoRT: Iterative Transformer for Slice-to-Volume Registration in Fetal Brain MRI](https://mlsanity.com/paper/2206.10802/) (2022)
- [Equivariant Filters for Efficient Tracking in 3D Imaging](https://mlsanity.com/paper/2103.10255/) (2021)
- [Geo-SIC: Learning Deformable Geometric Shapes in Deep Image Classifiers](https://mlsanity.com/paper/2210.13704/) (2022)
- [Deep Predictive Motion Tracking in Magnetic Resonance Imaging: Application to Fetal Imaging](https://mlsanity.com/paper/1909.11625/) (2019)
- [MetaMorph: Learning Metamorphic Image Transformation With Appearance Changes](https://mlsanity.com/paper/2303.04849/) (2023)
- [Deep Learning Framework for Real-time Fetal Brain Segmentation in MRI](https://mlsanity.com/paper/2205.01675/) (2022)
- [Temporal Registration in In-Utero Volumetric MRI Time Series](https://mlsanity.com/paper/1608.03907/) (2016)
- [Spatio-temporal motion correction and iterative reconstruction of in-utero fetal fMRI](https://mlsanity.com/paper/2209.08272/) (2022)

## Built on by (most cited first, 2 of 2)

- [A Unified Deep Learning Framework for Motion Correction in Medical Imaging](https://mlsanity.com/paper/2409.14204/) (2024)
- [Equivariant symmetry-aware head pose estimation for fetal MRI](https://mlsanity.com/paper/2512.04890/) (2025)

## Abstract (arXiv)

In this paper, we introduce SpaER, a pioneering method for fetal motion tracking that leverages equivariant filters and self-attention mechanisms to effectively learn spatio-temporal representations. Different from conventional approaches that statically estimate fetal brain motions from pairs of images, our method dynamically tracks the rigid movement patterns of the fetal head across temporal and spatial dimensions. Specifically, we first develop an equivariant neural network that efficiently learns rigid motion sequences through low-dimensional spatial representations of images. Subsequently, we learn spatio-temporal representations by incorporating time encoding and self-attention neural network layers. This approach allows for the capture of long-term dependencies of fetal brain motion and addresses alignment errors due to contrast changes and severe motion artifacts. Our model also provides a geometric deformation estimation that properly addresses image distortions among all time frames. To the best of our knowledge, our approach is the first to learn spatial-temporal representations via deep neural networks for fetal motion tracking without data augmentation. We validated our model using real fetal echo-planar images with simulated and real motions. Our method carries significant potential value in accurately measuring, tracking, and correcting fetal motion in fetal MRI sequences.