SE(3)-Equivariant and Noise-Invariant 3D Motion Tracking in Medical Images

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 github.com/BBillot/equitrack.

Intraoperative 2D/3D Image Registration via Differentiable X-ray Rendering

Surgical decisions are informed by aligning rapid portable 2D intraoperative images (e.g., X-rays) to a high-fidelity 3D preoperative reference scan (e.g., CT). 2D/3D image registration often fails in practice: conventional optimization methods are prohibitively slow and susceptible to local minima, while neural networks trained on small datasets fail on new patients or require impractical landmark supervision. We present DiffPose, a self-supervised approach that leverages patient-specific simulation and differentiable physics-based rendering to achieve accurate 2D/3D registration without relying on manually labeled data. Preoperatively, a CNN is trained to regress the pose of a randomly oriented synthetic X-ray rendered from the preoperative CT. The CNN then initializes rapid intraoperative test-time optimization that uses the differentiable X-ray renderer to refine the solution. Our work further proposes several geometrically principled methods for sampling camera poses from $\mathbf{SE}(3)$, for sparse differentiable rendering, and for driving registration in the tangent space $\mathfrak{se}(3)$ with geodesic and multiscale locality-sensitive losses. DiffPose achieves sub-millimeter accuracy across surgical datasets at intraoperative speeds, improving upon existing unsupervised methods by an order of magnitude and even outperforming supervised baselines. Our code is available at https://github.com/eigenvivek/DiffPose.

Shape-aware Segmentation of the Placenta in BOLD Fetal MRI Time Series

Blood oxygen level dependent (BOLD) MRI time series with maternal hyperoxia can assess placental oxygenation and function. Measuring precise BOLD changes in the placenta requires accurate temporal placental segmentation and is confounded by fetal and maternal motion, contractions, and hyperoxia-induced intensity changes. Current BOLD placenta segmentation methods warp a manually annotated subject-specific template to the entire time series. However, as the placenta is a thin, elongated, and highly non-rigid organ subject to large deformations and obfuscated edges, existing work cannot accurately segment the placental shape, especially near boundaries. In this work, we propose a machine learning segmentation framework for placental BOLD MRI and apply it to segmenting each volume in a time series. We use a placental-boundary weighted loss formulation and perform a comprehensive evaluation across several popular segmentation objectives. Our model is trained and tested on a cohort of 91 subjects containing healthy fetuses, fetuses with fetal growth restriction, and mothers with high BMI. Biomedically, our model performs reliably in segmenting volumes in both normoxic and hyperoxic points in the BOLD time series. We further find that boundary-weighting increases placental segmentation performance by 8.3% and 6.0% Dice coefficient for the cross-entropy and signed distance transform objectives, respectively. Our code and trained model is available at https://github.com/mabulnaga/automatic-placenta-segmentation.

Dynamic Neural Fields for Learning Atlases of 4D Fetal MRI Time-series

We present a method for fast biomedical image atlas construction using neural fields. Atlases are key to biomedical image analysis tasks, yet conventional and deep network estimation methods remain time-intensive. In this preliminary work, we frame subject-specific atlas building as learning a neural field of deformable spatiotemporal observations. We apply our method to learning subject-specific atlases and motion stabilization of dynamic BOLD MRI time-series of fetuses in utero. Our method yields high-quality atlases of fetal BOLD time-series with $\sim$5-7$\times$ faster convergence compared to existing work. While our method slightly underperforms well-tuned baselines in terms of anatomical overlap, it estimates templates significantly faster, thus enabling rapid processing and stabilization of large databases of 4D dynamic MRI acquisitions. Code is available at https://github.com/Kidrauh/neural-atlasing

Consistency Regularization Improves Placenta Segmentation in Fetal EPI MRI Time Series

The placenta plays a crucial role in fetal development. Automated 3D placenta segmentation from fetal EPI MRI holds promise for advancing prenatal care. This paper proposes an effective semi-supervised learning method for improving placenta segmentation in fetal EPI MRI time series. We employ consistency regularization loss that promotes consistency under spatial transformation of the same image and temporal consistency across nearby images in a time series. The experimental results show that the method improves the overall segmentation accuracy and provides better performance for outliers and hard samples. The evaluation also indicates that our method improves the temporal coherency of the prediction, which could lead to more accurate computation of temporal placental biomarkers. This work contributes to the study of the placenta and prenatal clinical decision-making. Code is available at https://github.com/firstmover/cr-seg.

Boundary-weighted logit consistency improves calibration of segmentation networks

Neural network prediction probabilities and accuracy are often only weakly-correlated. Inherent label ambiguity in training data for image segmentation aggravates such miscalibration. We show that logit consistency across stochastic transformations acts as a spatially varying regularizer that prevents overconfident predictions at pixels with ambiguous labels. Our boundary-weighted extension of this regularizer provides state-of-the-art calibration for prostate and heart MRI segmentation.

AnyStar: Domain randomized universal star-convex 3D instance segmentation

Star-convex shapes arise across bio-microscopy and radiology in the form of nuclei, nodules, metastases, and other units. Existing instance segmentation networks for such structures train on densely labeled instances for each dataset, which requires substantial and often impractical manual annotation effort. Further, significant reengineering or finetuning is needed when presented with new datasets and imaging modalities due to changes in contrast, shape, orientation, resolution, and density. We present AnyStar, a domain-randomized generative model that simulates synthetic training data of blob-like objects with randomized appearance, environments, and imaging physics to train general-purpose star-convex instance segmentation networks. As a result, networks trained using our generative model do not require annotated images from unseen datasets. A single network trained on our synthesized data accurately 3D segments C. elegans and P. dumerilii nuclei in fluorescence microscopy, mouse cortical nuclei in micro-CT, zebrafish brain nuclei in EM, and placental cotyledons in human fetal MRI, all without any retraining, finetuning, transfer learning, or domain adaptation. Code is available at https://github.com/neel-dey/AnyStar.

$E(3) \times SO(3)$-Equivariant Networks for Spherical Deconvolution in Diffusion MRI

We present Roto-Translation Equivariant Spherical Deconvolution (RT-ESD), an $E(3)\times SO(3)$ equivariant framework for sparse deconvolution of volumes where each voxel contains a spherical signal. Such 6D data naturally arises in diffusion MRI (dMRI), a medical imaging modality widely used to measure microstructure and structural connectivity. As each dMRI voxel is typically a mixture of various overlapping structures, there is a need for blind deconvolution to recover crossing anatomical structures such as white matter tracts. Existing dMRI work takes either an iterative or deep learning approach to sparse spherical deconvolution, yet it typically does not account for relationships between neighboring measurements. This work constructs equivariant deep learning layers which respect to symmetries of spatial rotations, reflections, and translations, alongside the symmetries of voxelwise spherical rotations. As a result, RT-ESD improves on previous work across several tasks including fiber recovery on the DiSCo dataset, deconvolution-derived partial volume estimation on real-world \textit{in vivo} human brain dMRI, and improved downstream reconstruction of fiber tractograms on the Tractometer dataset. Our implementation is available at https://github.com/AxelElaldi/e3so3_conv

Dual-Domain Self-Supervised Learning for Accelerated Non-Cartesian MRI Reconstruction

While enabling accelerated acquisition and improved reconstruction accuracy, current deep MRI reconstruction networks are typically supervised, require fully sampled data, and are limited to Cartesian sampling patterns. These factors limit their practical adoption as fully-sampled MRI is prohibitively time-consuming to acquire clinically. Further, non-Cartesian sampling patterns are particularly desirable as they are more amenable to acceleration and show improved motion robustness. To this end, we present a fully self-supervised approach for accelerated non-Cartesian MRI reconstruction which leverages self-supervision in both k-space and image domains. In training, the undersampled data are split into disjoint k-space domain partitions. For the k-space self-supervision, we train a network to reconstruct the input undersampled data from both the disjoint partitions and from itself. For the image-level self-supervision, we enforce appearance consistency obtained from the original undersampled data and the two partitions. Experimental results on our simulated multi-coil non-Cartesian MRI dataset demonstrate that DDSS can generate high-quality reconstruction that approaches the accuracy of the fully supervised reconstruction, outperforming previous baseline methods. Finally, DDSS is shown to scale to highly challenging real-world clinical MRI reconstruction acquired on a portable low-field (0.064 T) MRI scanner with no data available for supervised training while demonstrating improved image quality as compared to traditional reconstruction, as determined by a radiologist study.