# Anatomically Conditioned Recurrent Refinement for Topology-Aware Circle of Willis Segmentation

arXiv: https://arxiv.org/abs/2606.12319 · HTML: https://mlsanity.com/paper/2606.12319/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 20 references that are in the map.
- First posted on arXiv 10 Jun 2026.

## Builds on (most cited first, 12 of 12)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Swin-Unet: Unet-like Pure Transformer for Medical Image Segmentation](https://mlsanity.com/paper/2105.05537/) (2021)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)
- [nnU-Net Revisited: A Call for Rigorous Validation in 3D Medical Image Segmentation](https://mlsanity.com/paper/2404.09556/) (2024)
- [Tversky loss function for image segmentation using 3D fully convolutional deep networks](https://mlsanity.com/paper/1706.05721/) (2017)
- [Recurrent Residual Convolutional Neural Network based on U-Net (R2U-Net) for Medical Image Segmentation](https://mlsanity.com/paper/1802.06955/) (2018)
- [MedSegDiff: Medical Image Segmentation with Diffusion Probabilistic Model](https://mlsanity.com/paper/2211.00611/) (2022)
- [MedSegDiff-V2: Diffusion based Medical Image Segmentation with Transformer](https://mlsanity.com/paper/2301.11798/) (2023)
- [The TopCoW Challenge -- Topology-Aware Circle of Willis Segmentation for CT and MR Angiography](https://mlsanity.com/paper/2312.17670/) (2023)
- [Skeleton Recall Loss for Connectivity Conserving and Resource Efficient Segmentation of Thin Tubular Structures](https://mlsanity.com/paper/2404.03010/) (2024)
- [Automated Intracranial Artery Labeling using a Graph Neural Network and Hierarchical Refinement](https://mlsanity.com/paper/2007.14472/) (2020)
- [Does the Skeleton-Recall Loss Really Work?](https://mlsanity.com/paper/2508.11374/) (2025)

## Abstract (arXiv)

Segmenting the Circle of Willis (CoW) from Magnetic Resonance Angiography (MRA) is challenging due to complex topology and thin vascular structures that are prone to fragmentation. Standard Convolutional Neural Networks (CNNs) often fail to capture these topological constraints, resulting in "broken vessel" artifacts. To address this, we propose the Anatomically Conditioned Recurrent Refinement U-Net (AC2RUNet). Our architecture decouples segmentation into two streams: a Static Stream that extracts invariant anatomical features and a lightweight Dynamic Stream that iteratively refines topological errors over time. We further introduce a dynamic curriculum learning strategy that transitions from high-recall geometric supervision to topology-aware constraints. Validated on the TopCoW dataset, AC2RUNet substantially reduces Hausdorff Distance (4.72 mm vs 9.17 mm) and Betti number errors (0.19 vs 0.40), improving topological connectivity over the nnU-Net baseline while maintaining comparable volumetric Dice.