# Global Control for Local SO(3)-Equivariant Scale-Invariant Vessel Segmentation

arXiv: https://arxiv.org/abs/2403.15314 · HTML: https://mlsanity.com/paper/2403.15314/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 26 references that are in the map.
- First posted on arXiv 22 Mar 2024.

## Builds on (most cited first, 10 of 10)

- [TotalSegmentator: robust segmentation of 104 anatomical structures in CT images](https://mlsanity.com/paper/2208.05868/) (2022)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [Deep learning for cardiac image segmentation: A review](https://mlsanity.com/paper/1911.03723/) (2019)
- [Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs](https://mlsanity.com/paper/2003.05425/) (2020)
- [Numerical Coordinate Regression with Convolutional Neural Networks](https://mlsanity.com/paper/1801.07372/) (2018)
- [Graph Convolutional Networks for Coronary Artery Segmentation in Cardiac CT Angiography](https://mlsanity.com/paper/1908.05343/) (2019)
- [Coronary Artery Centerline Extraction in Cardiac CT Angiography Using a CNN-Based Orientation Classifier](https://mlsanity.com/paper/1810.03143/) (2018)
- [Going Off-Grid: Continuous Implicit Neural Representations for 3D Vascular Modeling](https://mlsanity.com/paper/2207.14663/) (2022)
- [Deep Learning-Based Carotid Artery Vessel Wall Segmentation in Black-Blood MRI Using Anatomical Priors](https://mlsanity.com/paper/2112.01137/) (2021)
- [SIRE: scale-invariant, rotation-equivariant estimation of artery orientations using graph neural networks](https://mlsanity.com/paper/2311.05400/) (2023)

## Built on by (most cited first, 1 of 1)

- [Wall Shear Stress Estimation in Abdominal Aortic Aneurysms: Towards Generalisable Neural Surrogate Models](https://mlsanity.com/paper/2507.22817/) (2025)

## Abstract (arXiv)

Personalized 3D vascular models can aid in a range of diagnostic, prognostic, and treatment-planning tasks relevant to cardiovascular disease management. Deep learning provides a means to obtain such models automatically from image data. Ideally, a user should have control over the included region in the vascular model. Additionally, the model should be watertight and highly accurate. To this end, we propose a combination of a global controller leveraging voxel mask segmentations to provide boundary conditions for vessels of interest to a local, iterative vessel segmentation model. We introduce the preservation of scale- and rotational symmetries in the local segmentation model, leading to generalisation to vessels of unseen sizes and orientations. Combined with the global controller, this enables flexible 3D vascular model building, without additional retraining. We demonstrate the potential of our method on a dataset containing abdominal aortic aneurysms (AAAs). Our method performs on par with a state-of-the-art segmentation model in the segmentation of AAAs, iliac arteries, and renal arteries, while providing a watertight, smooth surface representation. Moreover, we demonstrate that by adapting the global controller, we can easily extend vessel sections in the 3D model.