# MARVEL: Universal Murray's Law-informed Vessel Tree Segmentation and Topology Estimation

arXiv: https://arxiv.org/abs/2605.25363 · HTML: https://mlsanity.com/paper/2605.25363/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 67 references that are in the map.
- First posted on arXiv 25 May 2026.

## Builds on (most cited first, 20 of 20)

- [SegFormer: Simple and Efficient Design for Semantic Segmentation with Transformers](https://mlsanity.com/paper/2105.15203/) (2021)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [Deep learning for cardiac image segmentation: A review](https://mlsanity.com/paper/1911.03723/) (2019)
- [Beyond the Pixel-Wise Loss for Topology-Aware Delineation](https://mlsanity.com/paper/1712.02190/) (2017)
- [ImageCAS: A Large-Scale Dataset and Benchmark for Coronary Artery Segmentation based on Computed Tomography Angiography Images](https://mlsanity.com/paper/2211.01607/) (2022)
- [CS2-Net: Deep Learning Segmentation of Curvilinear Structures in Medical Imaging](https://mlsanity.com/paper/2010.07486/) (2020)
- [Topologically faithful image segmentation via induced matching of persistence barcodes](https://mlsanity.com/paper/2211.15272/) (2022)
- [Skeleton Recall Loss for Connectivity Conserving and Resource Efficient Segmentation of Thin Tubular Structures](https://mlsanity.com/paper/2404.03010/) (2024)
- [Topology-Aware Uncertainty for Image Segmentation](https://mlsanity.com/paper/2306.05671/) (2023)
- [Towards a glaucoma risk index based on simulated hemodynamics from fundus images](https://mlsanity.com/paper/1805.10273/) (2018)
- [Centerline Boundary Dice Loss for Vascular Segmentation](https://mlsanity.com/paper/2407.01517/) (2024)
- [Segmentation and Vascular Vectorization for Coronary Artery by Geometry-based Cascaded Neural Network](https://mlsanity.com/paper/2305.04208/) (2023)
- [Physics-informed neural networks for myocardial perfusion MRI quantification](https://mlsanity.com/paper/2011.12844/) (2020)
- [Adversarial Deformation Regularization for Training Image Registration Neural Networks](https://mlsanity.com/paper/1805.10665/) (2018)
- [GLCP: Global-to-Local Connectivity Preservation for Tubular Structure Segmentation](https://mlsanity.com/paper/2507.21328/) (2025)
- [RRWNet: Recursive Refinement Network for effective retinal artery/vein segmentation and classification](https://mlsanity.com/paper/2402.03166/) (2024)
- [A Recursive Bayesian Approach To Describe Retinal Vasculature Geometry](https://mlsanity.com/paper/1711.10521/) (2017)

## Abstract (arXiv)

Vascular circulation follows fundamental biophysical principles that optimize mass transport and metabolic energy expenditure, which can be effectively modeled by Murray's law. However, contemporary deep learning methods for vascular segmentation often neglect these biophysical constraints. This leads to physiologically implausible branching and misclassification vascular trees, rendering. These automated segmentation results are unreliable unreliable for downstream clinical tasks such as blood flow simulation or disease quantification. In this paper, we introduce MARVEL (Universal MurrAy's law-infoRmed Vessel sEgmentation and topoLogy estimation), a backbone-agnostic framework that integrates biophysical priors into vascular tree extraction. MARVEL combines per-pixel supervision with explicit radius predictions to enforce local bifurcation constraints derived from an empirical width-exponent mapping. We implement these constraints as differentiable regularizers during training to guide models toward physiologically consistent reconstructions. We evaluate MARVEL on eight public datasets across multiple vascular modalities and segmentation backbones. Results demonstrate MARVEL's superior performance in segmentation accuracy, topological consistency, and physiological plausibility. By converting segmented masks into graph-based hemodynamic simulations, we demonstrate that MARVEL preserves the subtle pathological narrowing and topological connectivity required to distinguish hypertensive from normotensive eyes. Results show that MARVEL significantly improves the classification of hypertension via arteriovenous pressure differences in the eye (p < 0.001), outperforming baseline models in both topological consistency and clinical predictive value.