# Parametric shape models for vessels learned from segmentations via differentiable voxelization

arXiv: https://arxiv.org/abs/2507.02576 · HTML: https://mlsanity.com/paper/2507.02576/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 3 Jul 2025.

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

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [SlowFast Networks for Video Recognition](https://mlsanity.com/paper/1812.03982/) (2018)
- [nnU-Net Revisited: A Call for Rigorous Validation in 3D Medical Image Segmentation](https://mlsanity.com/paper/2404.09556/) (2024)
- [The Road Less Scheduled](https://mlsanity.com/paper/2405.15682/) (2024)
- [The TopCoW Challenge -- Topology-Aware Circle of Willis Segmentation for CT and MR Angiography](https://mlsanity.com/paper/2312.17670/) (2023)
- [Scalable Robust Graph and Feature Extraction for Arbitrary Vessel Networks in Large Volumetric Datasets](https://mlsanity.com/paper/2102.03444/) (2021)
- [A skeletonization algorithm for gradient-based optimization](https://mlsanity.com/paper/2309.02527/) (2023)
- [DeepMesh: Mesh-based Cardiac Motion Tracking using Deep Learning](https://mlsanity.com/paper/2309.14306/) (2023)
- [Multi-Class Segmentation of Aortic Branches and Zones in Computed Tomography Angiography: The AortaSeg24 Challenge](https://mlsanity.com/paper/2502.05330/) (2025)
- [Implicit Neural Representations for Modeling of Abdominal Aortic Aneurysm Progression](https://mlsanity.com/paper/2303.01069/) (2023)

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

- [rNCA: Self-Repairing Segmentation Masks](https://mlsanity.com/paper/2512.13397/) (2025)

## Abstract (arXiv)

Vessels are complex structures in the body that have been studied extensively in multiple representations. While voxelization is the most common of them, meshes and parametric models are critical in various applications due to their desirable properties. However, these representations are typically extracted through segmentations and used disjointly from each other. We propose a framework that joins the three representations under differentiable transformations. By leveraging differentiable voxelization, we automatically extract a parametric shape model of the vessels through shape-to-segmentation fitting, where we learn shape parameters from segmentations without the explicit need for ground-truth shape parameters. The vessel is parametrized as centerlines and radii using cubic B-splines, ensuring smoothness and continuity by construction. Meshes are differentiably extracted from the learned shape parameters, resulting in high-fidelity meshes that can be manipulated post-fit. Our method can accurately capture the geometry of complex vessels, as demonstrated by the volumetric fits in experiments on aortas, aneurysms, and brain vessels.