Parametric shape models for vessels learned from segmentations via differentiable voxelization

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.

@article{dima2025_2507.02576,
  title={ Parametric shape models for vessels learned from segmentations via differentiable voxelization },
  author={ Alina F. Dima and Suprosanna Shit and Huaqi Qiu and Robbie Holland and Tamara T. Mueller and Fabio Antonio Musio and Kaiyuan Yang and Bjoern Menze and Rickmer Braren and Marcus Makowski and Daniel Rueckert },
  journal={arXiv preprint arXiv:2507.02576},
  year={ 2025 }
}