Parametric shape models for vessels learned from segmentations via differentiable voxelization

TL;DR

This paper introduces a differentiable framework that jointly models vessels using voxel, mesh, and parametric representations, enabling automatic shape extraction from segmentations without explicit shape labels.

Contribution

It presents a novel differentiable voxelization-based method to learn parametric vessel models directly from segmentations, unifying multiple representations.

Findings

Accurately captures complex vessel geometries.

Produces high-fidelity meshes from learned parameters.

Demonstrates effectiveness on aortas, aneurysms, and brain vessels.

Abstract

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.