Parametric shape models for vessels learned from segmentations via differentiable voxelization

2025-07-03

AI Summary

This work addresses the challenge of automatically converting vascular segmentation results into editable parametric models. We propose the first end-to-end differentiable vascular shape modeling framework. Methodologically, it jointly parameterizes the centerline and radius using cubic B-splines and introduces a differentiable voxelization layer to enable unsupervised mapping from segmentation masks to parametric models, unifying voxel, mesh, and parametric representations. The framework directly generates high-fidelity, smooth, and backpropagation-enabled meshes from segmentation inputs. Its key innovation lies in eliminating reliance on ground-truth parametric annotations—enabling shape-level gradient backpropagation and post-hoc geometric editing. Evaluated on aortic, aneurysmal, and cerebral vascular datasets, our method significantly reduces volumetric segmentation matching error and achieves state-of-the-art performance in geometric reconstruction accuracy and mesh quality.

Technology Category

• Computer Vision: Segmentation
• Machine Learning: Calibration & Uncertainty Quantification
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

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.

Problem

• Develop parametric vessel models from segmentations via differentiable voxelization
• Unify voxel, mesh, and parametric representations under differentiable transformations
• Learn shape parameters from segmentations without ground-truth shape data

Innovation

• Differentiable voxelization for parametric shape models
• Shape-to-segmentation fitting without ground-truth parameters
• Differentiable mesh extraction from learned shape parameters