Advanced Geometric-Topological Transfer Learning for 3D Vessel Segmentation

Overview

This study introduces FlowAxis, a novel vessel segmentation framework that models vascular structures as continuous manifolds embedded in three-dimensional space. By leveraging optimal transport theory and advanced geometric-topological principles, the method enables robust transfer learning across imaging domains, overcoming limitations of traditional voxel-wise approaches.

Background

Accurate delineation and three-dimensional reconstruction of vascular networks are critical for diagnosing and treating pathological conditions affecting neural and myocardial vasculature. Conventional segmentation methods rely on discrete voxel-based representations, which struggle to capture the continuous geometric and topological properties of vessels, leading to fragmented and inconsistent predictions. These challenges are exacerbated in transfer learning scenarios where imaging protocols and patient demographics vary, necessitating a mathematically rigorous framework that preserves vascular geometry during domain adaptation.

Data Highlights

The FlowAxis framework models vessels as medial axes within Fréchet manifolds of smooth curves, enabling continuous representation of vascular geometry. The segmentation problem is formulated as an optimal transport task between probability measures on these manifolds, incorporating geometric distances and information-theoretic divergences. Iterative refinement uses Wasserstein gradient flows with entropic regularization and geometric penalties, ensuring global convergence despite non-convex optimization landscapes. Mutual information exchange via parallel transport operators and McKean-Vlasov dynamics facilitates consistent feature aggregation across vascular trajectories.

Key Findings

• Traditional voxel-wise segmentation methods fail to maintain topological consistency and are sensitive to local perturbations, resulting in fragmented vessel delineations.
• FlowAxis represents vessels as continuous medial axes embedded in infinite-dimensional function spaces, capturing smooth geometric and topological features.
• Optimal transport theory enables principled domain adaptation by minimizing Wasserstein distances between source and target vascular distributions.
• The framework integrates spectral methods, parallel transport, and McKean-Vlasov dynamics to ensure smooth interpolation and consistent feature propagation along vessels.
• Iterative refinement via Wasserstein gradient flows with entropic and geometric regularization guarantees global convergence and robustness across imaging modalities.

Clinical Implications

The FlowAxis approach provides clinicians with more accurate and topologically consistent vessel segmentations, enhancing the evaluation of complex vascular anatomies in computed tomographic angiography. Its robust transfer learning capabilities facilitate reliable application across diverse imaging protocols and patient populations, potentially improving diagnostic precision and therapeutic planning in neurovascular and myocardial pathologies.

Conclusion

By re-conceptualizing vessel segmentation as an optimal transport problem on continuous manifolds, FlowAxis overcomes fundamental limitations of discrete methods, enabling accurate, topologically consistent, and transferable vascular delineations in three-dimensional medical imaging.

References

1. Roger et al.1 -- Pathological conditions affecting neural vasculature and myocardial systems
2. Leipsic et al.2 -- Three-dimensional reconstruction and evaluation of vascular networks
3. Araujo et al.3, Qi et al.4, Shin et al.5, Shit et al.6, Wang et al.7,8 -- Established voxel-wise vessel segmentation methods
4. Qi et al.4, Shin et al.5, Wang et al.8, Kong et al.9, Zhang et al.10, Zhao et al.11 -- Integration of geometric constraints in neural architectures
5. Araujo et al.3, Shit et al.6, Hu et al.12 -- Connectivity-aware objective functions for vessel segmentation