Geometric-topological deep transfer learning for precise vessel segmentation in 3D medical volumes.

Precise delineation and parametric modeling of curvilinear vascular architectures in volumetric medical imaging are pivotal for advancing clinical diagnostics and therapeutic planning. Prevailing methodologies predominantly adopt discrete voxel-wise representations, such as binary masks, which are prone to topological disruptions and artifact-induced fragmentation arising from inherent per-voxel classification biases. To address these challenges, we present FlowAxis, a pioneering continuous parameterization paradigm leveraging Adaptive Vessel Axes (AVA), wherein adaptive keypoints function as interconnected vertices to encapsulate intrinsic spatial topologies. FlowAxis distinguishes itself through superior topological coherence guaranteed by displacement convexity of the energy functional. Comprehensive empirical validations across four benchmark datasets for three-dimensional vascular segmentation substantiate FlowAxis's performance, achieving significant improvements in both topological accuracy (clDice) and geometric fidelity (Hausdorff distance). Furthermore, qualitative assessments via curved planar reformations highlight its transformative potential in clinical workflows, while theoretical guarantees ensure reliability in safety-critical medical applications. Our work bridges the gap between mathematical rigor and practical medical imaging, providing the first complete theoretical framework for continuous vessel representation with provable optimality and convergence guarantees.