In the field of 3D medical imaging, accurately extracting and representing the blood vessels with curvilinear structures holds paramount importance for clinical diagnosis. Previous methods have commonly relied on discrete representation like mask, often resulting in local fractures or scattered fragments due to the inherent limitations of the per-pixel classification paradigm. In this work, we introduce DeformCL, a new continuous representation based on Deformable Centerlines, where centerline points act as nodes connected by edges that capture spatial relationships. Compared with previous representations, DeformCL offers three key advantages: natural connectivity, noise robustness, and interaction facility. We present a comprehensive training pipeline structured in a cascaded manner to fully exploit these favorable properties of DeformCL. Extensive experiments on four 3D vessel segmentation datasets demonstrate the effectiveness and superiority of our method. Furthermore, the visualization of curved planar reformation images validates the clinical significance of the proposed framework. We release the code in https://github.com/barry664/DeformCL.

Accurately restoring topology is both challenging and crucial in tubular structure extraction tasks, such as blood vessel segmentation and road network extraction. Diverging from traditional approaches based on pixel-level classification, our proposed method, named GraphMorph, focuses on branch-level features of tubular structures to achieve more topologically accurate predictions. GraphMorph comprises two main components: a Graph Decoder and a Morph Module. Utilizing multi-scale features extracted from an image patch by the segmentation network, the Graph Decoder facilitates the learning of branch-level features and generates a graph that accurately represents the tubular structure in this patch. The Morph Module processes two primary inputs: the graph and the centerline probability map, provided by the Graph Decoder and the segmentation network, respectively. Employing a novel SkeletonDijkstra algorithm, the Morph Module produces a centerline mask that aligns with the predicted graph. Furthermore, we observe that employing centerline masks predicted by GraphMorph significantly reduces false positives in the segmentation task, which is achieved by a simple yet effective post-processing strategy. The efficacy of our method in the centerline extraction and segmentation tasks has been substantiated through experimental evaluations across various datasets. Source code will be released soon.