Organizations: Institute of Medical Robotics, Shanghai Jiao Tong University, Shanghai, China. · School of Automation and Intelligent Sensing, Shanghai Jiao Tong University, Shanghai, China. · Shanghai AI Lab, Shanghai, China.
Automatic extraction of vessel skeletons is crucial for many clinical applications. However, achieving topologically faithful delineation of thin vessel skeletons remains highly challenging, primarily due to frequent discontinuities and the presence of spurious skeleton segments. To address these difficulties, we propose TopoVST, a topology-fidelitious vessel skeleton tracker. TopoVST constructs multi-scale sphere graphs to sample the input image and employs graph neural networks to jointly estimate tracking directions and vessel radii. The utilization of multi-scale representations is enhanced through a gating-based feature fusion mechanism, while the issue of class imbalance during training is mitigated by embedding a geometry-aware weighting scheme into the directional loss. In addition, we design a wave-propagation-based skeleton tracking algorithm that explicitly mitigates the generation of spurious skeletons through space-occupancy filtering. We evaluate TopoVST on two vessel datasets with different geometries. Extensive comparisons with state-of-the-art baselines demonstrate that TopoVST achieves competitive performance in both overlapping and topological metrics. Our source code is available at: https://github.com/EndoluminalSurgicalVision-IMR/TopoVST.
Figures & tables
Fig. 1: On the left, we provide a visual description and results of two vessel skeleton extraction pipelines, highlighting breakage and redundancy in colored boxes. On the right, we provide the results of TopoVST. (a) Segmentation-based skeleton extraction . The CT image is first segmented and then thinned. This method may cause β0 -errors due to false-negative breakage during segmentation. (b) Tracking-based skeleton extraction . A number of seed points are first acquired from the CT image. Then a tracker starts from these seed points and extracts the skeleton. This method is β1 -error-prone due to the aggregation of redundant skeleton branches during tracking.
Fig. 2: Our Framework . (a) Offline Training . At a given position in the image, multi-scale sampling is performed to obtain graphs at different scales. These graphs are processed by a GNN encoder in parallel to extract node representations at different scales, which are passed through a gating module and summed to obtain aggregated node features. The aggregated node features are then used to decode node-level direction prediction Gpred and graph-level radius prediction Rpred . (b) Online Tracking . We apply local maximum operation on the predicted graph to obtain candidate directions. The estimated radius provides both the tracking step size and radial-ball occupation in 3D space. Using the candidate directions and tracking step size, we determine the next-step positions in the vessel. These positions are subsequently filtered by the radial-ball occupations. We adopted a wave-propagation skeleton tree expansion algorithm to extract the final skeleton.
Fig. 3: Correspondence between unit directions and graph nodes in two similar sphere graphs at different scales, S1 and S2 . Four unit directions, d1,d2,d3,d4 are plotted with orange arrows. Four nodes, V1,V2,V3,V4 represent four points on the sphere mesh. Correspondence between each unit direction di and node Vi can be found consistently in both scales, as denoted by orange dotted lines. Thus, direction modeling by the sphere graph is scale-invariant .
Fig. 4: Illustration of multi-scale sampling, direction target formulation and loss weighting . (a) Multi-scale sampling . Given a sampling position inside the vessel, n sphere mesh graphs G1,G2,…,Gn at scales S1,S2,…,Sn are constructed. Each graph covers a different spherical region around the sampling point. For a node Vi on graph Gm , we draw a line from the sampling position to Vi and sample image intensities at C=64 points along the line. These intensities are concatenated into a feature vector in RC , denoted by fm0(Vi) . (b) Direction target formulation and loss weighting . For a given sampling position, we locate the intersections between its radial ball and the reference skeleton. Target directions can be calculated from these intersections and projected onto the predefined spherical graph. Nodes corresponding to the target directions are labeled as positive, and the remaining are labeled as negative. After projection, the target binary graph Gtarget is acquired and can be used to compute the direction loss. Based on Gtarget , geometry-aware loss weights wgeo can be computed from haversine distance. The loss weight w can be obtained by combining wgeo and the minority class weight wp .
Fig. 5: Illustration of Wave-propagation Skeleton Tracking Algorithm . For simplicity, downward tracking is not demonstrated. From left to right, we show the wave-propagation tracking procedure in each iteration. Wave fronts are enclosed in black dotted lines. Radial-ball occupancy is used to remove invalid tracking directions (red dotted arrows) that lead the tracker back to explored regions. The tracked skeleton tree is updated in every iteration.
Fig. 6: Qualitative Evaluation on ASOCA Dataset . The first case demonstrates a thin vessel segment in the coronary arteries. The second case demonstrates a tortuous vessel segment in the coronary arteries. TopoVST successfully extracts skeletons in these vessel segments. ov: Overlap.
Fig. 7: Recall of the Reference Skeleton . Here, we provide the recall of the reference skeleton. For effective comparison, we split the reference skeleton into five groups based on radius distributions and derive the statistics. (a) show the recall on ASOCA, and (b) shows the recall on AortaSeg24. It can be observed that TopoVST achieves the highest recall in most of the groups.
Fig. 8: Qualitative Evaluation on AortaSeg24 Dataset . The first case demonstrates spatially adjacent vessel segments in the aorta. The second case demonstrates calcified vessel segments in the aorta. TopoVST extracts accurate skeletons in these vessel segments without redundancy. ov: Overlap.
Fig. 9: Elongation of Tracked Vessel Skeleton . Here we provide the Curved Planar Reformat(CPR) plot on two different datasets. Vessel regions labeled in GT and extracted by TopoVST are highlighted with red and blue rectangular boxes, respectively. (a) provides a view on ASOCA dataset and (b) provides a view on AortaSeg24 dataset. On these two plots it can be observed that skeleton extracted by our method extends beyond the coverage of GT mask, but still remains within the same part of vessels.