TopoVST: Toward Topology-fidelitous Vessel Skeleton Tracking

Abstract

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 (9)

• Figure 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 $\beta_0$-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 $\beta_1$-error-prone due to the aggregation of redundant skeleton branches during tracking.
• Figure 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 $G_{pred}$ and graph-level radius prediction $R_{pred}$. (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.
• Figure 3: Correspondence between unit directions and graph nodes in two similar sphere graphs at different scales, $S_1$ and $S_2$. Four unit directions, $\mathbf{d_1}, \mathbf{d_2}, \mathbf{d_3}, \mathbf{d_4}$ are plotted with orange arrows. Four nodes, $V_1, V_2, V_3, V_4$ represent four points on the sphere mesh. Correspondence between each unit direction $\mathbf{d_i}$ and node $V_i$ can be found consistently in both scales, as denoted by orange dotted lines. Thus, direction modeling by the sphere graph is scale-invariant.
• Figure 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 $G_1,G_2,\dots,G_n$ at scales $S_1, S_2, \dots, S_n$ are constructed. Each graph covers a different spherical region around the sampling point. For a node $V_i$ on graph $G_{m}$, we draw a line from the sampling position to $V_i$ and sample image intensities at $C=64$ points along the line. These intensities are concatenated into a feature vector in $\mathbb{R}^{C}$, denoted by $f_m^{0}(V_i)$. (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 $G_{target}$ is acquired and can be used to compute the direction loss. Based on $G_{target}$, geometry-aware loss weights $w_{geo}$ can be computed from haversine distance. The loss weight $w$ can be obtained by combining $w_{geo}$ and the minority class weight $w_p$.
• Figure 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.