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Dynamic Snake Convolution based on Topological Geometric Constraints for Tubular Structure Segmentation
Yaolei Qi, Yuting He, Xiaoming Qi, Yuan Zhang, Guanyu Yang
TL;DR
Tubular-structure segmentation is important but challenged by thin local structures and variable global morphology. DSCNet addresses these issues with morphology-aware convolution, multi-view fusion, and Persistent Homology-based continuity constraints, and is reported to improve accuracy and continuity across 2D and 3D datasets. The authors identify broader applicability to other morphological targets as an open question.
Problem
Tubular-structure segmentation matters for downstream tasks but is difficult because structures are thin, tortuous, fragile, and globally variable.
Method
DSCNet enhances tubular-structure perception through Dynamic Snake Convolution, multi-view feature fusion, and a Persistent Homology-based topological continuity loss.
Results
DSCNet provides better accuracy and continuity than several methods on tubular-structure segmentation across 2D and 3D datasets.
Takeaways & Limitations
The framework integrates morphological features with topological knowledge to guide tubular-structure segmentation and constrain its continuity.
Takeaways & Limitations
Whether the same paradigm improves segmentation of other morphological targets remains an open research question requiring further experimental and theoretical validation.
Abstract
from arXiv · showhide
Accurate segmentation of topological tubular structures, such as blood vessels and roads, is crucial in various fields, ensuring accuracy and efficiency in downstream tasks. However, many factors complicate the task, including thin local structures and variable global morphologies. In this work, we note the specificity of tubular structures and use this knowledge to guide our DSCNet to simultaneously enhance perception in three stages: feature extraction, feature fusion, and loss constraint. First, we propose a dynamic snake convolution to accurately capture the features of tubular structures by adaptively focusing on slender and tortuous local structures. Subsequently, we propose a multi-view feature fusion strategy to complement the attention to features from multiple perspectives during feature fusion, ensuring the retention of important information from different global morphologies. Finally, a continuity constraint loss function, based on persistent homology, is proposed to constrain the topological continuity of the segmentation better. Experiments on 2D and 3D datasets show that our DSCNet provides better accuracy and continuity on the tubular structure segmentation task compared with several methods. Our codes will be publicly available.
1. Introduction
Tubular-structure segmentation is important for downstream clinical and remote-sensing tasks but is hindered by thin, fragile local structures and complex, variable morphology. DSCNet addresses these obstacles through morphology-aware convolution, multi-view fusion, and topological continuity constraints.
- Accurate tubular-structure segmentation supports computational hemodynamics, lesion localization and diagnosis, and route planning.
- Thin structures occupy few pixels, are vulnerable to complex backgrounds, and can produce fractured segmentations.
- Existing approaches use domain knowledge such as geometric topology and tree structure to improve local accuracy and global continuity.
- DSConv adaptively focuses on thin, curved local features while constraining geometric learning according to tubular snake-like morphology.
- DSCNet combines multi-view feature fusion with a Persistent Homology-based topological continuity loss to retain morphology information and reduce segmentation fractures.
- The framework is reported to achieve accurate tubular-structure segmentation on both 2D and 3D datasets, using internal and external test data.
2. Related Work
Related work addresses tubular structures through convolutional kernels, network architectures, feature fusion, and loss functions. DSCNet instead integrates tubular morphology knowledge to stabilize feature extraction and combines geometric and topological constraints.
- Dilated and deformable convolutions address CNNs’ limited geometric transformation, with DUNet adapting receptive fields to vessel scales and shapes.
- Network-design methods model tubular geometry and topology using point sets or tree-structured recurrent units.
- DSCNet integrates tubular morphology knowledge to stabilize feature extraction rather than allowing geometric changes to be learned completely freely.
- Feature-fusion methods supplement tubular representations with additional information, including cross-network multi-scale and deep-shallow hierarchical fusion.
- Loss-based methods add segmentation constraints through centerline Dice, distance transforms, morphological closing, or topological data analysis.
3. Methodology
DSCNet combines dynamic snake convolution, multi-view feature fusion, and a persistent-homology-based continuity loss to model tubular structures from local geometry through topology.
- Dynamic Snake Convolution: DSConv adaptively deforms convolutional sampling to focus on slender, tortuous tubular features while constraining attention continuity.Iterative offsets depend on preceding grid positions, limiting perceptual drift; the deformed kernel covers a 9 × 9 range.
- Dynamic Snake Convolution: The DSConv coordinate construction straightens kernels along the x- and y-axes using cumulative offsets, producing a linear morphological structure.The method applies the same design in both spatial directions and uses bilinear interpolation for fractional sampling locations.
- Multi-view Feature Fusion Strategy: Multi-view fusion extracts x-axis and y-axis feature maps, forms multiple DSConv-based morphological templates, and combines them to observe targets from different perspectives.Weights are computed through a cumulative approach, while random dropping reduces redundant noise and helps prevent overfitting without additional computational burden.
- Topological Continuity Constraint Loss: TCLoss uses persistent homology to represent topological features as persistence diagrams and compare prediction with ground truth using bidirectional Hausdorff distance.Unlike modified Wasserstein matching, the Hausdorff formulation retains sensitivity to unmatched outlier points associated with anomalous topological relations.
- Topological Continuity Constraint Loss: The final loss combines cross entropy with the persistent-homology loss, jointly constraining topology and accuracy to support continuous tubular segmentation.The continuity constraint targets fractures associated with abnormally low pixel or voxel distributions.
4. Experiments Configurations
The framework is evaluated on 2D retinal-vessel and road datasets and a 3D cardiac CCTA dataset using comparative and ablation experiments. Performance is assessed through volumetric, topology, and distance-based measures.
- Three datasets are used: DRIVE and Massachusetts Roads in 2D, plus Cardiac CCTA Data in 3D.
- Comparisons include U-Net, CS2-Net, DCU-net, and Transunet to assess accuracy, network design, and feature-fusion performance.
- Volumetric evaluation uses Dice, RDice, clDice, ACC, and AUC.
- Topology evaluation includes Betti Errors for β0 and β1 and overlap until first error to measure coronary-centerline completeness.
- Hausdorff Distance measures point-set similarity and is used to evaluate thin tubular structures.
5. Results and Discussion
Experiments on 2D and 3D tubular-structure datasets show that DSCNet achieves strong segmentation accuracy and topological continuity, while TCLoss improves continuity across models. Ablations and visualizations attribute these gains to DSConv’s tubular focus and TCLoss’s continuity constraint, although broader morphology generalization remains open.
- Quantitative evaluation: DSCNet achieves better results on both 2D and 3D datasets across the evaluated metrics.The experiments assess volumetric accuracy, topological connectivity, and distance error.
- Quantitative evaluation: On DRIVE, DSCNet reaches Dice of 82.06%, clDice of 82.07%, and β1 error of 0.803 while achieving the best reported segmentation and topology results.It also reports RDice of 90.17%, ACC of 96.87%, AUC of 90.27%, and β0 error of 0.998.
- Quantitative evaluation: On Massachusetts Roads, DSCNet with TCLoss achieves Dice of 78.21%, RDice of 85.85%, and clDice of 87.64%, with improvements over UNet.The reported maximum improvements are 1.31% Dice, 1.78% RDice, and 0.77% clDice.
- Quantitative evaluation: On Cardiac CCTA, DSCNet achieves Dice of 80.27%, RDice of 86.37%, and clDice of 85.26%, while OF improves by 6.00% for LAD, 3.78% for LCX, and 3.30% for RCA.The authors report these results as evidence of improved 3D segmentation and vessel continuity.
- Ablation and qualitative analysis: Ablations show that DSConv improves thin-tubular feature capture, whereas adding TCLoss improves topological continuity across different models.Visualizations further report better continuity in hard-to-segment regions and attention concentrated on tubular structures.
- Limitations and future work: The authors identify whether similar performance extends to other morphological targets as an open topic for future research.They also call for further experimental and theoretical validation.
6. Conclusion
The conclusion presents DSCNet as a tubular-structure segmentation framework that enhances perception through dynamic convolution, multi-view fusion, and topological continuity loss. Evaluations on 2D and 3D datasets report better accuracy and continuity than several methods.
- Conclusion: DSCNet combines dynamic snake convolution, multi-view feature fusion, and topological continuity loss across feature extraction, fusion, and loss constraint.The components target thin tortuous structures, varied global morphology, and segmentation continuity, respectively.
- Conclusion: Experiments on 2D and 3D datasets show better accuracy and continuity for tubular-structure segmentation than several methods.The conclusion states this as the overall verified outcome of the framework.