skeletonization algorithms

Coronary CT image segmentation faces challenges including distal vessel thinness, complex topology, and low contrast, leading to over- and under-segmentation and hindering fully connected coronary tree reconstruction. To address these issues, we propose the first topology-preserving three-stage framework: (1) a centerline-enhanced loss function to improve segmentation accuracy for fine vessels; (2) a robust random-walk algorithm regularized by distance, probability, and directional cosine metrics to reconnect fragmented centerlines; and (3) implicit neural representations (INRs) for geometry-driven, continuous reconstruction of missing vascular segments. Evaluated on ASOCA and PDSCA datasets, our method achieves Dice scores of 88.53% and 85.07%, and Hausdorff distances of 1.07 mm and 1.63 mm—substantially outperforming state-of-the-art approaches. The framework ensures structural integrity and topological connectivity of the reconstructed coronary tree.

To address the challenge of topological recovery in tubular structure extraction (e.g., vessels, roads), this paper proposes GraphMorph—a graph-level structural modeling approach that abandons conventional pixel-wise classification. Methodologically, it introduces a novel collaborative architecture integrating a graph neural decoder with a morphological deformation module; proposes SkeletonDijkstra, a geometric alignment algorithm that bridges graph topology and centerline probability maps; and employs centerline masks to guide post-processing segmentation, effectively suppressing false positives. By fusing multi-scale features and centerline-guided morphological deformation, GraphMorph achieves substantial improvements across multiple public benchmarks: topological accuracy increases by 5.2–9.8%, centerline extraction precision improves significantly, and the false positive rate decreases by an average of 37.6%, outperforming state-of-the-art segmentation and graph-generation methods.

This work addresses the challenge faced by visually impaired users in accessing node-link diagrams commonly distributed as bitmap images, a task for which existing assistive technologies are ill-suited due to their reliance on structured data rather than visual input. The paper presents the first lightweight deep learning approach for semantic segmentation of such diagram images, training a compact model on a large-scale synthetic dataset to achieve pixel-level parsing. The proposed method attains over 93% pixel accuracy on synthetic data and demonstrates strong performance both quantitatively and qualitatively. By enabling precise extraction of diagram semantics directly from rasterized images, this approach establishes a viable foundation for non-visual interaction and effectively bridges a critical gap in accessibility technology for bitmap-based graphical content.

Existing geometric data augmentation methods often disrupt the topological connectivity between inner and outer boundaries of ring-shaped polygon annotations, leading to structural information loss. This work proposes a topology-preserving polygon augmentation strategy that first applies geometric transformations in mask space, then projects surviving vertices back into index space and reconstructs the original traversal order via a cyclic adjacency restoration algorithm. Designed specifically for ring-shaped polygons, this approach introduces the first mechanism explicitly tailored to preserve topological integrity during augmentation. It achieves near-perfect cyclic adjacency preservation (CAP) rates under both single and composite augmentation settings, effectively balancing computational efficiency with structural fidelity.

Existing image segmentation methods predominantly rely on pixel-wise losses (e.g., Dice), neglecting topological consistency; mainstream topology-aware approaches either lack rigorous theoretical guarantees or suffer from high computational cost and poor generalizability. Method: We propose the first differentiable, lightweight, and formally guaranteed topology-preserving framework: (i) we introduce and optimize a strict homotopy equivalence metric; (ii) we construct a differentiable component graph based on connected components, enabling local neighborhood-sensitive topological modeling and loss computation; (iii) we employ graph neural networks for feature aggregation and homotopy classification to enforce homotopy equivalence between predictions and ground truth. Contribution/Results: Our method achieves state-of-the-art performance on diverse multi-class medical and natural image segmentation benchmarks. It significantly improves topological accuracy and accelerates topological loss computation by 5× compared to persistent homology–based methods.

This work proposes an end-to-end road extraction framework that addresses the limitations of existing methods in modeling long-range dependencies and complex topologies in road networks. By constructing a sparse Euclidean graph and transforming it into a line graph, the approach applies a Graph Transformer on the line graph to predict connectivity, thereby integrating line graph representations with Graph Transformers for the first time. This combination overcomes the representational limitations of conventional endpoint embeddings regarding isomorphic links. To further enhance structural integrity, the framework incorporates an overpass identification head and a coupled non-maximum suppression strategy. Evaluated on three benchmarks—City-scale, SpaceNet, and Global-scale—the method achieves state-of-the-art performance, significantly outperforming prior approaches in TOPO-F1 and APLS metrics while preserving fine visual details suitable for real-world deployment.

This work addresses the fragmentation problem in segmenting fine structures—such as wires, cracks, and lane markings—caused by traditional pixel-wise representations that disrupt topological connectivity. To preserve structural continuity, the authors propose a topology-preserving, parameterized graph minor representation that compresses the input image into super-nodes via a boundary-aligned contraction criterion. This approach achieves substantial dimensionality reduction while rigorously maintaining the connectivity of fine structures. A lightweight graph neural network is then employed for classification, followed by bidirectional pixel-to-graph mapping to enable full-resolution inference. Evaluated on TTPLA, CrackSeg9k, and SkyScapes Lane datasets, the method matches or surpasses state-of-the-art domain-specific approaches in Dice, IoU, and Boundary F1 scores, while reducing mask fragmentation by at least 4.6×.

Computing an ideal medial axis transform (MAT) on discrete triangle meshes that simultaneously achieves high fidelity and structural alignment—such as preserving the trajectory of rolling-ball centers in filleted regions—remains challenging. This work proposes a novel approach that initializes the MAT from a surface-sampled 3D Voronoi diagram and explicitly maintains correspondences between MAT vertices and their originating surface regions throughout simplification. A geometry-aware edge collapse prioritization strategy is introduced to preserve intrinsic symmetries among medial sheets. By explicitly modeling and tracking surface-to-MAT correspondences during simplification—a first in MAT processing—the method yields structurally aligned, boundary-regular, and noise-resilient simplified MATs. Experiments demonstrate that complex CAD and articulated models can be accurately represented with only a few hundred vertices while outperforming existing methods in overall quality.

High-resolution 3D modeling of vascular structures faces dual challenges of geometric complexity and computational efficiency. This work proposes the first graph tokenization framework tailored for tubular anatomical structures, leveraging centerline points and pseudo-radii to construct a neural implicit representation that encodes both geometric and topological information into compact, generalizable latent tokens. The approach enables efficient solutions to inverse problems such as reconstruction, generation, and link prediction. Extensive experiments on pulmonary airways, pulmonary vasculature, and cerebral vasculature demonstrate the method’s strong cross-anatomical generalization capability and anatomically plausible generation performance.