Topology-Preserving Image Segmentation

Retinal vessel segmentation methods based on standard overlap losses tend to miss thin peripheral vessels because these structures occupy very few pixels and have low contrast against the background. We propose HMS-VesselNet, a hierarchical multi-scale network that processes fundus images across four parallel branches at different resolutions and combines their outputs using learned fusion weights. The training loss combines Dice, binary cross-entropy, and centerline Dice to jointly optimize area overlap and vessel continuity. Hard example mining is applied from epoch 20 onward to concentrate gradient updates on the most difficult training images. Tested on 68 images from DRIVE, STARE, and CHASE_DB1 using 5-fold cross-validation, the model achieves a mean Dice of 88.72 +/- 0.67%, Sensitivity of 90.78 +/- 1.42%, and AUC of 98.25 +/- 0.21%. In leave-one-dataset-out experiments, AUC remains above 95% on each unseen dataset. The largest improvement is in the recall of thin peripheral vessels, which are the structures most frequently missed by standard methods and most critical for early detection of diabetic retinopathy.

In this work, we present SYSU-HiRoads, a large-scale hierarchical road dataset, and RoadReasoner, a vision-language-geometry framework for automatic multi-grade road mapping from remote sensing imagery. SYSU-HiRoads is built from GF-2 imagery covering 3631 km2 in Henan Province, China, and contains 1079 image tiles at 0.8 m spatial resolution. Each tile is annotated with dense road masks, vectorized centerlines, and three-level hierarchy labels, enabling the joint training and evaluation of segmentation, topology reconstruction, and hierarchy classification. Building on this dataset, RoadReasoner is designed to generate robust road surface masks, topology-preserving road networks, and semantically coherent hierarchy assignments. We strengthen road feature representation and network connectivity by explicitly enhancing frequency-sensitive cues and multi-scale context. Moreover, we perform hierarchy inference at the skeleton-segment level with geometric descriptors and geometry-aware textual prompts, queried by vision-language models to obtain linguistically interpretable grade decisions. Experiments on SYSU-HiRoads and the CHN6-CUG dataset show that RoadReasoner surpasses state-of-the-art road extraction baselines and produces accurate and semantically consistent road hierarchy maps with 72.6% OA, 64.2% F1 score, and 60.6% SegAcc. The dataset and code will be publicly released to support automated transport infrastructure mapping, road inventory updating, and broader infrastructure management applications.

Conventional pixel-wise loss functions fail to enforce topological constraints in coronary vessel segmentation, producing fragmented vascular trees despite high pixel-level accuracy. We present ARIADNE, a two-stage framework coupling preference-aligned perception with RL-based diagnostic reasoning for topologically coherent stenosis detection. The perception module employs DPO to fine-tune the Sa2VA vision-language foundation model using Betti number constraints as preference signals, aligning the policy toward geometrically complete vessel structures rather than pixel-wise overlap metrics. The reasoning module formulates stenosis localization as a Markov Decision Process with an explicit rejection mechanism that autonomously defers ambiguous anatomical candidates such as bifurcations and vessel crossings, shifting from coverage maximization to reliability optimization. On 1,400 clinical angiograms, ARIADNE achieves state-of-the-art centerline Dice of 0.838, reduces false positives by 41% compared to geometric baselines. External validation on multi-center benchmarks ARCADE and XCAD confirms generalization across acquisition protocols. This represents the first application of DPO for topological alignment in medical imaging, demonstrating that preference-based learning over structural constraints mitigates topological violations while maintaining diagnostic sensitivity in interventional cardiology workflows.

Standard deep learning models for image segmentation cannot guarantee topology accuracy, failing to preserve the correct number of connected components or structures. This, in turn, affects the quality of the segmentations and compromises the reliability of the subsequent quantification analyses. Previous works have proposed to enhance topology accuracy with specialized frameworks, architectures, and loss functions. However, these methods are often cumbersome to integrate into existing training pipelines, they are computationally very expensive, or they are restricted to structures with tubular morphology. We present SCNP, an efficient method that improves topology accuracy by penalizing the logits with their poorest-classified neighbor, forcing the model to improve the prediction at the pixels' neighbors before allowing it to improve the pixels themselves. We show the effectiveness of SCNP across 13 datasets, covering different structure morphologies and image modalities, and integrate it into three frameworks for semantic and instance segmentation. Additionally, we show that SCNP can be integrated into several loss functions, making them improve topology accuracy. Our code can be found at https://jmlipman.github.io/SCNP-SameClassNeighborPenalization.

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.

Geometric data augmentation is widely used in segmentation workflows, but polygon annotations are often assumed to remain valid after transformation. This assumption can fail in structured domains such as architectural floorplan analysis, where a region may contain an interior void encoded as part of a single ordered polygon chain. Cropping or clipping can remove bridge vertices in this chain, causing one semantic region to split into disconnected components. We propose a lightweight topology-preserving augmentation strategy that repairs missing adjacency relations in index space while preserving the original vertex order. The method adds minimal overhead and can be integrated into existing preprocessing workflows. Experiments show that the proposed approach achieves near-perfect Cyclic Adjacency Preservation (CAP) across common geometric transformations and improves annotation consistency in polygon-based segmentation.

Segmenting thin structures like infrastructure cracks and anatomical vessels is a task hampered by topology-sensitive geometry, high annotation costs, and poor generalization across domains. Existing methods address these challenges in isolation. We propose FMS$^2$, a flow-matching framework with two modules. (1) SegFlow is a 2.96M-parameter segmentation model built on a standard encoder-decoder backbone that recasts prediction as continuous image $\rightarrow$ mask transport. It learns a time-indexed velocity field with a flow-matching regression loss and outputs the mask via ODE integration, rather than supervising only end-state logits. This trajectory-level supervision improves thin-structure continuity and sharpness, compared with tuned topology-aware loss baselines, without auxiliary topology heads, post-processing, or multi-term loss engineering. (2) SynFlow is a mask-conditioned mask $\rightarrow$ image generator that produces pixel-aligned synthetic image-mask pairs. It injects mask geometry at multiple scales and emphasizes boundary bands via edge-aware gating, while a controllable mask generator expands sparsity, width, and branching regimes. On five crack and vessel benchmarks, SegFlow alone outperforms strong CNN, Transformer, Mamba, and generative baselines, improving the volumetric metric (mean IoU) from 0.511 to 0.599 (+17.2%) and reducing the topological metric (Betti matching error) from 82.145 to 51.524 (-37.3%). When training with limited labels, augmenting SegFlow with SynFlow-generated pairs recovers near-full performance using 25% of real annotations and improves cross-domain IoU by 0.11 on average. Unlike classical data augmentation that promotes invariance via label-preserving transforms, SynFlow provides pixel-aligned paired supervision with controllable structural shifts (e.g., sparsity, width, branching), which is particularly effective under domain shift.

High-resolution sea ice mapping using Synthetic Aperture Radar (SAR) is crucial for Arctic navigation and climate monitoring. However, operational ice charts provide only coarse, region-level polygons (weak labels), forcing automated segmentation models to struggle with pixel-level accuracy and often yielding under-confident, blurred concentration maps. In this paper, we propose a weakly supervised deep learning pipeline that fuses Sentinel-1 SAR and AMSR-2 radiometry data using a U-Net architecture trained with a region-based loss. To overcome the severe under-confidence caused by weak labels, we introduce an Analytical Logit Scaling method applied post-inference. By dynamically calculating the temperature and bias based on the latent space percentiles (2% and 98%) of each scene, we force a physical binarization of the predictions. This adaptive scaling acts as a topological extractor, successfully revealing fine-grained sea ice fractures (leads) at a 40-meter resolution without requiring any manual pixel-level annotations. Our approach not only resolves local topology but also perfectly preserves regional macroscopic concentrations, achieving a 78% accuracy on highly fragmented summer scenes, thereby bridging the gap between weakly supervised learning and high-resolution physical segmentation.

Modeling medical vessel-like anatomy is challenging due to its intricate topology and sensitivity to dataset shifts. Consequently, task-specific models often suffer from topological inconsistencies, including artificial disconnections and spurious merges. Motivated by the promise of multimodal large language models (MLLMs) for zero-shot generalization, we propose TubeMLLM, a unified foundation model that couples structured understanding with controllable generation for medical vessel-like anatomy. By integrating topological priors through explicit natural language prompting and aligning them with visual representations in a shared-attention architecture, TubeMLLM significantly enhances topology-aware perception. Furthermore, we construct TubeMData, a pionner multimodal benchmark comprising comprehensive topology-centric tasks, and introduce an adaptive loss weighting strategy to emphasize topology-critical regions during training. Extensive experiments on fifteen diverse datasets demonstrate our superiority. Quantitatively, TubeMLLM achieves state-of-the-art out-of-distribution performance, substantially reducing global topological discrepancies on color fundus photography (decreasing the $β_{0}$ number error from 37.42 to 8.58 compared to baselines). Notably, TubeMLLM exhibits exceptional zero-shot cross-modality transferring ability on unseen X-ray angiography, achieving a Dice score of 67.50% while significantly reducing the $β_{0}$ error to 1.21. TubeMLLM also maintains robustness against degradations such as blur, noise, and low resolution. Furthermore, in topology-aware understanding tasks, the model achieves 97.38% accuracy in evaluating mask topological quality, significantly outperforming standard vision-language baselines.

Extracting routable road networks from satellite imagery requires accurate topology recovery beyond pixel-level segmentation. Recent methods decompose the task into keypoint detection and connectivity prediction, but reliably inferring road connectivity under structural ambiguity remains challenging. Overpasses introduce non-planar crossings that can create false shortcuts, and occlusions break visual continuity, requiring long-range structural reasoning. We formulate road extraction as fully unobserved connectivity inference and construct a global but sparse Euclidean graph from detected keypoints to better leverage the long-term context. To improve link prediction, we transform this graph into its line graph and perform reasoning using a Graph Transformer. We propose an end-to-end pipeline that integrates vision-based segmentation, sparse graph construction, and structured inference. Our method explicitly models overpasses and uses topology-preserving vertex extraction to mitigate routing-critical errors. This approach achieves state-of-the-art performance on City-scale, SpaceNet, and Global-scale benchmarks in topology metrics including TOPO-F1 and APLS. In addition to quantitative gains, our method improves reconstruction of multi-level road structures crucial for real-world routing reliability. The code is available at: https://github.com/wzzzzzzy/LineGraph2Road.

Accurate Couinaud liver segmentation is critical for preoperative surgical planning and tumor localization.However, existing methods primarily rely on image intensity and spatial location cues, without explicitly modeling vascular topology. As a result, they often produce indistinct boundaries near vessels and show limited generalization under anatomical variability.We propose VasGuideNet, the first Couinaud segmentation framework explicitly guided by vascular topology. Specifically, skeletonized vessels, Euclidean distance transform (EDT)--derived geometry, and k-nearest neighbor (kNN) connectivity are encoded into topology features using Graph Convolutional Networks (GCNs). These features are then injected into a 3D encoder--decoder backbone via a cross-attention fusion module. To further improve inter-class separability and anatomical consistency, we introduce a Structural Contrastive Loss (SCL) with a global memory bank.On Task08_HepaticVessel and our private LASSD dataset, VasGuideNet achieves Dice scores of 83.68% and 76.65% with RVDs of 1.68 and 7.08, respectively. It consistently outperforms representative baselines including UNETR, Swin UNETR, and G-UNETR++, delivering higher Dice/mIoU and lower RVD across datasets, demonstrating its effectiveness for anatomically consistent segmentation. Code is available at https://github.com/Qacket/VasGuideNet.git.

Graph-based medical image segmentation represents anatomical structures using boundary graphs, providing fixed-topology landmarks and inherent population-level correspondences. However, their clinical adoption has been hindered by a major requirement: training datasets with manually annotated landmarks that maintain point-to-point correspondences across patients rarely exist in practice. We introduce Mask-HybridGNet, a framework that trains graph-based models directly using standard pixel-wise masks, eliminating the need for manual landmark annotations. Our approach aligns variable-length ground truth boundaries with fixed-length landmark predictions by combining Chamfer distance supervision and edge-based regularization to ensure local smoothness and regular landmark distribution, further refined via differentiable rasterization. A significant emergent property of this framework is that predicted landmark positions become consistently associated with specific anatomical locations across patients without explicit correspondence supervision. This implicit atlas learning enables temporal tracking, cross-slice reconstruction, and morphological population analyses. Beyond direct segmentation, Mask-HybridGNet can extract correspondences from existing segmentation masks, allowing it to generate stable anatomical atlases from any high-quality pixel-based model. Experiments across chest radiography, cardiac ultrasound, cardiac MRI, and fetal imaging demonstrate that our model achieves competitive results against state-of-the-art pixel-based methods, while ensuring anatomical plausibility by enforcing boundary connectivity through a fixed graph adjacency matrix. This framework leverages the vast availability of standard segmentation masks to build structured models that maintain topological integrity and provide implicit correspondences.

Accurate segmentation of thin, tubular structures (e.g., blood vessels) is challenging for deep neural networks. These networks classify individual pixels, and even minor misclassifications can break the thin connections within these structures. Existing methods that focus on improving topology accuracy, such as topology loss functions, require very precise training labels with the correct topology, which is difficult to obtain. Low image resolution and contrast can further complicate the annotation by causing these structures to appear disconnected. We present CoLeTra, a data augmentation method that improves topology accuracy, even on datasets with topologically inaccurate training labels. CoLeTra achieves this by artificially breaking the structures in the images while maintaining the original labels, incorporating to the models the prior knowledge that structures can be continuous even if they appear disconnected. Our extensive experiments, involving different architectures, loss functions, and datasets, demonstrate that CoLeTra leads to segmentations topologically more accurate while often improving the Dice coefficient and clDice. We also release a dataset specifically suited for image segmentation methods with a focus on topology accuracy. CoLetra's code can be found at https://jmlipman.github.io/CoLeTra.