Topology-Preserving Polygon Augmentation for Segmentation in Structured Visual Domains

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.

Agricultural parcel polygons play a fundamental role in geospatial applications such as precision agriculture, land administration, and crop monitoring. Beyond regular polygon geometry and low vertex redundancy, practical parcel maps should avoid topological conflicts and preserve common boundaries between adjacent fields. Yet this requirement remains largely unresolved: segmentation-based methods mainly produce parcel masks or raster boundary cues and rely on heuristic raster-to-vector conversion, instance- and contour-based methods reconstruct parcels independently, and recent vector-oriented methods improve polygon regularity but do not explicitly recover adjacent parcels from a shared topological structure. To address this gap, we propose a semantic-guided diffusion framework for topologically consistent agricultural parcel vectorization. It couples joint edge--vertex latent diffusion with supervised multi-cue conditioning to generate geometrically regularised parcel-boundary and vertex primitives while suppressing false-positive responses. A topology-aware parcel polygon reconstruction method then converts these primitives into regular polygons by reconstructing parcel faces from a common planar graph, enabling adjacent predicted parcels to reuse shared boundaries and avoid mutual interior intrusion. Extensive experiments on the AI4SmallFarms and iFLYTEK datasets evaluate parcel vectorization in terms of pixel-level coverage, geometric fidelity, object-level correctness, and topological consistency. The results show strong and competitive performance, with zero measured intrusion ratio and the highest shared-edge recall, demonstrating the potential of the proposed framework for accurate, regular, and topologically consistent agricultural parcel vectorization.

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.