Bridging the Geometry Mismatch: Frequency-Aware Anisotropic Serialization for Thin-Structure SSMs

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-performance semantic segmentation has achieved significant progress in recent years, often driven by increasingly large backbones and higher computational budgets. While effective, such approaches introduce substantial computational overhead and limit accessibility under constrained hardware settings. In this paper, we propose DGM-Net (Directional Geometric Mamba Network), an efficient architecture that improves modeling capability through structural design rather than increasing model capacity. We introduce Directional Geometric Mamba (G-Mamba), a linear-complexity O(N) operator as an alternative to conventional context modeling modules such as ASPP and PPM. To further enhance structural awareness in state space model (SSM)-based modeling, we design the DGM-Module, which extracts centripetal flow fields and topological skeletons to guide the scanning process and improve boundary preservation. Without relying on large-scale pretraining or heavy backbone scaling, DGM-Net achieves 80.8% mIoU within 28k iterations, 82.3% mIoU on Cityscapes test set, and 45.24% mIoU on ADE20K. In addition, the model maintains stable performance under constrained hardware settings (e.g., batch size of 2 on 8GB VRAM), highlighting its efficiency and practicality. These results demonstrate that incorporating geometric guidance into SSM-based architectures provides an effective and resource-efficient direction for semantic segmentation.

Vision State Space Models (SSMs) like Vim, VMamba, and SiMBA rely on complex scanning strategies to adapt sequential SSMs to process 2D images, introducing computational overhead and architectural complexity. We propose HAMSA, a scanning-free SSM operating directly in the spectral domain. HAMSA introduces three key innovations: (1) simplified kernel parameterization-a single Gaussian-initialized complex kernel replacing traditional (A, B, C) matrices, eliminating discretization instabilities; (2) SpectralPulseNet (SPN)-an input-dependent frequency gating mechanism enabling adaptive spectral modulation; and (3) Spectral Adaptive Gating Unit (SAGU)-magnitude-based gating for stable gradient flow in the frequency domain. By leveraging FFT-based convolution, HAMSA eliminates sequential scanning while achieving O(L log L) complexity with superior simplicity and efficiency. On ImageNet-1K, HAMSA reaches 85.7% top-1 accuracy (state-of-the-art among SSMs), with 2.2 X faster inference than transformers (4.2ms vs 9.2ms for DeiT-S) and 1.4-1.9X speedup over scanning-based SSMs, while using less memory (2.1GB vs 3.2-4.5GB) and energy (12.5J vs 18-25J). HAMSA demonstrates strong generalization across transfer learning and dense prediction tasks.