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

arXiv: https://arxiv.org/abs/2603.28503 · HTML: https://mlsanity.com/paper/2603.28503/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 42 of its 48 references that are in the map.
- First posted on arXiv 30 Mar 2026.

## Builds on (most cited first, 30 of 42)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Deformable DETR: Deformable Transformers for End-to-End Object Detection](https://mlsanity.com/paper/2010.04159/) (2020)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model](https://mlsanity.com/paper/2401.09417/) (2024)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [ECA-Net: Efficient Channel Attention for Deep Convolutional Neural Networks](https://mlsanity.com/paper/1910.03151/) (2019)
- [U-Mamba: Enhancing Long-range Dependency for Biomedical Image Segmentation](https://mlsanity.com/paper/2401.04722/) (2024)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)
- [VM-UNet: Vision Mamba UNet for Medical Image Segmentation](https://mlsanity.com/paper/2402.02491/) (2024)
- [LocalMamba: Visual State Space Model with Windowed Selective Scan](https://mlsanity.com/paper/2403.09338/) (2024)
- [FcaNet: Frequency Channel Attention Networks](https://mlsanity.com/paper/2012.11879/) (2020)
- [Swin-UMamba: Mamba-based UNet with ImageNet-based pretraining](https://mlsanity.com/paper/2402.03302/) (2024)
- [Gated-SCNN: Gated Shape CNNs for Semantic Segmentation](https://mlsanity.com/paper/1907.05740/) (2019)
- [PlainMamba: Improving Non-Hierarchical Mamba in Visual Recognition](https://mlsanity.com/paper/2403.17695/) (2024)
- [Strip Pooling: Rethinking Spatial Pooling for Scene Parsing](https://mlsanity.com/paper/2003.13328/) (2020)
- [Demystify Mamba in Vision: A Linear Attention Perspective](https://mlsanity.com/paper/2405.16605/) (2024)
- [Mamba-ND: Selective State Space Modeling for Multi-Dimensional Data](https://mlsanity.com/paper/2402.05892/) (2024)
- [Beyond the Pixel-Wise Loss for Topology-Aware Delineation](https://mlsanity.com/paper/1712.02190/) (2017)
- [Feature Pyramid and Hierarchical Boosting Network for Pavement Crack Detection](https://mlsanity.com/paper/1901.06340/) (2019)
- [GFF: Gated Fully Fusion for Semantic Segmentation](https://mlsanity.com/paper/1904.01803/) (2019)
- [CS2-Net: Deep Learning Segmentation of Curvilinear Structures in Medical Imaging](https://mlsanity.com/paper/2010.07486/) (2020)
- [Spatial-Mamba: Effective Visual State Space Models via Structure-aware State Fusion](https://mlsanity.com/paper/2410.15091/) (2024)
- [RINDNet: Edge Detection for Discontinuity in Reflectance, Illumination, Normal and Depth](https://mlsanity.com/paper/2108.00616/) (2021)
- [SegMAN: Omni-scale Context Modeling with State Space Models and Local Attention for Semantic Segmentation](https://mlsanity.com/paper/2412.11890/) (2024)

## Abstract (arXiv)

The segmentation of thin linear structures is inherently topology allowbreak-critical, where minor local errors can sever long-range connectivity. While recent State-Space Models (SSMs) offer efficient long-range modeling, their isotropic serialization (e.g., raster scanning) creates a geometry mismatch for anisotropic targets, causing state propagation across rather than along the structure trajectories. To address this, we propose FGOS-Net, a framework based on frequency allowbreak-geometric disentanglement. We first decompose features into a stable topology carrier and directional high-frequency bands, leveraging the latter to explicitly correct spatial misalignments induced by downsampling. Building on this calibrated topology, we introduce frequency-aligned scanning that elevates serialization to a geometry-conditioned decision, preserving direction-consistent traces. Coupled with an active probing strategy to selectively inject high-frequency details and suppress texture ambiguity, FGOS-Net consistently outperforms strong baselines across four challenging benchmarks. Notably, it achieves 91.3% mIoU and 97.1% clDice on DeepCrack while running at 80 FPS with only 7.87 GFLOPs.