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.
@article{arxiv.2603.28503,
title = {Bridging the Geometry Mismatch: Frequency-Aware Anisotropic Serialization for Thin-Structure SSMs},
author = {Jin Bai and Huiyao Zhang and Qi Wen and Ningyang Li and Shengyang Li and Atta ur Rahman and Xiaolin Tian},
journal= {arXiv preprint arXiv:2603.28503},
year = {2026}
}