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

Jin Bai; Huiyao Zhang; Qi Wen; Ningyang Li; Shengyang Li; Atta ur Rahman; Xiaolin Tian

cs.CVMar 30, 2026

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

Authors: Jin Bai, Huiyao Zhang, Qi Wen, Ningyang Li, Shengyang Li, Atta ur Rahman, Xiaolin Tian

Organizations: University of Chinese Academy of Sciences · Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences · University of Peshawar, Pakistan · Macau University of Science and Technology, China

Abstract

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.

Figures & tables

Figure 1: Overview of FGOS-Net. Each FGOS block performs: (1) DWT-based frequency disentanglement into topology carrier $X_{LL}$ and directional details $X_{HF}$ ; (2) detail-driven alignment of $X_{LL}$ ; (3) geometry-aligned FA-Scan for topology modeling and ASGP for topology-conditioned detail gating; (4) IDWT-based reconstruction. A parallel GFA decoder and BRM head fuse multi-scale features and refine boundaries.

Figure 2: FA-Block components. Left: FA-Scan assigns deterministic, sub-band-aligned serialization trajectories (Horizontal/Vertical for directional bands, Hilbert for isotropic bands). Right: The LightGate Bottleneck (LGB) employs a symmetric bottleneck ( $C{\to}C/4{\to}C$ ) modulated by stage-adaptive gating (ECA [ 41 ] / GSE [ 12 ] ), reducing parameters by $\approx 94\%$ vs. standard FFNs. ECA and GSE denote Efficient Channel Attention and Grouped Squeeze-and-Excitation, respectively.

Figure 3: Active Spectral-Geometric Probing (ASGP). The module resolves high-frequency ambiguity via: (i) Coarse Perception: Initializing probes on the topology carrier $\tilde{X}_{LL}$ ; (ii) Gradient-Guided Evolution: Iteratively refining probe positions ( $t=0{\to}T$ ) via differentiable gradient ascent on the potential field $M_{0}$ ; (iii) Gating & Injection: Generating a topology-validated mask $M$ to selectively gate high-frequency details ( $X_{HF}\odot M$ ).

Method	DeepCrack (%)						Crack500 (%)
Method	mIoU	F1	Prec	Recall	ODS	clDice	mIoU	F1	Prec	Recall	ODS	clDice
RIND [ 30 ]	81.27	84.40	82.22	86.64	90.72	95.69	78.24	72.98	70.85	79.41	72.98	80.93
CT-CrackSeg [ 39 ]	84.25	88.53	90.55	88.77	91.63	96.46	77.81	74.06	75.65	72.53	74.38	82.98
SimCrack [ 15 ]	83.50	90.79	87.59	90.22	91.55	96.28	78.76	74.35	74.55	78.25	74.42	82.03
Swin-UMamba [ 21 ]	83.52	83.72	91.02	90.12	91.74	95.91	77.52	72.86	74.05	76.37	73.02	80.53
VMamba [ 24 ]	73.97	80.65	75.06	89.67	80.67	92.18	77.35	72.66	73.38	76.39	72.87	79.83

Table 1: Quantitative comparison on four crack benchmarks. We report region metrics (mIoU/F1/Precision/Recall), boundary metric (ODS), and the connectivity-aware clDice [ 37 ] . Best results are highlighted in bold , and second-best are underlined .

Method	Year	Params $\downarrow$	FLOPs $\downarrow$	Size $\downarrow$	FPS $\uparrow$
RIND [ 30 ]	2021	30.63M	247.6G	117.06MB	28.46
CT-CrackSeg [ 39 ]	2023	22.88M	78.94G	87.37MB	66.0
SimCrack [ 15 ]	2023	29.58M	286.62G	225MB	40.81
Swin-UMamba [ 21 ]	2024	63.38M	104.1G	241.77MB	43.1
VMamba [ 24 ]	2024	19.50M	395.24G	65.54MB	28.8
VM-UNet [ 33 ]	2024	27.25M	29.42G	105.92MB	27.9

Table 2: Efficiency analysis. All metrics are measured on a single NVIDIA RTX 3090 with input size

256{\times}256

and batch size 1, averaged over 100 runs. FGOS-Net achieves a competitive accuracy–efficiency profile.

A. LGB Gating Policy
Policy	mIoU	F1	P	R	ODS
None	87.81	86.77	86.20	91.69	87.08
EEEE	88.54	87.62	86.75	92.06	88.42
GGGG	88.76	87.89	87.16	92.18	88.80
GEGE	88.84	87.99	87.67	91.80	88.85
GGEE	88.86	88.00	88.58	91.91	88.93

Table 3: System Diagnostics on DeepCrack. We conduct controlled ablations to verify: (A) The impact of stage-adaptive gating policies in LGB; (B) The sensitivity of ASGP to evolution steps (

T

) and probe count (

N

); (C) The geometric sensitivity of different scan trajectories for specific frequency bands; and (D) The stepwise contribution of each module, explicitly isolating the gains from the FA-Scan encoder versus the GFA/BRM decoder.

Figure 4: Feature Response Analysis: Raster vs. FA-Scan. Feature maps are extracted from the Stage-2 encoder output (before IDWT), and profiles are sampled along the crack structure (highlighted in pink). The centerline is derived from the ground-truth skeleton for visualization purposes. Raster Scan: Features exhibit sharp signal drops when the scan path cuts across the crack, leading to fragmentation. FA-Scan: By aligning the scan trajectory with sub-band orientation, our method maintains a continuous, high-amplitude response (measured as the $\ell_{2}$ -normalized mean channel activation), verifying the preservation of connectivity.

Figure 5: Qualitative comparison on challenging scenarios. We visualize predictions from representative CNN/SSM baselines against FGOS-Net (Ours). All methods are visualized on the same test samples. Red Boxes (Topology): In low-contrast regions, baselines suffer from connectivity breaks, creating fragmented masks. Ours maintains continuous traces. Green Boxes (Texture): Under heavy clutter ( e.g . , water stains, oil spots), baselines yield false positives (texture leakage). Ours successfully suppresses these artifacts via topology-gated injection.

Method	CHASEDB1 (Vessels) [%]				Massachusetts (Roads) [%]
Method	mIoU	F1	Prec	clDice	mIoU	F1	Prec	clDice
SimCrack [ 15 ]	75.82	74.11	69.37	75.24	72.63	65.81	75.10	71.94
VMamba [ 24 ]	73.00	70.32	57.21	76.01	71.51	62.89	73.78	71.20
SCSegamba [ 20 ]	78.17	76.65	67.25	77.30	75.41	64.22	76.14	73.40
FGOS-Net (Ours)	80.45	79.12	76.71	83.35	79.83	69.32	80.99	80.86

Table 4: Cross-domain generalization. All models follow identical training settings. Best results are highlighted in bold .

Thin-Structure Segmentation

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Mar 14, 2026J/K move · Enter open · S save

FMS $^2$ : Unified Flow Matching for Segmentation and Synthesis of Thin Structures

Babak Asadi, Peiyang Wu, Mani Golparvar-Fard, Viraj Shah+1

University of Illinois at Urbana-Champaign

Thin-Structure Segmentation Topology-Preserving Image Segmentation Medical Image Segmentation Crack Segmentation Flow Matching Conditional Image Generation

Open paper AskPDF arXiv

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.

Abstract

Thin-Structure Segmentation

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