# FermatSyn: SAM2-Enhanced Bidirectional Mamba with Isotropic Spiral Scanning for Multi-Modal Medical Image Synthesis

arXiv: https://arxiv.org/abs/2505.07687 · HTML: https://mlsanity.com/paper/2505.07687/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Mamba for medical image analysis, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 12 of its 22 references that are in the map.
- First posted on arXiv 12 May 2025.

## Placed in

- State-space sequence models (S4, Mamba) / [Mamba for medical image analysis](https://mlsanity.com/ssm/mamba-for-medical-image-analysis/)

## Builds on (most cited first, 12 of 12)

- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [SAM 2: Segment Anything in Images and Videos](https://mlsanity.com/paper/2408.00714/) (2024)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [The RSNA-ASNR-MICCAI BraTS 2021 Benchmark on Brain Tumor Segmentation and Radiogenomic Classification](https://mlsanity.com/paper/2107.02314/) (2021)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [ResViT: Residual vision transformers for multi-modal medical image synthesis](https://mlsanity.com/paper/2106.16031/) (2021)
- [Image Synthesis in Multi-Contrast MRI with Conditional Generative Adversarial Networks](https://mlsanity.com/paper/1802.01221/) (2018)
- [Missing MRI Pulse Sequence Synthesis using Multi-Modal Generative Adversarial Network](https://mlsanity.com/paper/1904.12200/) (2019)
- [SynthRAD2023 Grand Challenge dataset: generating synthetic CT for radiotherapy](https://mlsanity.com/paper/2303.16320/) (2023)
- [I2I-Mamba: Multi-modal medical image synthesis via selective state space modeling](https://mlsanity.com/paper/2405.14022/) (2024)
- [SAM-I2I: Unleash the Power of Segment Anything Model for Medical Image Translation](https://mlsanity.com/paper/2411.12755/) (2024)

## Built on by (most cited first, 1 of 1)

- [Med-K2N: Flexible K-to-N Modality Translation for Medical Image Synthesis](https://mlsanity.com/paper/2510.02815/) (2025)

## Abstract (arXiv)

Multi-modal medical image synthesis is pivotal for alleviating clinical data scarcity, yet existing methods fail to reconcile global anatomical consistency with high-fidelity local detail. We propose FermatSyn, which addresses three persistent limitations: (1) SAM2-based Prior Encoder that injects domain-aware anatomical knowledge via LoRA+ efficient fine-tuning of a frozen SAM2 Vision Transformer; (2) Hierarchical Residual Downsampling Module (HRDM) coupled with a Cross-scale Integration Network (CIN) that preserves high-frequency lesion details and adaptively fuses global--local representations; and (3) continuity constrained Fermat Spiral Scanning strategy within a Bidirectional Fermat Scan Mamba (BFS-Mamba), constructing an approximately isotropic receptive field that substantially reduces the directional bias of raster or spiral serialization. Experiments on SynthRAD2023, BraTS2019, BraTS-MEN, and BraTS-MET show FermatSyn surpasses state-of-the-art methods in PSNR, SSIM, FID, and 3D structural consistency. Downstream segmentation on synthesized images yields no significant difference from real-image training (p>0.05), confirming clinical utility. Code is available at https://github.com/gatina-yone/FermatSyn.