# SSFMamba: Learning Symmetry-driven Spatial-Frequency Modeling for Physically Consistent 3D Medical Image Segmentation

arXiv: https://arxiv.org/abs/2508.03069 · HTML: https://mlsanity.com/paper/2508.03069/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 57 references that are in the map.
- First posted on arXiv 5 Aug 2025.

## Builds on (most cited first, 30 of 35)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Swin-Unet: Unet-like Pure Transformer for Medical Image Segmentation](https://mlsanity.com/paper/2105.05537/) (2021)
- [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)
- [UNETR: Transformers for 3D Medical Image Segmentation](https://mlsanity.com/paper/2103.10504/) (2021)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [TotalSegmentator: robust segmentation of 104 anatomical structures in CT images](https://mlsanity.com/paper/2208.05868/) (2022)
- [Identifying the Best Machine Learning Algorithms for Brain Tumor Segmentation, Progression Assessment, and Overall Survival Prediction in the BRATS Challenge](https://mlsanity.com/paper/1811.02629/) (2018)
- [Self-Supervised Pre-Training of Swin Transformers for 3D Medical Image Analysis](https://mlsanity.com/paper/2111.14791/) (2021)
- [SegMamba: Long-range Sequential Modeling Mamba For 3D Medical Image Segmentation](https://mlsanity.com/paper/2401.13560/) (2024)
- [TransBTS: Multimodal Brain Tumor Segmentation Using Transformer](https://mlsanity.com/paper/2103.04430/) (2021)
- [LocalMamba: Visual State Space Model with Windowed Selective Scan](https://mlsanity.com/paper/2403.09338/) (2024)
- [CDDFuse: Correlation-Driven Dual-Branch Feature Decomposition for Multi-Modality Image Fusion](https://mlsanity.com/paper/2211.14461/) (2022)
- [Cross-Entropy Loss Functions: Theoretical Analysis and Applications](https://mlsanity.com/paper/2304.07288/) (2023)
- [Learning in the Frequency Domain](https://mlsanity.com/paper/2002.12416/) (2020)
- [Swin-UMamba: Mamba-based UNet with ImageNet-based pretraining](https://mlsanity.com/paper/2402.03302/) (2024)
- [Efficient Frequency Domain-based Transformers for High-Quality Image Deblurring](https://mlsanity.com/paper/2211.12250/) (2022)
- [MedNeXt: Transformer-driven Scaling of ConvNets for Medical Image Segmentation](https://mlsanity.com/paper/2303.09975/) (2023)
- [MedMamba: Vision Mamba for Medical Image Classification](https://mlsanity.com/paper/2403.03849/) (2024)
- [FreqMamba: Viewing Mamba from a Frequency Perspective for Image Deraining](https://mlsanity.com/paper/2404.09476/) (2024)
- [Vision Mamba: A Comprehensive Survey and Taxonomy](https://mlsanity.com/paper/2405.04404/) (2024)
- [The Brain Tumor Segmentation (BraTS) Challenge 2023: Focus on Pediatrics (CBTN-CONNECT-DIPGR-ASNR-MICCAI BraTS-PEDs)](https://mlsanity.com/paper/2305.17033/) (2023)
- [Wave-Mamba: Wavelet State Space Model for Ultra-High-Definition Low-Light Image Enhancement](https://mlsanity.com/paper/2408.01276/) (2024)
- [Burstormer: Burst Image Restoration and Enhancement Transformer](https://mlsanity.com/paper/2304.01194/) (2023)
- [SFFNet: A Wavelet-Based Spatial and Frequency Domain Fusion Network for Remote Sensing Segmentation](https://mlsanity.com/paper/2405.01992/) (2024)
- [LC-FDNet: Learned Lossless Image Compression with Frequency Decomposition Network](https://mlsanity.com/paper/2112.06417/) (2021)

## Abstract (arXiv)

Accurate 3D medical image segmentation requires a delicate balance between fine-grained local details and global contextual understanding. While spatial-domain models often struggle with long-range dependencies, existing frequency-based approaches frequently overlook intrinsic spectral properties such as Hermitian symmetry, leading to suboptimal feature integration. In this paper, we propose SSFMamba, a Mamba based Symmetry-driven Spatial-Frequency fusion framework tailored for 3D medical imaging. Our architecture employs a complementary dual-branch design: the spatial branch preserves intricate anatomical textures, while the frequency branch captures global contextual dependencies in the frequency domain. A core innovation is the 3D Multi-Directional Scanning Mechanism (MDSM), which integrates Hermitian symmetry with the causal nature of State Space Models (SSMs) to enable direction-aware global modeling. Crucially, by shifting the modeling focus to frequency-domain spectral components, SSFMamba captures the underlying structural characteristics of anatomical tissues. This leads to a highly adaptable framework that excels in both MRI and CT applications, regardless of the significant variations in intensity distributions. Extensive evaluations on the BraTS2020, BraTS2023, and BTCV datasets demonstrate that SSFMamba consistently outperforms state-of-the-art methods. Notably, our approach achieves exceptional performance on low-contrast organs such as the pancreas (81.97% Dice), underscoring its potential as a unified and physically consistent perception framework for diverse 3D clinical applications.