TopoMamba: Topology-Aware Scanning and Fusion for Segmenting Heterogeneous Medical Visual Media

CNN- and Transformer-based architectures have achieved strong performance in medical image segmentation, but CNNs are limited in modeling long-range dependencies, while Transformers often suffer from quadratic computational and memory complexity. State space models, especially Mamba-based networks, offer an efficient alternative with linear sequence complexity. However, existing Mamba segmentation models still face two limitations: pixel-wise directional scanning can disrupt local 2D spatial structure, and simple summation-based fusion of scan directions cannot adapt well to diverse object sizes, shapes, and boundaries. To address these issues, we propose \textit{Patch-MoE Mamba}, a patch-ordered mixture-of-experts state space architecture for medical image segmentation. It introduces a hierarchical patch-ordered scanning mechanism that preserves local spatial neighborhoods while capturing multi-scale context, and an MoE-based directional fusion module that adaptively combines multiple Mamba scanner outputs using four directional experts, a learnable concatenation expert, and residual directional aggregation. Experiments on five public polyp segmentation benchmarks and the ISIC 2017/2018 skin lesion segmentation datasets demonstrate the effectiveness and generality of Patch-MoE Mamba.

Accurate 3D medical image segmentation requires both long-range volumetric context and fine boundary preservation. CNN-based methods have limited global dependency modeling, while Transformer-based models are often computationally expensive for dense 3D inputs. Recent Mamba-based methods provide an efficient alternative, but existing volumetric designs still depend on repeated high-resolution scanning, forward-only sequential modeling, and fixed directional summation, causing high cost, scan-order bias, and suboptimal directional aggregation. We propose BiSegMamba, an efficient bidirectional tri-oriented Mamba network for 3D medical image segmentation. BiSegMamba follows a compact-to-detail design, where a progressive compacting stem (PCS) enables efficient latent-space reasoning while retaining shallow high-resolution features for reconstruction. A multi-scale spatial mixer (MSSM) captures local anatomical patterns in early stages, and the proposed bidirectional tri-oriented Ortho Mamba (Bi-ToOM) block models long-range dependencies from multiple orthogonal views using jointly processed forward and backward scan sequences. Adaptive directional fusion (ADF) learns input-dependent channel-wise weights across scan orientations, replacing fixed summation with orientation-aware fusion. Experiments on a collected carotid CTA dataset and three public benchmarks, BraTS2023, ACDC, and AMOS-CT, show that BiSegMamba generalizes well across vascular, cardiac, brain tumor, and abdominal multi-organ segmentation tasks. Compared with SegMamba-V2, BiSegMamba achieves slightly better performance on BraTS2023 and clear improvements on ACDC and the carotid dataset, while reducing computational cost by up to 77.9% FLOPs, demonstrating a strong accuracy-efficiency balance for general 3D medical image segmentation.

We propose parameter-efficient SSM-based U-Net architectures for 3D medical image segmentation. Convolutional U-Nets afford O(n) local mixing per layer but lack explicit global context; transformers provide global reasoning at O(n^2) cost in sequence length $n$. State-space models (SSMs), such as Mamba, offer $O(n)$ global propagation per block. Yet, existing medical SSM segmenters rely on fixed scan patterns and large parameter budgets. Dynamic Adaptive Scan (DAS), which learns data-dependent reordering before selective scan, has not been applied to medical imaging or extended to 3D volumes. We propose DAMamba-UNet3D, a hybrid encoder-decoder that integrates tri-plane 3D-DAS blocks at encoder stages E2-E4 while retaining convolutions elsewhere (~5.3M parameters). On BraTS 2020 five-fold cross-validation, DAMamba-UNet3D achieves mean Dice 0.815+/-0.013 (full-volume per-case evaluation) at ~13x lower parameter cost than SegMamba (0.824+-0.014, ~70M). At comparable scale, DAMamba-L (~70M), a wide DAS-native variant with encoder-only DAMamba and a convolutional bottleneck, reaches 0.829+-0.012, surpassing retrained SegMamba by 0.5pt. Component ablations show that encoder-only DAS placement is critical as bottleneck and decoder SSM blocks lower Dice. Together, the results suggest that learned tri-plane DAS in a hybrid U-Net is competitive with, and under our large-scale design may improve upon, SegMamba's fixed Tri-orientated Mamba (ToM) scanning on BraTS 2020. Code: https://github.com/marafathussain/DAMamba-UNet3D.