OcTreeMamba: Topology-Aware Mamba for 3D Medical Segmentation via Octree Sparsification

Accurate segmentation of 3D anatomical structures is crucial to medical image analysis. Recently, Mamba-based approaches have achieved promising segmentation performance in capturing long-range dependencies with linear-time computational complexity. However, heuristic selective scanning strategies inherently disrupt the intrinsic spatial hierarchy and increase computational redundancy, ignoring the inherent sparsity of 3D anatomical structures. To this end, we propose OcTreeMamba, a hierarchical framework that incorporates Octree structures into SSM, achieving 3D topology-aware long-range context feature propagation and integration. Specifically, a Structure Learner performs anatomy-adaptive structured sparsification through hierarchical gating and Gumbel-Softmax sampling, enabling differentiable selection of anatomical regions. The selected regions are subsequently organized by a Dynamic Octree Builder into a multi-level topology that preserves their hierarchical connectivity. Based on the constructed Octree, a bidirectional Tree-SSM propagates and integrates contextual features along connectivity-aware leaf--parent--root and root--parent--leaf trajectories. Extensive experiments on four benchmark datasets show that our proposed OcTreeMamba achieves competitive performance \wrt topological continuity and computational efficiency, particularly for recovering the complex structure on vascular datasets. The code is available at https://github.com/MikeMak123/OcTreeMamba.