GeoSemba: Reconstructing State Space Model for Cross Paradigm Representation in Medical Image Segmentation

Recently, the Vision Mamba architecture has emerged as a promising paradigm for medical image segmentation. However, representation discrepancies often arise between anatomical structures and their associated tissue types, while crucial diagnostic cues tend to be spatially entangled, constraining the performance of Mamba architectures in this domain. To address these limitations, we propose $\textbf{GeoSemba}$, a novel Mamba-based segmentation framework that unifies geometric–semantic and spatial–channel representations. Specifically, we reformulate the Mamba’s state-space equations with two key components, a Semantic-guided State Refiner (SSR) and a Cross-dimensional Affinity Refiner (CAR). SSR reconstructs information flow within an abstract semantic space to forge a synergistic representation between anatomical textures and geometric contours. Concurrently, CAR adaptively models spatial–channel affinities to capture the intrinsic tissue heterogeneity common in medical imaging. By jointly integrating SSR and CAR in a complementary manner, $\textbf{GeoSemba}$ only requires a single scan to effectively achieve cross-dimensional consistency and cross-level interaction. Extensive experiments on public datasets spanning six medical imaging modalities demonstrate that $\textbf{GeoSemba}$ consistently delivers superior segmentation accuracy while maintaining high computational efficiency.