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

Mamba-based models have emerged as a promising paradigm for medical image segmentation due to their linear-complexity state-space modeling. However, their effectiveness is still limited by the mismatch between anatomical geometry and tissue-specific semantics, as well as by spatially entangled diagnostic cues. To address these limitations, we propose GeoSemba, a Mamba-based segmentation framework that jointly models cross-level geometric-semantic interactions and cross-dimensional spatial-channel dependencies within a single scan. To this end, GeoSemba comprises two complementary components. The Semantic-guided State Refiner (SSR) derives semantically discriminative region representatives and leverages geometry-conditioned inter-region dependencies to enable coherent semantic propagation across structurally related regions. The Cross-dimensional Affinity Refiner (CAR) adopts a coarse-to-fine strategy of macro-perception and micro-focus to selectively enhance informative spatial-channel interactions while suppressing weak and noisy correlations. Extensive experiments on benchmark datasets spanning six medical imaging modalities show that GeoSemba consistently delivers superior segmentation accuracy while maintaining high computational efficiency.