Selective state space U net for linear complexity globally coherent high resolution image segmentation

Accurate segmentation of high-resolution images requires the simultaneous preservation of fine-grained spatial details and the modeling of long-range contextual dependencies. Conventional convolutional neural networks efficiently capture local structures but are limited by restricted receptive fields, whereas transformer-based architectures provide global context at the cost of quadratic computational complexity. Recent selective state-space models (SSMs), particularly Mamba-based architectures, offer an attractive alternative by enabling global dependency modeling with linear computational complexity. However, existing vision-oriented implementations largely rely on empirical architectural choices, resulting in fragmented design strategies and limited reproducibility. Here, we introduce Selective State-Space U-Net (SSS-U-Net), a unified architectural framework that systematically formalizes the integration of selective state-space dynamics within encoder-decoder segmentation networks. The proposed framework establishes a comprehensive taxonomy of three macro-integration topologies-sequential, parallel, and bottleneck state-space routing-and defines multi-directional spatial scanning mechanisms that preserve two-dimensional structural coherence while leveraging one-dimensional state-space representations. Furthermore, we provide a standardized design protocol that maps continuous-time selective state-space dynamics onto high-resolution visual domains while maintaining strict linear-complexity scaling. The framework is validated across representative biomedical and industrial imaging benchmarks, including Kvasir-SEG for polyp segmentation and MVTec AD for anomaly detection. Experimental evaluation demonstrates strong predictive performance, achieving 94.2% mean Dice score on Kvasir-SEG and 98.6% pixel-level AUROC on MVTec AD, while maintaining substantially lower memory consumption and computational overhead than attention-based alternatives. Ablation analyses further reveal the complementary roles of selective state-space gating, multi-directional scanning, and hybrid CNN-Mamba feature fusion in improving segmentation fidelity and anomaly localization. These findings establish a reproducible architectural blueprint for integrating selective state-space models into dense prediction systems and provide practical design guidelines for scalable high-resolution image analysis across biomedical, industrial, and resource-constrained vision applications.